Mr. Kuffer
AP Physics 1
NET
applied
Isaac Newton
(1642- 1727)
Prior to Isaac Newton’s Birth
1625 - Last major outbreak of Bubonic Plague.
1642 (October) - Isaac Newton Sr. (young Isaac’s father) passes away.
Isaac Newton is Born
1642 (Dec. 25) - Galileo dies. Later that same year Isaac Newton is born. He
almost died during the birth.
- Born into the Yeoman (working) class in Woolsthorpe
Lincoinshire, England.
Boyhood
- Isaac was brought up by his grandmother and mother,
(who eventually remarried).
- Isaac attended Grantham Free Grammar School. He stayed with a host
family (the Clarks) for his schooling there.
1656 - Isaac returns to Woolsthorpe to work on the farm at his mothers request.
Age 14 ½ .
1659 - Isaac starts to compile a notebook of his thoughts and studies of Euclid,
Galileo, and others.
1660 - Newton finalizes his Grantham education.
Higher Education
1661 (June 5) - Begins Schooling at Trinity College in Cambridge.
- Continues to compile notebooks of his studies.
1662 - Develops a deep religious fervor. List all of his sins in a coded shorthand.
1665 - Introduces integration and Calculus to mathematically explain the world
around him.
1665 (June / July) - Isaac returns home due to the Plague. (June 7, Plague
infection in London).
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1666 (January) - Isaac develops his Theory of Colors. He uses a prism to show all
colors present in light.
1666 (March 20) - Isaac returns home due to Plague.
1667 (April) - Returns home after earning a Bachelor of Arts degree.
1668 - Isaac Newton earns his Masters of Arts degree.
** 1667- 1668 - Isaac revolutionized work in Optics
- Studied space and time, chemical experiments, and mathematics.
** 1669- 1673 - Newton became a Professor of Mathematics and Chemistry at
Cambridge.
Emergence into Public Life
1687
- The Principia is published
- A publication of his works done at Cambridge (Optics, Mathematics,
Chemistry, and Mechanics).
1693 - Mental Breakdown
1699 - Became Master of the Mint
1705 - Newton was knighted by Queen Anne of England.
1713 - Publication of the Second Edition of The Principia.
1726 - Publication of the Third Edition of The Principia.
1727 - Isaac Newton died at the age of 85, and was buried at
Westminster Abbey with the kings and queens of England.
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Force Notes:
I.
Contact vs. Long-Range:
A)
contact forces – push or pull on an object through touching it
(contact)
B)
Long range – push or pull on an object without direct contact
C)
Agents – cause of force (i.e. “applied”, gravity, “normal”,
friction, … among others)
II.
Newton’s 1st Law:
A)
An object at rest will remain at rest and an object in motion will
remain in motion (with a constant velocity), unless acted on by
an outside force.
B)
Inertia – Tendency of an object to resist change in motion
C)
Equilibrium – an object is in equilibrium if it is at rest or moving
with a constant velocity (note: rest is a constant velocity of
zero). (For this to be achieved the NET force has to be zero,
more about this later)
III.
Mass vs. Weight:
A)
B)
C)
D)
Differentiate between mass and weight…
Apparent weight – force exerted by a scale
Weightlessness – an apparent weight of zero
W = Fg = mg
Problem:
Your mass is 75 kg. You stand on a scale in an elevator that is going up
at 2.0 m/s2. What is your apparent weight? Is this larger, smaller, or equal
to your weight at rest?
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IV.
Newton’s 2nd Law:
A)
Experiments show that the acceleration of an object is
proportional to the net force and inversely proportional to its
mass (a = F/m)
B)
More commonly written as F = ma
V.
The Newton:
A) A Newton is the amount of force it takes 1 kg to be accelerated at
1 m/s2. Therefore the unit Newton (N) is equal to 1 kg·m/s2.
VI.
Newton’s 3rd Law:
A)
Whenever one object exerts a force on a second object, the
second object exerts an equal and opposite force on the first
object.
B)
This is referred to as ‘Action – Reaction’ pairs.
VII.
Free Body Diagrams:
(How to represent several forces all at once)
A)
Draw the object as a dot (for simplicity)
B)
Show all forces acting on the object (draw vector arrows in the
direction of the force, with their tails on the dot).
FN
Ff
FA
Fg
VIII. The Normal Force:
A)
Often referred to as the ‘support’ force
B)
Example: Gravity pulls down on a book… the desk pushes back
up… Otherwise the book would fall to the ground… And it
doesn’t… why, you ask? Because it is ‘normal’ for the book to not
fall… Hence the ‘Normal Force’
IX.
The NET Force:
A)
The Net Force (notice the different subscript… ‘NET’) is a
combination of all forces acting on an object.
B)
If we say it has no NET force, we mean that all of the forces
add to zero… not that there is no force on the object.
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X.
Frictional Forces:
A)
B)
Ff is proportional to the Fg (weight) and the normal force FN,
and depends on the surfaces in contact. Example:
More weightharder to push
On ice  easier to push
On cement  harder to push
A model used to represent this is…
F f =  FN
Where  is the coefficient of friction between the two
surfaces
C)
A table of all coefficients of friction can be found on page 131
of your text.
Frictional Forces
You push a 25-kg wooden box across a wooden floor at a constant
velocity. How much force do you exert on the box? (Hint: b/c the box has a
constant velocity Ff has got to equal FA)
If the force you exerted on the box is doubled, what is the resulting
acceleration of the box?
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XI.
Universal Gravitation:
Gravity is the other common force. Newton was the first person to
study it seriously, and he came up with the law of universal
gravitation:
Each particle of matter attracts every other particle with a force
which is directly proportional to the product of their masses and
inversely proportional to the square of the distance between them.
The standard formula for gravity is:
Gravitational force = (G * m1 * m2) / (d2)
where G is the gravitational constant, m1 and m2 are the masses of
the two objects for which you are calculating the force, and d is the
distance between the centers of gravity of the two masses.
G has the value of 6.67 x 10-11 N·m2/kg2
The Inverse Square Law
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XII. Centripetal Force: (Fc = mac)
We Know…
ac = v2/r
Where…
So…
v = d/t = 2πr / T
v2 = 4π2r2 / T2
So…
ac = (4π2 r2)/ rT2
Therefore…
ac = 4π2 r/ T2
Finally…
Fc = m (v2/r)
OR
Fc = m (4π2 r/ T2)
XIII. Banked Curve:
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XIV.
Uniform Satellite Motion:
FYI: There is only one speed that a satellite can have if the satellite
remains in orbit with a fixed radius… any faster it spirals outward…
any slower it spirals inward.
Simplify and solve for ‘v’…
XV.
Apparent Weightlessness:
In each case, what is the weight recorded by the scale?
Simulated Gravity
Apparent weight equal to weight on earth
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XVI. Vertical Circular Motion: (4 critical points of interest)
Note: If FN3 is zero the instant the object reaches the top of the loop, we
can determine the minimum V3 at that location.
Where FN3 is zero…
Solve for V3…
V3 =
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XVII. Kepler’s Laws:
We know that ac is equal to 42r / T2
Therefore we can say that…
F = mp 42r / T2
We also know that, based on Newton’s Universal Law of Gravitation…
F = G mamb / r2
If we set the two equations equal to each other, using a planet and the sun
as the two masses, we get…
mplanet 42r / T2 = F = G msunmplanet / r2
Notice that mplanet can be factored out…
42r / T2 = F = G ms / r2
If we solve for T2, we see that Kepler’s 3rd law agrees with Newton’s work…
T2 = 42r3 / G msun
Notice that the square of the period is proportional to the cube of the
radius, as stated in Kepler’s 3rd Law...
(TA / TB)2 = (rA / rB)3
Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a
telescope, developed three laws which described the motion of the planets across the sky.
1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal
times.
3. The Law of Periods: The square of the period of any planet is proportional to the cube of the
semimajor axis of its orbit.
Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.
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Newton’s 1st Law
Name:_________________
Date:__________
Circle the correct answer. Write a clear and concise explanation .
Luke Autbeloe drops a 5.0 kg box of shingles (weight approximately 50.0 N) off the
barn house roof into a haystack below. Upon hitting the haystack, the box of shingles
encounters an upward restraining force of 50.0 N . Use this description to answer the
following questions.
1. Which one of the following velocity-time graphs best describes the motion of
the shingles? Support your answer with sound reasoning.
2. Which one of the following ticker tapes best describes the motion of the falling
shingles from the time they are dropped to the time they hit the ground? The arrows
on the diagram represent the point at which the shingles hit the haystack. Support
your answer with sound reasoning.
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3. Several of Luke's friends were watching the motion of the falling shingles. Being
"physics types", they began discussing the motion and made the following comments.
Indicate whether each of the comments is correct or incorrect. Support your
answers. (true or false)
_________
Once the shingles hit the haystack, the forces are balanced and the
shingles will stop.
_________
Upon hitting the haystack, the shingles will accelerate upwards
because the haystack applies an upward force.
_________
Upon hitting the haystack, the shingles will bounce upwards due to
the upward force.
4. If the forces acting upon an object are balanced, then the object
A. must not be moving.
B. must be moving with a constant velocity.
C. must not be accelerating.
D. none of the above.
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Name:_____________________
Period:_______________
Inertial Balance Lab
Objective:
Experimentally verify that mass is the measure of inertia
and be able to describe why mass is more fundamental
than weight.
Procedure:
1. Set up the lab exactly as it was discussed in prep.
2. Displace the balance and time how long it takes the
balance to swing through 20 complete cycles.
3. Repeat step #2. Average the two times.
4. Calculate the time for 1 cycle.
5. Create a graph that shows the relationship that exists
between time and total mass of the inertial balance.
In Short:
1. Start with just the clamp
2. Add mass cylinders, one
at a time (3 total).
3. Add 100g, one at a time.
4. Add “Mystery Mass” to
tray.
5. Record data, create graph,
answer Q’s, determine
mystery mass with graph,
measure “mystery mass”,
determine % error!
Data Tables
Total mass
g
Time for 20 Cycles
s
Time for 20 Cycles
s
Ave Time for 20 Cycles
s
Time for 1 Cycle
s
Analysis:
1. What kind of relationship exists between time and mass? Explain.
2. Does this agree or disagree with the Law of Inertia? Explain.
3. Interpolate to find the mass of the unknown mass. Show your interpolation lines on the
graph. (You will later determine the percent error of your unknown mass. To do so, you
will eventually have to measure the actual mass of the unknown using the scale
provided.)
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Newton’s 2nd Law
Mr. Kuffer
AP Physics 1
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Complete the Free-Body Diagrams for the following situations
Apply the method described in the paragraph above to construct free-body diagrams
for the situations described below. Answers are shown at the bottom of this page.
1. A book is at rest on a table top. Diagram the forces acting on the book.
2. A girl is suspended motionless from a bar which hangs from the ceiling by two
ropes. Diagram the forces acting on the girl.
3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the
forces acting on the egg as it falls.
4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant
velocity. Consider air resistance. Diagram the forces acting on the squirrel.
5. A rightward force is applied to a book in order to move it across a desk with a
rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the
forces acting on the book.
6. A rightward force is applied to a book in order to move it across a desk at
constant velocity. Consider frictional forces. Neglect air resistance. Diagram the
forces acting on the book.
7. A college student rests a backpack upon his shoulder. The pack is suspended
motionless by one strap from one shoulder. Diagram the vertical forces acting on the
backpack.
8. A skydiver is descending with a constant velocity. Consider air resistance. Diagram
the forces acting upon the skydiver.
9. A force is applied to the right to drag a sled across loosely-packed snow with a
rightward acceleration. Diagram the forces acting upon the sled.
10. A football is moving upwards towards its peak after having been booted by the
punter. Neglect air resistance. Diagram the forces acting upon the football as it rises
upward towards its peak.
11. A car is coasting to the right and slowing down. Diagram the forces acting upon
the car.
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Newton’s 2nd Law Lab
AP Physics 1
Mr. Kuffer
Objective: TSW be able to verify the relationship between mass, force and acceleration in
accordance with Newton’s 2nd Law of Motion.
Procedure:
1. Set up the Vernier Logger Pro Bundle, you know the drill.
2. Using Logger Pro and the motion detector, determine
the acceleration of the cart. (slope of v/t graph)
Perform 3 trials. Calculate average acceleration.
Record on data table
3. Calculate “Pulling Force”. Record on data table
4. Calculate “total mass”. Record on data table.
5. A-E Graph accel (Y) vs. FP (X)
6. F-K Graph accel (Y) vs. MTOT (X)
Pulley
M2
M.D.
Track
M1
Tips and Reminders:
1. To attain the total Cart mass: Add Column #3 + Column #4
2. See me after trials A – E
3. In trials A – E: Mass is constant. Vary the pulling force (a.k.a. add mass to
hanger).
4. In trials F – J: Pulling force is constant. Vary the mass of the cart system.
5. Convert all distances to meters.
6. Convert all masses to kilograms.
7. Using the mass, calculate the weight (or force) multiply by -10 m/s2
Example: Fg = mg
(.35 kg)(-10 m/s2)
= -3.5 N
8. Do not let the masses crash to the ground! Do not let the carts run off the
table! If this happens ONCE your group will receive a zero for the lab! Don’t
be “that guy”!
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Important Equation:
ΣF = ma
Analysis:
1.
2.
3.
4.
5.
For Trials A – E create a graph of acceleration and pulling force. What is the
significance of this relationship?
For Trials F – K create a graph of acceleration and total mass. What is the
significance of this relationship?
How does this lab validate Newton’s Second Law? Explain in terms of both
graphs.
Calculate acceleration…
Solve for % error.
Data Table:
M1
Trial
Pulling
mass
(kg)
A
B
C
D
E
F
G
H
I
J
.100
.150
.200
.250
.300
.200
.200
.200
.200
.200
M2
Pulling Mass Extra
Force of
mass
(N)
Cart in
(kg)
cart
(kg)
.5
.5
.5
.5
.5
.5
.5
.5
.5
.5
M2TOT
Total Accel.
mass (m/s2)
(kg)
Trial
#1
Accel.
(m/s2)
Trial
#2
Accel. Average
(m/s2) Accel.
Trial
(m/s2)
#3
.20
.15
.10
.05
.00
.00
.05
.10
.15
.20
Calculations and Analysis in Lab Notebook!
Graphs on Excel!
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Forces:
Free Body Diagrams and NET Forces
Name:__________________
Date:_________
Description of Motion:
NET Force?
YES or NO
__________
__________
__________
__________
__________
__________
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1. Free-body diagrams for four situations are shown below. For each situation,
determine the net force acting upon the object.
A) ______________
______________
______________
______________
B) ______________
______________
______________
______________
C) ______________
______________
______________
______________
D) ______________
______________
______________
______________
2. Free-body diagrams for four situations are shown below. In each case, the net
force is known. However, the magnitudes of some of the individual forces are not
known. Analyze each situation individually to determine the magnitude of the
unknown forces.
F = _____
A = _____
B = _____
C = _____
D = _____
E = _____
G = _____
H = _____
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Newton’s Second Law
Name:_____________
F= ma
Date:_________
1. What acceleration will result when a 12-N net force is applied to a 3kg object? A 6-kg object?
2. A net force of 16 N causes a mass to accelerate at the rate of 5 m/s2.
Determine the mass.
3. An object is accelerating at 2 m/s2. If the net force is tripled and the
mass of the object is doubled, what is the new acceleration?
4. An object is accelerating at 2 m/s2. If the net force is tripled and the
mass of the object is halved, what is the new acceleration?
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Newton’s Second Law
Name:_____________
F= ma
Date:_________
5. Sidney Crosby strikes a 1 kg hockey puck wit his stick. The puck is
accelerated at 5 m/s2. With what force (in newtons) did Crosby strike
the puck?
6. What acceleration will result when a 12-N net force is applied to a 4kg object? A 8-kg object?
7. A net force of 20 N causes a mass to accelerate at the rate of 5
m/s2. Determine the mass.
8. An object is accelerating at 2 m/s2. If the net force is doubled and
the mass of the object remains the same, what is the new
acceleration?
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Newton’s 3rd Law & Forces in
Two Dimensions
Mr. Kuffer
AP Physics 1
Y
X
30°
Fg
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Newton’s 3rd Law
Name:_______________
Period:____
1. In the interaction between a hammer and the nail it hits…
a. Is the forces exerted on the nail?
b. On the hammer?
c. How many forces occur in this interaction?
2. When the hammer exerts a force on the nail…
a. How does the amount of force compare with that of the nail on
the hammer?
3. When you walk along the floor…
a. What pushes you along?
4. When you swim, you push water backwards – call this the action. What
is the reaction force?
5. When a rifle is fired…
a. How does the size of the force of the rifle on the bullet
compare with the force of the bullet on the rifle?
b. How does the acceleration of the rifle compare with that of the
bullet? (defend your answer)
6. Your weight is the result of the gravitational force of the earth on
your body. What is the corresponding reaction force?
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7. Why can’t you hit a feather in midair with a force of 200N?
8. A bullet is fired from a rifle. The mass of the bullet is .0075 kg. The
mass of the rifle is 4.2 kg. The bullet pushes the rifle with a force of
-6.5 N (recoil force).
a. What is the force by the rifle on the bullet?
b. Draw a Free-Body Diagram of the scenario (indicate the
magnitude and direction of the forces and accelerations)
Force
Acceleration
c. What is the acceleration of the bullet and the rifle?
Bullet:
Rifle:
d. Not counting air resistance, how fast will the bullet be traveling
in 0.7 seconds?
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Newton’s 3rd Law
Name:___________________
Date:______________
1. While driving, Anna Litical observed a bug striking the windshield of her car.
Obviously, a case of Newton's third law of motion. The bug hit the windshield and
the windshield hit the bug. Which of the two forces is greater: the force on the
bug or the force on the windshield?
2. Rockets are unable to accelerate in space because ...
a.
b.
c.
d.
there is no air in space for the rockets to push off of.
there is no gravity is in space.
there is no air resistance in space.
... nonsense! Rockets do accelerate in space.
3. A gun recoils when it is fired. The recoil is the result of action-reaction force
pairs. As the gases from the gunpowder explosion expand, the gun pushes the
bullet forwards and the bullet pushes the gun backwards. The acceleration of the
recoiling gun is ...
a. greater than the acceleration of the bullet.
b. smaller than the acceleration of the bullet.
c. the same size as the acceleration of the bullet.
4. In the top picture, a physics student is pulling upon a rope which is attached to
a wall. In the bottom picture, the physics student is pulling upon a rope which is
held by the Strongman. In each case, the force scale reads 500 Newtons. The
physics student is pulling
a. with more force when the rope is attached to the wall.
b. with more force when the rope is attached to the Strongman.
c. the same force in each case.
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Newton’s 3rd Law
1. State Newton’s 3rd law.
2. Give three everyday examples of his 3rd law.
3. A bullet (mass = 8g) is fired from a rifle (mass = 3.5 kg). The bullet
pushes the rifle with a force of -6.5 N.
a. What is the force by the rifle on the bullet?
b. Draw a sketch of the scenario (indicate direction and magnitude
of the forces and accelerations)
c. What is the acceleration of the bullet and the rifle?
d. Not counting air resistance, how fast will the bullet be traveling
in .67 seconds?
e. Not counting air resistance, how far will the bullet travel in .67
seconds?
4. A 2.5 kg object falls to the earth. Calculate the acceleration of both
the earth and the object. (Mass of the earth is 5.96 x 1024 kg)
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Recall:
Newton says ‘For every action there is an equal and opposite reaction’
FAonB = -FBonA
Native American Lady Bug
Mass = 3.5 g
Velocity = 4.8 m/s, South
Force supplied by the truck = ______
2008 F-150
Mass = 2289 kg (5000 lbs)
Velocity = 24.6 m/s (55mph), North
Force supplied by the bug = -10 N
AND THE WINNER IS…
Let’s talk acceleration…
What is the bug’s acceleration?
What is the truck’s acceleration?
HHHMMMmm?
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Universal Gravitation: The Falling Moon
According to Newton, there were two things needed for an object to fall
around or orbit the earth. Label the diagram below with these two things:
____________________
_______________
Newton had the foresight to compare the falling apple to the moon. He knew
that objects tended to move in a straight line unless they were acted upon
by __________________________. His idea was that gravity was
universal. That is- it existed… _______________________________.
Mass doesn’t Count for much! Newton knew that in the absence of air
resistance, a heavy and a light object dropped at the same time on the
surface of the earth would fall at the same rate. In other words, they were
affected by gravity the same way.
Distance was the important thing!
Re = 6,370,000 m
= 3,955 miles
Average earth-moon
distance:
384,000,000 m
Or
230,600 miles
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On Earth:
In one second an object will fall…
d = ½ gt2
On Moon:
6O X the radius of the Earth…
So. The moon should fall _____________________
A satellite at 30 X radius of the Earth should fall
Main Idea:
________________________
________________________
________________________
________________________
________________________
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Universal Gravitation Practice Problems
Directions: Solve the following problems and questions. Remember to use the
correct equation and also watch sig. figs. and units.
1. Earth is attracted to the sun by the force of gravity. Why doesn’t the Earth fall
into the sun? Explain.
2. If the Earth begins to shrink but its mass remains the same, what would happen
to the value of g on Earth’s surface?
3. Cavendish did his experiment using lead balls. Suppose he had used equal masses
of copper instead. Would his value of G been the same or different?
4. Why did Newton think that a force must act on the moon?
5. What provides the force that causes the centripetal acceleration of a satellite in
orbit?
6. How do you answer the question, “What keeps a satellite up?”
7. What is the force of gravity between a student with a mass of 75 kg and another
student with a mass of 95 kg, if they are standing 0.50 m apart?
8. What is the gravitational force between a 15 g squirrel and the earth if the
squirrel is in a tree 5.0 m above the earth?
9. A 150 kg person experiences a gravitational force of 7.80 x 109 N. Where is the
person standing?
10. Solve for the gravitational force between each planet and the sun:
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Gravity and Distance Problems
Given the equation:
F = G (m1 m2) / d2
Consider a 1 kg apple at various places with respect to the earth’s center of
gravity. (1r = 6,380,000 m)
1r
2r
3r
4r
5r…
Complete the following Chart:
( g = Gm/r2 )
Strength of the field (N/Kg)
Distance
Weight of Apple (N)
1r
2r
3r
4r
5r
6r
*Graph the above data on a separate sheet of paper!! (Weight vertical and
Distance horizontal)*
1. Given the fact that 2.2 lbs = 1 kg, find your mass in kg.
Your mass = ___________ kg
2. What would your weight be in Ocean City, MD? (It is at sea level, so r =
6.38 x 106 m)
3. What would your weight be in Denver, CO? (“Mile high city” – 1 mi.)
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Gravitational Fields Within The Planet
IMAGINE: A hole dug through the earth. Forget about the
impracticalities such as lava and very high temperatures…
a = _____________
Notes:
a = _____________
How long would a one-way trip
take? _________
(If you stepped into the hole
bored completely through the
earth and made no attempt to
grab the edge at either end)
a = _____________
a = _____________
a = _____________
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Gravitational Interactions
Complete the table below using your understanding of gravitational fields
g = GM/R2
G = 6.67 x 10-11 N·m2/kg2
Q: What is Universal Gravitation?
A: Simply put, Everything is attracted
to everything else!!
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Simulated Gravity:
1. Most of the energy of train systems is used in starting and stopping. The
design of the rotating train platform saves energy, because passengers can
board or leave a train while the train is still moving. Study the sketch and
convince yourself that this is true. The small circular platform in the middle
is stationary, and is connected to a stationary stairway.
a. If there is to be no relative motion between the train and the edge of the
platform, how fast must the train move compared to the rim speed of the
rotating platform?
_________________________________________________________
b. Why is the stairway located at the center of the platform?
_________________________________________________________
2. The design below shows a train that makes round trips in a continuous loop
from Station A to Station B.
a. How is the size of the round platform and train speed related to the
amount of time that passengers have for boarding?
_____________________________________________________
b. Why would a rotating platform be impractical for high speed trains?
______________________________________________________________
____________________________________________________
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3. Here are some people standing on a giant, rotating platform in a fun house.
In the view shown, the platform is not rotating and the people stand at rest.
When the platform rotates, the person in the middle stands as before. The person
at the edge must lean inward as shown. Make a sketch of the missing people to show
how they must lean in comparison.
4. The left-hand sketch below shows a stationary container of water and some
floating toy ducks. The right-hand sketch is the same container rotating
about a central axis at constant speed. Note the curved surface of the
water. The duck in the center floats as before. Make a sketch to show the
orientation of the other two ducks with respect to the water surface.
5. Consider an automobile tire half filled with water. In the cross-sectional
views below, the left- hand sketch shows the water surface when the tire is
not rotating. The right-hand sketch shows the water surface when the tire
rotates about its central axis.
Now suppose the tire is rotating while in orbit in outer space. Draw the shape of
the water surface in the cross-sectional view below.
In your mind, scale up the rotating tire model to a rotating space habitat
orbiting in space. If the space habitat were half filled with water, could
inhabitants float on the surface as they do here on earth? Discuss this with
your classmates.
39
Using a Pendulum to Determine “g”
Objective:
Recall that a Period (Ƭ) is the time an object takes to make one complete cycle,
whether that be a complete circle or a swing back and forth. (spinning student demo).
The equation to calculate the period of a pendulum is…
Ƭ = 2 π √(r/g)
eqn 1
Rearrange this equation to solve for “g” and get…
Look familiar???...
g = 4π2 r / Ƭ2
eqn 2
ac = 4π2 r / Ƭ2
eqn 3
Remember that “Ƭ” is the period, which is the time for ONE COMPLETE CYCLE of the
pendulum… BACK AND FORTH!!
Procedure and Analysis:
1. Set up the equipment as shown.
2. Varying the length of the pendulum decreasing them by 5cm (0.05m) each trial.
Swing the .pendulum and time how long it takes for 20 complete cycles. Do half
of the cycles with one pendulum bob, and change the bob to another one for the
second half of the trials
3. Complete the Data Table.
4. Make a graph of radial distance (length of string) vs. Ƭ2
5. Calculate the slope of the graph (r / Ƭ2)
6. Multiply the slope by 4π2 (refer to eqn 2 above)
7. Calculate the percent error between the experimental “g” obtained in step 6 and
the accepted value of 9.8m/s2.
Report the percent error here ___________%
o o o
40
Mass
(kg)
Length
(m)
Time for
20 Swings
(sec)
Period = T
(sec)
Period2 =
T2
(sec2)
Experimental
Gravitational
Acceleration
(m/s2)
%
Error
% Error = Experimental -Actual / Actual X 100%
41
Universal Gravitation
***** Refer to pages 40 and 43 of packet for planetary data *****
1. An apparatus like the one Cavendish used to find G has a large lead
ball that is 5.9 kg and a small one that is 0.047 kg. Their centers are
separated by 0.055 m. Find the force of attraction between them.
2. Use the date on pages 4 and 7 of the packet to compute the
gravitational force the sun exerts on Jupiter.
3. Counahan has a mass of 70.0 kg and Libby has a mass of 50.0 kg.
Counahan and Libby are standing 20.0 m apart on the dance floor.
Counahan looks up and sees her and feels an attraction. If the
attraction is gravitational, find its size.
4. Two spheres have their centers 2.0 m apart. One has a mass of 8.0 kg.
The other has a mass of 6.0 kg. What is the gravitational force
between them?
5. Two bowling balls each have a mass of 6.8 kg. They are located next to
one another with their centers 21.8 cm apart. What gravitational
force do they exert on each other?
6. Kristi V. has a mass of 50.0 kg and Earth has a mass of 5.98 x 1024 kg.
The radius of the Earth is 6.38 x 106 m.
a. What is the force of gravitational attraction between Kristi V.
and the Earth?
b. What is Kristi’s weight?
7. The gravitational force between two electrons 1.0 m apart is 5.42 x
10-71 N. Find the mass of one of the electrons.
8. Two spherical balls are placed so their centers are 2.6 m apart. The
force between them is 2.75 x 10-12 N. What is the mass of each ball if
one ball is twice the mass of the other?
9. Using the fact that a 1.0 kg mass weighs 9.8 N on the surface of
Earth and the radius of Earth is roughly 6.4 x 106 m,
a. Calculate the mass of Earth.
b. Calculate the average density of the Earth.
10. The moon is 3.9 x 105 km from Earth’s center and 1.5 x 108 km from
the sun’s center. If the masses of the moon, Earth, and sun are 7.3 x
1022 kg, 6.0 x 1024 kg, and 2.0 x 1030 kg, respectively, find the ratio of
the gravitational forces exerted by Earth and the sun on the moon.
42
11. What is the force of attraction between two metal spheres, each of
which has a mass of 2.0 x 104 kg, if the distance between their
centers is 4.0 m?
12. Two students in a physics class sit 80 cm apart. Their masses are 42
kg and 58 kg. By how much are they attracted to each other?
13. The force of gravitational attraction between two lead spheres 2.00
m apart is 4.832 x 10-3 N. The mass of one sphere is 4500 kg. What is
the mass of the other?
14. Calculate the gravitational force of attraction between a proton and a
neutron separated by a distance of 1.2 x 10-11 cm if the masses of the
two particles are 1.673 x 10-24 g and 1.675 x 10-24 g respectively.
15. The gravitational force between the moon and the Earth is 1.9 x 1020
N. The masses of these two bodies are 7.36 x 1022 kg and 5.98 x 1024
kg respectively. The distance between them is 3.80 x 105 km. From
this information, calculate the value of G, the gravitational constant.
43
Universal G
Why did Newton
think the moon was
falling?
Calculation for the
falling moon?
What does
Universal
Gravitation mean?
Who discovered
Universal Grav.?
Describe the
Cavendish
Experiment!
What was the result
of the Cav. Exp.?
What is the InverseSquare-Law?
What is the Fg
between…
M1 = 100 kg
M2 = 85 kg
d=5m
????
What is meant by
the quote “Pick a
flower, move the
farthest planet.”
Universal Gravitation Review
Effects of Gravity Problem Solving
Name 3 things that
A person weighs
would happen to the 600 N on earth.
human body in a 0g What would they
environment.
weigh on Mars?
Are you taller in the What is Mercury’s
morning or in the
gravitational field
afternoon?
strength?
Why?
The earth and the
What is the
moon are
attractive force
gravitationally
between
attracted to each
M1 300 kg
other. Which pulls
M2 30 kg
with a greater force? d = 3m
?????
What would g be at What is the period
twice the earth’s
of 1.36 m pendulum
radius?
on the surface of the
moon?
Why is the earth
On Planet Y, g = 19
round?
m/s2. What is the
period of an 85 cm
long pendulum?
Jupiter is 300 times If two objects are
more massive as the attracted to each
earth. But an object other with a force of
on Jupiter only
1.9 x 10-9 N, and the
weighs about 2.5
masses are 45 and
times more… why? 60 kg, what distance
separates them?
If the earth were to
What is the
shrink in volume,
gravitation force
but not mass, what
between the earth
would happen to
and a 150 g apple at
your weight?
sea level?
Why don’t you feel Calculate the
the gravitational
gravitational field
effects of large
strength on planet
masses like
X:
buildings?
M = 3.97 x 1022 kg
r = 2.48 x 105 m
Why doesn’t the
Determine g on
moon crash into the Pluto!
earth?
Catch-All
What are Kepler’s
three laws?
Which planet has a
shorter year?
Neptune?
Saturn?
What is a
perturbation?
Age of the universe?
Age of the earth?
What is a field?
Can a gravitational
field exist within a
planet?
Jump out of a
airplane! Are you
truly weightless?
Why?
Why not?
Who had a several
metallic noses?
What is he best
known for?
44
Review Solutions
Universal G
Effects of Gravity Problem Solving
It was not moving in Heart shrinks, bones gmars = 3.72 m/s2
a straight line at a
become brittle,
Fg = 223.2 N
constant speed.
become bloated,
muscles weaken
Catch-All
1. Elliptical
Orbit
2. Equal Area
in Equal
Time
3. r3 / Ƭ2 =
Constant
Saturn is shorter
because it is closer
to the sun.
1/602 x 4.9 =
1.4 mm
Morning, gravity
compresses your
spinal disks during
the day.
Gmercury = 3.7 m/s2
Everything is
attracted to
everything else!!!
SAME… SAME!!
Action-reaction
pairs
Fg = 6.67 x 10-8 N
A wobble in the
orbit of a planet due
to gravitational
interaction with a
nearby passing
planet.
Newton
¼ g!! (2.45 m/s2)
Ƭ = 2π√1.36 m /
1.66 m/s2
13.7 billion years
Ƭ = 5.68 s
See chapter 12
G-R-A-V-I-T-Y!!!
Ƭ = 2π√0.85 m / 19
m/s2
4 – 5 billion years
Ƭ = 1.32 s
G = 6.67 x10-11
Nm2/kg2
Fg α 1/d2
d↑, Fg↓↓
It has a very large
radius! As r↑, Fg↓↓
Your weight would
increase. Same
mass, but closer to
the center of mass.
d = 9.37 m
Fg = mg
See definition in
text
Yes. See 13.3
F = 1.47 N
Fg = 2.27 x 10-8 N
They are there… but g = GM/r2
they are negligible
g = 43.1 m/s2
(too small to feel)
As d↓, Fg ↑↑, as in
Fg = G m1m2 / d2
It has inertia (a.k.a.
tangential velocity)
g = GM/r2
g = 0.757 m/s2
No. The earth would
still be exerting a
force on you.
Tycho Brahe
(1546-1601)
45
Friction Lab
Objective:
Calculate the coefficient of friction between two surfaces.
Theory:
If an applied force pulls horizontally on a mass and moves
the mass at a constant speed, then the free-body diagram is as
follows:
FN
Ff
FA
Fg
Applying Newton’s 2nd Law:
FNET = FA – Ff
OR
FNET = FA – ( µFN)  b/c Ff = µFN
OR
46
FNET = FA – ( µmg)
Procedure:
Spring
Scale
Wood block
Pull this way
1. Using the spring scale, measure the weight of the block (Fg)
2. Using the spring scale, pull the block of wood across the
wooden surface at a constant speed. The reading on the
scale is the applied force (FA)
3. Add 100g of mass to the wood block. Determine the entire
weight of the block and mass. (this is trial #1)
4. Repeat steps 2 and 3 until reaching 1000g
5. Repeat all steps for felt on wood
6. Create a graph of Ff vs. FN.  Hint  Ff = µFN
7. Determine the slope of the graph and its meaning.
8. Determine the Percent error.
47
Name_______________
Inclined Planes
1. A 10-kg block on a hill that makes a 30 angle with the horizontal
begins to accelerate down the hill.
a) Draw the pictorial diagram and free-body diagram
b) What is the component of the block’s weight parallel to the incline
plane?
c) What is the normal force?
d) What is the net force on the block if the coefficient of friction
between the block and the hill is .11?
2. A 794-N skier on a hill that makes a 25 angle with the horizontal
begins to accelerate down the hill.
a) Draw the pictorial diagram and free-body diagram
b) What is the component of the skier’s weight parallel to the
incline plane?
c) What is the normal force?
d) What is the net force on the skier if the coefficient of friction
between the skis and the snow is .11?
48
REVIEW PROBLEMS
Name: _______________
_________
Two Dimensional Forces
I.
Short answer
Date:
F
Figure 1:
1. Describe the relationship between F, Fx, and Fy.
This figure is
F
________________________________________________ y
to be used
________________________________________________
with short
answer
Fx
________________________________________________
problems 1-4.
____________________________________________________________________
____________________________________________________________________
2. If Fx were negative, how would diagram be different?
____________________________________________________________________
____________________________________________________________________
3. If you only know the values of F and Fy, what equation would you use to solve for Fx?
_________________________.
4. If you increase the angle at which F acts to 55, how will the components be affected?
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
49
Fgx
Fg
30
Fgy
Figure 2:
This figure is to
be used with
short answer
problems 5-9.
5. If the angle of the incline were decreased to 15, how would the
components of Fg be
affected?_______________________________________________
_________________________________________________________
_________________________________________________________
______________________
6. If you only know the values of Fg and , what equation could you use to
find
Fgy?___________________________________________________.
7. If you only know the values of Fg and , what equation could you use to
find
Fgx?___________________________________________________.
8. If the inclined plane is a frictionless surface, what other force besides
those labeled acts on the trunk?
___________________________________________________.
9. Draw the force (vector) from the previous question on Figure 2.
50
Tension Problem (In Class)
Show Work on Next Page
51
Tension Problem Work Page (In Class)
52
Accelerating Block Problem - Incline/Tension/Pulley (In Class)
53
Accelerating Block Problem Work Page - Incline/Tension/Pulley (In Class)
54
FNET & Motion II
Name:______________________
EQN:
Date:__________
FNET = F1 ± F2 ± F3± …
1. A 4,500 kg helicopter accelerates upward at 2.0 m/s2.
a. What lift force is exerted by the air on the propellers? (right)
b. What lift force is exerted by the air on the propellers if it is
lifting the jeep, 3760–kg? (left)
2. The maximum force a grocery sack can withstand before ripping is
250N If 20.0 kg of groceries are lifted from the floor to the table
with an acceleration of 5.0 m/s2, will the sack hold?
55
Force and Motion
Name:_______________
Date:__________
1. A 0.0050 kg bullet traveling with a speed of 200 m/s penetrates a
large wooden fence post to a depth of 0.030 m. What was the average
resisting force exerted on the bullet?
2. A 0.0048 kg bullet traveling with a speed of 400 m/s penetrates into
a large wooden fence post. If the average resisting force exerted on
the bullet was 4.5 x 103N, how far into the fence post did the bullet
penetrate?
56
Additional Practice Problems
1. (a) A 20.0 kg bucket is lowered by a rope with a constant velocity of
0.500 m/s. What is the tension in the rope?
(b) A 20.0 kg is lowered by a rope with a constant downward velocity
of 1.0 m/s. What is the tension in the rope?
(c) A 15.0 kg bucket is raised with a constant upward velocity of 1.0
m/s. What is the tension in the rope?
2. Two air-track gliders m1 and m2 are joined together with a light string.
A constant horizontal force of 5.0 N to the right is applied to m2.
(a) If m1 = 2.0 kg and m2 = 0.50 kg, what is the acceleration of the
glider?
(b) What is the tension in the cord joining them?
m1
m2
3. Find the accelerations and the tension for the situation in the diagram
above given that m1 = 0.5 kg and m2 = 2.0 kg.
4. A classroom demonstration is done with an Atwood machine. The
masses are m1 = 1.00 kg and m2 = 1.10 kg. If the larger mass descends
a distance of 3.00 m (h) from rest in 3.6 s, what is the acceleration of
gravity at that place? (Ignore the effects of pulley mass and friction.)
57
Name:_______________
Date:___________
Period:____
Equilibrant Force - Force Table Lab
Purpose:
The objective of this lab experience is to practice and apply
the principles of vector addition by using force tables to determine
equilibrant forces (resultants).
Procedure:
Part 1
1. Set up the force table as discussed in class.
2. Add some washers to each of the hangers.
Use a different number of washers on each hanger
3. Measure the mass of the washer and the hanger. Add the masses
together to determine the total mass.
4. Adjust the pulleys so that the white ring is centered on the force
table. That means it is lined up with the painted black ring.
Important note: When the pulleys are adjusted correctly, the
threads should extend from the white ring perpendicularly and the
thread should be in line with the notch in the pulley holder.
5. Record and perform the calculation as indicated to find the resultant
force on the white ring.
58
Data Collection:
Part 1
Hanger
Mass of
Hanger
Mass of
Washers
Total
Mass
Acceleration
(g)
Force
(N)
Angle Measured
with respect
to x-axis
A
9.8 m/s2
B
9.8 m/s2
C
9.8 m/s2
Note: the “total mass” column is the magnitude of each vector. The direction
comes from the angle.
Sketch your three vectors below o the left. Label each one “A”, “B”, and “C”.
Be sure to show the magnitude and direction of each vector. Do not draw in
any components yet; we haven’t yet done any replacement.
=
Resultants
Components
Now we will replace vectors A, B, and C with their components that point
only down one axis. Sketch you component vectors above on the right. Label
“Ax”, “Ay”, “Bx”, “By”, “Cx” and “Cy”.
59
Vector Components:
Force Vector
Set-Up for
x-component
A
B
C
Actual
x-component
Set-Up for
y-component
Actual
y-component
Note: The “Set-Up” column is what you will type into your calculator. An
example might be 8.6 (cos 35). The “Actual” column is the result the
calculator gives you. An example might be 7.04 N.
Resultant Vector:
Analysis:
1. What is the sum of all your x-components? Show math!
2. What is the sum of all your y-components? Show math!
3. Ideally, what would these two sums have been? Why? (one word
answer)
60
Part 2
1.
2.
3.
4.
Obtain an unknown mass and hang it on one of the hangers.
Place washers on the other 2 hangers and record those masses.
Adjust the pulleys until the ring is centered again.
Knowing the conditions for equilibrium from part 1, work backward to
calculate the mass of the unknown.
Data Collection:
Hanger
Mass of
Acceleration Weight of Hanger
Angle Measured
Hanger &
(g)
and Washers (N)
with respect
Washers
[F=ma]
to x-axis
A
9.8 m/s2
B
9.8 m/s2
C
X
9.8 m/s2
Note: the “total mass” column is the magnitude of each vector. The direction
comes from the angle.
Sketch your three vectors below o the left. Label each one “A”, “B”, and “C”.
Be sure to show the magnitude and direction of each vector. Do not draw in
any components yet; we haven’t yet done any replacement.
=
Resultants
Components
Now we will replace vectors A, B, and C with their components that point
only down one axis. Sketch you component vectors above on the right. Label
“Ax”, “Ay”, “Bx”, “By”, “Cx” and “Cy”.
61
Vector Components:
Force Vector
Set-Up for
x-component
A
B
C
Actual
x-component
Set-Up for
y-component
Actual
y-component
Calculation of Unknown:
Now calculate the mass of the unknown by working backwards. Show
your work below. Solve for percent error!
Percent Error:
Actual – Experimental x 100% =
Actual
62
Name_______________
Equilibrant & NET Forces
1. A 180-N sign is suspended by two wires that make an angle of 120 with
each other. The tension in the wires are equal.
a) Draw the pictorial diagram and free-body diagram
b) What is the tension in the wires
2. Joe wishes to hang a sign weighing 275 N so that the cable A attached to
the store makes a 38 angle, as shown below. What is the force of
tension in rope B?
A
38
B
JOE’S
3. The sign from #1 is now hung by ropes that each make an angle of 42º
with the horizontal. What force does each rope exert?
Adding Vectors (Tip-to-Tail)
4. An 8.0 N weight has one horizontal rope exerting a force of 6.0 N on it.
a) What is the magnitude and direction of the resultant force on the
weight?
b) What force (magnitude and direction) is needed to put the weight
into equilibrium?
5. Two ropes pull on a ring. One exerts a 62 N force at 30º, the other a 62
N force at 60º.
b) What is the NET force on the ring?
c) What is the magnitude and direction of the force that would cause
a state of equilibrium?
6. Two forces act on an object. A 36 N force acts at 225º and a 48 N force
acts at 315º. What are the magnitude and direction of the equilibrant?
63
II.
PROBLEMS
1. Joe wishes to hang a sign weighing 275 N so that the cable A attached to
the store makes a 12 angle, as shown below. What is the force of tension
in rope B?
12 A
B
JOE’
S
2. You push a 451-N box up a 25 incline plane at a constant velocity by
exerting a 317-N force parallel to the incline plane’s surface.
A) What is the component of the box’s weight parallel to the plane?
B) What is the sum of all the forces on the box?
C) What is the magnitude and direction of the friction force?
D) What is the coefficient of friction?
64
Investigating Newton’s Second Law
AP Physics 1
Purpose:
The purpose of this laboratory exercise is to investigate the validity
of Newton’s Second Law of Motion. You will use a single pulley apparatus as
shown below. This apparatus is commonly referred to as an “Atwood
Machine”. The Atwood Machine allows one object to hoist another object
using only gravity.
Fixed
Frictionless
Pulley
Lightweight
String
M2
M
1
Figure One:
A representation of the Atwood Machine setup used to conduct the laboratory (The
single pulley with mass M2 > mass M1).
Materials:
1. Single pulley apparatus on a support stand; pulleys rotate with
minimal friction
2. Different masses M1 and M2
3. Vernier LabPro
4. Computer
65
Theory:
In short, your theory section must explain all of the skills and
knowledge that are used to validate Newton’s Second Law of Motion. Your
explanations should be catered to a person who has little, if any, prior
knowledge related to this lab. Your theory must include, but should not be
limited to, the following: a discussion of the effects of gravitational force
on the mass’s position, velocity, and acceleration, (i.e. a kinematical
description of what happens when the mass is released). Derivations of all
equations used to validate Newton’s Second Law of Motion are included and
explained, specifically the theoretical formula for the acceleration of the
system in terms of mass one (M1), mass two (M2), and g (9.8 m/s2). In the
derivation, assume the pulley is completely frictionless. Your theoretical
formula should NOT have time, t, in it. Show your free-body diagram, label
vectors, and show your algebra. This complete derivation should be typed in
your lab report in an organized manner. Include definitions and explanations
of Newton’s Second Law of Motion, forces and their agents, and the system
being evaluated, among other related terms.
Feel free to use any resources that may help you explain the
background information involved in this laboratory, including the internet,
textbooks, and notes. However be aware of the school wide policy involving
plagiarism, and site your sources where appropriate.
Procedure:
**Note: In your lab report, the procedure should be written in past-tense,
passive-voice, unlike the following. The procedure listed below is a very
general outline and should be expanded upon.
1. Set up the Atwood Machine apparatus using the pulley mechanism
provided. Hang the heavier falling mass M2 from the highest
altitude, at about lab table height. Make sure there is enough
string connecting the two masses so that the heavier falling mass
M2 can hit the floor before the rising mass M1 hits the pulley.
2. Hang a total of 50 grams for the smaller mass, M1, keeping in mind
that the mass hangers themselves are 50 grams. Hang 10 grams
more (than 50) for mass M2 (total of 60 grams). Then
66
experimentally determine the acceleration of your system (3
trials). Repeat this step after adding two more increments of 10
grams to M2 (Thus, an M2 of 70 and 80 grams respectively, again 3
trials). Use the Examine tool to draw a linear best-fit line. This
can be drawn on your Velocity-Time graph. The Vernier Logger Pro
Program will calculate the acceleration for you, via the slope.
3. Releasing M2 in the same place each trial, collect time data for at
least 3 trials for the specific mass combination above. TIP –
Students in the past have felt that the heavier mass should be
placed on the same side of the pulley for each trial.
Data Collection and Analysis:
Slope
M1
M2
M2-M1
M1+M2
[(M2-M1)/( M1+M2)*g]
Using your derived formula, compute the theoretical acceleration of
your system after substituting your [M1 and M2] mass values used during the
trials. Briefly explain what data you collected and how you used the data
to determine the experimental value of acceleration of the system. Display
your data in a well-organized fashion. Compute % error between your
theoretical value of acceleration for the system compared to your
experimental value of acceleration.


Attach a graph of the experimental accelerations of the
masses (Velocity-Time graph with best-fit line).
Include one labeled sample calculation for each calculation
necessary to complete the laboratory. Each sample
calculation should include the equation, substitution with
numbers and units, and a result with units.
67
Questions: (Answer the following questions in a discussion format)
1. Based on your data, was Newton’s Second Law of Motion verified
to YOUR satisfaction?
2. Did your theoretical model accurately predict how well the Atwood
Machine “should” perform in this lab?
3. Did your masses experience “free-fall”? If not, specifically why
not? – Briefly explain!
4. Looking at your theoretical formula for acceleration, for what
combination of M1 and M2 will the masses experience free-fall
where a = g? – Briefly explain!
Error Analysis:
Definition: A “systemic error” is an error that uniformly affects all
the data points equally throughout an experimental procedure, i.e. an error
that affects the entire system in a uniform manner. For example, not taking
temperature into account could introduce a systemic error in some lab
experiments (though not necessarily in this one). One can notice systemic
errors showing up if there is a constant difference between experimental
and theoretical data over the entire range of data. In “real life” the
researcher must take the systemic error into account in his/her analysis of
a problem. Now look at your experimental and theoretical results. While
your experimental values may be “too low” or “too high” for your satisfaction,
is there the same “trend” in throughout your trials? If so, such a matching
“trend” may indicate a systemic error in the experiment. Figure out what
the systemic error could be in your lab.

Provide % error calculations and explanations.
Conclusion:
Restate the purpose. State your experimental result and compare it
to the theoretical value for the acceleration of the masses. Comment on the
success (or lack thereof) of your experiment.
68
Formal Lab Requirements
Format
Purpose/Objective
Theory
Procedure
Data
Collection/Analysis
Error Analysis
Conclusion
Total Possible Points
Total Points Your Score
Total
All Graphs labeled
Work Cited/Citations
Neatness/Organization
Title
20
5
5
5
5
Total
Clearly Stated Objective
Clearly Stated Hypothesis
20
10
10
Total
All Equation Derivations
Explanation of Eqn. Der.
Clearly explain WHAT you are
trying to accomplish
Clearly explain HOW you are
trying to accomplish it
Additional Information
22
5
5
5
Total
Diagram of Setup
Clear and Precise Steps
Material List
20
10
5
5
Total
32
Tables/Graphs Clearly ill.& Exp.
Sample Calculations w/ Exp.
Questions & Answer
Additional
10
10
10
2
Total
Systemic Error
% Error and its meaning
10
5
5
Total
List and Explain Numerical
Outcome
Revisit Hypothesis and
Objective
Additional
21
10
5
2
10
1
145
Comments:
69
Supertanker Tow Problem (In Class)
70
Supertanker Tow Work Page (In Class)
71
Practice Problems – Uniform Circular Motion
1. What is the direction of the force that acts on the clothes in the spin cycle of a
washing machine? What exerts the force?
2. Describe all the forces acting on a child riding a horse on a merry-go-round.
Which of these forces provides the centripetal acceleration of the child?
3. Will the acceleration of a car be the same when it travels around a sharp
curve at 60 km/h as when it travels around a gentle curve at the same speed?
Explain.
4. What does centripetal mean?
5. What does centrifugal mean?
Answer centripetal or centrifugal to the following statements:
6. A false force used to describe what one feels when their frame of reference is
rotating ________________.
7. Force required for any object to travel in a circular path _____________.
8. This type of force is responsible for keeping the moon in an almost perfectly
circular orbit _________________.
9. “center fleeing” _________________.
10. “center seeking” ________________.
11. How much centripetal force is required for an 850 kg race car traveling at 200
mile/hr (89.4 m/s) to go around a bend with a radius of 195 meters?
12. A runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m.
What is the centripetal acceleration of the runner, and what exerts the
centripetal force on the runner?
13. An airplane traveling at 201 m/s makes a turn. What is the smallest radius of
the circular path (in km) the pilot can make and keep the centripetal
acceleration under 5.0 m/s2?
14. A 16 gram ball at the end of a 1.4 m string is swung in a horizontal circle. It
revolves once every 1.09 second. What is the magnitude of the string’s
tension?
72
Centripetal Acceleration & Centripetal Force
A quick Review:
1. What are the two things needed in order for an object, any object, to
travel in a circular path?
a.
b.
2. Since an object moving in a circle is constantly changing direction, it is
also _______________
Some important Equations:
ac = v2/r
OR
&
ac = (4π2 r)/ T2
Fc = mac
1. It takes a 615 kg racing car 14.3 s to travel at a uniform speed around a
circular racetrack of 50.0 m radius.
a. Is the car accelerating?
b. What is the acceleration of the car?
c. What average force must the track exert on the tires to produce
this acceleration?
2. An athlete (Idowu) whirls a 7.0kg hammer tied to the end of a 1.3 m chain in
a horizontal circle. The hammer moves at a rate of 1.0 rev/second.
a. What I the centripetal acceleration of the hammer?
b. What is the tension of the chain?
3. Kimble whirls a yo-yo in a horizontal circle. The yo-yo has a mass of 0.20 kg
and is attached to a string 0.80 m long.
a. If the yo-yo makes 1 complete revolution each second, what force
does the string exert on it?
b. Sam increases the speed of the yo-yo to 2.0 rev/sec., what force
does the string now exert?
4. According to the Guinness Book of World Records, the highest tangential
speed ever attained was 2010 m/s (4500mph). The rotating rod was 15.3 cm
(0.153 m) long. Assume the speed quoted was at the end of the rod.
a. What is the centripetal acceleration at the end of the rod?
b. What is the period of rotation of the rod, T?
5. The “Enterprise” at KENNYWOOD takes 2.4 seconds to make one revolution
when it is spinning the fastest. When you are in your seat, you are 15 m from
the center.
a. What is the centripetal acceleration or the rider when the ride is
spinning the fastest?
73
Hammer throw
The modern or Olympic hammer throw is an athletic
throwing event where the object is to throw a heavy metal ball
attached to a wire and handle. The name "hammer throw" is
derived from older competitions where an actual sledge
hammer was thrown. Such competitions are still part of the
Scottish Highland Games, where the implement used is a steel
or lead weight at the end of a cane handle.
Like other throwing events, the competition is decided by who
can throw the ball the farthest. The men's hammer weighs 16
pounds (7.257 kg) and measures 3 feet 11 3⁄4 inches (121.5 cm)
in length and the women's hammer weighs 8.82 lb (4 kg) and
3 feet 11 inches (119.5 cm) in length. Competitors gain
maximum distance by swinging the hammer above their head
to set up the circular motion. Then they apply force and pick up
speed by completing one to four turns in the circle. In
competition, most throwers turn three or four times. The ball
moves in a circular path, gradually increasing in velocity with
each turn with the high point of the ball toward the sector and
the low point at the back of the circle. The thrower releases the
ball from the front of the circle. The two most important factors
for a long throw are the angle of release (45° up from the
ground) and the speed of the ball (the highest possible).
Centripetal Force Pre-Lab
1.
2.
3.
4.
5.
6.
Measure your arm length…
Determine the radius of the circle…
Determine the period (T) of the Hammer…
Calculate the angular speed (ω)…
Calculate the linear speed…
Calculate the Centripetal Force (FC)…
________________ m
________________ m
________________ s
________________ rad/s
________________ m/s
________________ N
http://www.youtube.com/watch?v=LYf8NZnh0oI
74
Centripetal Force Lab
Objective:
Name:______________
Verify the relationship between Fc, m, v , and r.
Fc = m (v2 / r)
Trial #
Mass of Stopper
(kg)
Mass of Washers
(kg)
Fc = m (9.8m/s2)
(N)
1
2
3
4
5
6
7
8
9
10
11
12
Radius
(m)
Time for 20
Swings
Τ
(t/20)
(s)
(s)
ω = 2π(rad)
Τ
(rad/s)
ν
(ν = ω r)
(m/s)
1.00
1.00
1.00
1.00
0.6
0.6
0.6
0.6
1.2
0.8
0.5
0.3
75
GRAPHS: Each person will be required to create three (3) graphs
from your data. The graphs include:
#1
#2
#3
For trials 1-4
For trials 5-8
For trials 9-12
ν vs. Fc (vary Fc)
ν vs. m (vary m)
ν vs. r (vary r)
TIPS AND REMINDERS:
*** USE YOUR FLAG TO KEEP THE RADIUS CONSTANT.
THE FLAG SHOULD BE ½ INCH BELOW THE TUBE BOTTOM AT ALL
TIMES.
*** WHEN VARYING THE Fc, THE NUMBER OF WASHERS SHOULD
CHANGE BY 3 OR 4 EACH TRIAL.
*** BE CAREFUL!!!!
***YOU DO NOT HAVE TO CUT THE STRING. JUST MOVE THE
FLAG UP AND DOWN TO VARY THE RADIUS
76
Banked Curve Problem (In Class)
77
Banked Curve Work Page (In Class)
78
The Hubble Space Telescope Problem (In Class)
The Hubble Space Telescope Work Space (In Class)
79
80
Johannes Kepler
(Creepy looking guy to the right)
Danish astronomer Tycho Brahe
(1546-1601) spent years
cataloguing the stars and planets
with great accuracy. His assistant
Johannes Kepler (1571-1630) put
his observations to good use. He
developed three important laws of
astronomy. His first law describes
the shapes of planetary orbits. His
second law describes the speed at
which the planets travel along
their orbits. His third law relates
the different planetary orbits to
one another. FYI: Newton, born in
1642, came after Kepler.
Kepler’s Laws
Kepler's three laws of planetary motion can be described as follows:
1. The path of the planets about
the sun are elliptical in shape, with the
center of the sun being located at one
focus. (The Law of Ellipses)
2. An imaginary line drawn from
the center of the sun to the center of
the planet will sweep out equal areas in
equal intervals of time. (The Law of
Equal Areas)
3. The ratio of the squares of the
periods of any two planets is equal to
the ratio of the cubes of their
average distances from the sun. (The
Law of Harmonies)
81
Determining Planetary Gravitational Forces
Instructions: Using the data in your packet, complete the following chart.
Make sure you change miles to meters and do not forget to square the
distance in the denominator.
Fg = Gm1m2/ d2
Planet
Fg @ Perihelion (N)
Fg @ Aphelion
(N)
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
82
Did you know that all but two planets (Mercury and Pluto)
have orbits in the same plane?
83
The Orbit Lab
Objective: The student will draw an ellipse to simulate the orbit of a planet and then
analyze how the gravitational force varies with position in the orbit.
Important terms:
Perihelion
Aphelion
Materials:
2 thumbtacks, 21 cm x 28 cm piece of cardboard,
Sheet of unlined paper, 30 cm of string or thread
Procedure:
1. Push the thumbtacks into the paper and cardboard so that they are between 6
and 10 cm apart.
2. Make a loop with the string. Place the loop over the two thumbtacks. Keep the
loop tight as you draw the ellipse.
3. Remove the tacks and string. Draw a small star centered as one of the tack
holes.
Observation and Data:
1. Draw the position of the planet in the orbit where it is farthest from the star.
2. Draw the position of the planet when it is nearest the star.
3. Determine the distance from these positions to the star’s center (below).
Analysis:
1. Choose one of the planets in the solar system.
2. Calculate the gravitational force when the planet is at perihelion and aphelion.
You will need to use the enclosed charts to find the distances and masses
required. Draw your planet at the perihelion and aphelion distances and label
the force vectors accordingly.
3. Draw your planet at two additional phases. Draw the tangential velocity vector
at each phase (all four phases).
NAME
MASS (kg)
Sun
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
1.991 x 1030
3.2 x 1023
4.88 x 1024
5.979 x 1024
6.42 x 1023
1.901 x 1027
5.68 x 1028
8.68 x 1026
1.03 x 1026
1.2 x 1022
PLANETARY DATA
PERIHELION
APHELION DIST.
DIST. (megamiles) (megamiles)
PERIHELION
Date
APHELION
Date
28.6
66.8
91.4
128.4
460.3
837.6
1699.0
2771.0
2756.0
10/16/95
8/11/95
12/21/95
2/19/96
5/5/99
5/26/03
3/1/2050
3/2030
8/1989
11/29/95
12/1/95
6/21/96
1/28/97
3/29/2005
2/8/2018
4/17/2008
2/2112
8/2113
43.4
67.7
94.5
154.9
507.2
936.2
1868.0
2819.0
4555.0
84
AP Physics 1
Mr. Kuffer
Orbit Lab Work
NAME:_________________
Period: ________
85
*Show all work below. This should include several conversion for aphelion and
perihelion from Megamiles to meters and the gravitational force of attraction at those two
points. Every number should have a unit attached to it. If it does not… IT IS WRONG!
Recall:
1 megamile = _______ x 106 miles
1 mile = 1609 m
Planet Chosen: _______________________
Distance at Aphelion:
Distance at Perihelion:
Difference in Distance:
Fg at Aphelion:
Fg at Perihelion:
Difference in Fg:
86
AP Physics 1 Lab
Hooke's Law & Spring Constants (k)
Period:
Names:
How Strong Is That Spring?
Everyone knows that springs can exert forces, but what everyone may not realize that this force
is not constant. Rather, as the spring gets stretched, it resists more and more, attempting to
regain its original relaxed shape.
Hooke’s Law
Fsp = – kx
This relationship was first discovered by Robert
Hooke (1635 – 1703). Mathematically, this idea
is
The objective of this lab is to determine the relationship between Force and Distance (x) for a
spring, and the force constant (k) of a spring.
Materials: spring, slotted masses, meter stick, unknown mass,
ring stand, horizontal rod, rod clamp
Procedure:
1. Set up as shown in Fig. 1
2. Record starting position of spring (xo = 0 cm).
3. Add some mass to extend the spring (x); record mass and x.
Figure 1
4. Repeat for 4 more trials.
5. Place an unknown mass on the spring and record the position
(x), then find INTERPOLATE its actual mass.
Mass
(kg)
0
Force
(N)
0
Distance
(cm)
Wimpy Spring
Stretch
(cm)
Mass
(kg)
0
Force
(N)
0
Distance
(cm)
Robust Spring
Stretch
(cm)
87
Unknown
Mass Data:
Spring
Chosen:
Distance
Stretch
Experimental Experimental
Weight
Mass
Actual
mass
Analysis:
1. Plot a graph of Force (in Newtons)(y-axis) vs. stretch (in centimeters) (x-axis).
2. Find the slope of the line. What are the units and what does the slope represent?
3. Using one of your graphs (the more appropriate one), determine the weight of
your unknown object from its x. Calculate its mass (F/g). Determine a % error.
4. Why would the other spring have given a less reliable answer?
5. Write an equation relating Force (F), distance ( x), and the force constant of a
spring (k). State Hooke's Law in a sentence.
88
Notes:
89