CH 4 NOTES & Inc Plane Notes – Newtons Laws
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Fundamental Forces
Law vs Theory
Newtons 3 laws
Freebody Diagrams
Friction
Tension
Inclined Planes
INTRO: 4 Fundamental Force
Force- A disturbance that can cause a change in velocity of an object (a push or pull)
There are 4 fundamental forces of nature:
1. Gravity – caused by mass
- Weakest of all the forces (10-39x)
It is attractive force
Very long ranged
We normally think of gravity as very strong. This is simply because the Earth is so much more massive
than us, and it acts over very long distances.
2. Electromagnetism – Electricity and magnetism are caused by the same effect. A magnet can produce
electricity, and electricity can produce magnetism.
Anything with a charge has E&M force. Holds e-‘s around nucleus of atom
- 2nd strongest force (.007x)
Attractive and repulsive
Short ranged force
3. Strong Force – Holds nucleus of atoms together (holds P+ together, the E&M force would want P+ to
move away from each other. The strong force keeps them all together in the nucleus.
- Strongest force (1x)
Short ranged (size of nucleus)
4. Weak Force – Holds subatomic particles together. P+ and N are made of smaller things (quarks), these
quarks are held together by weak force. This force is responsible for gamma radioactive decay.
- 2nd weakest force (10-6x) – Gravity is weaker!
Very short ranged (size of protons)
MASS VS WEIGHT
(demos: space guy and planets & alien)
Mass and Weight are two concepts easily confused. In this unit, we must clearly know the difference between
them.
Mass – The amount of matter in an object
Units – Kg (a gram is tiny, so the standard SI unit is KG)
The english system uses slugs (from sluggish) a more massive object is harder to move, or more
sluggish. For most of history, there wasn’t a unit for mass, since most people just use weight.
English units: Slug (for sluggish) – 1 slug = 14.6 kg
Mass doesn’t change, unless you physically add or take away pieces of the object.
Weight – The force of gravity acting on an object.
Fg = M x a
SI units: Newton (N) = 1 kg m/s2
English units – Pound. 1 pound = 4.5 N
On earth, a = 9.8 m/s2. However, on other planets acceleration of g is different, so weight can change.
Also, in water, you are bouyant, so you weigh less.
Weight can change, mass stays constant
The only way to change mass is to physically add or subtract matter from an object.
Where the confusion begins: On earth, gravity is always 9.8, so weight seems constant. Allot of people
confuse mass with weight. This is also compounded by the english system. The unit for mass is the Slug
(sluggish).
No one really uses a “slug” most people just equate pounds (weight) with mass. On earth, 1 pound of weight =
2.2 kg
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Law Vs Theory
Law: A description of a natural phenomena
Laws were developed by early physicists to describe nature in order to predict it.
Laws are facts on nature, they don’t explain why something occurs
For example, by using Newton’s Law of Gravity one can calculate gravities effeects on mass, but one cannot
describe how gravity works using his law.
The ideal gas law says PV = nRT – it’s a statement that describes nature. We can calcualte a gasses properties
based on this law. However, we cannot explain why a gas behaves like this using the law.
Laws are not absolut truths about nature. They just help us describe nature. For example, Newton’s laws are
only approximations that work on the large scale. Ohm’s Law only works for specific temperature ranges,
etc… However, this does not mean laws are not useful for us today.
Theory – An explananation for a natural phenomena
A theory has also been tested and proven over and over again (If it hasn’t it is called a hypothesis).
If the experimental results don’t match with the theory, the theory can/will be adjusted. This is the nature of
science.
Theories try to explain WHY things happen. For example, we have the law of gravity, which can be used to
predict gravity’s influence, however it doesn’t explain why gravity works. However, we have a Theory of
gravity (from Einstien) that tries to explain how gravity works.
We have the theory of relativity which tries to explain WHY space and time are interconnected. Relativity has
been tested and proven over and over again. Today it is necessary to use it for GPS navigation systems, space
travel, etc…
Today, Laws have fallen out of usage. Since we now know Laws are not absolute truths of nature, no new
physciststs will make new laws. Today, if someone discovered the “laws of thermodynamics” they would call
them “theories of thermodynamics”
So… Netwon’s Laws describe forces in nature. They don’t explain why they occur.
Newton’s 1st Law
(demos: tablecloth pull, card and nickels, cart and flying doll)
An object in motion will tend to stay in motion, an object at rest will tend to stay at rest, unless acted
upon by an unbalanced (external) force.
Example. A book sitting on a table has gravity pushing down, but the table stopping it. The forces are
balanced. It will stay there until some other force disturbes it, causing motion.
A spacecraft launched to another planet: Once it leaves earth, the rockets shut off, and it simply coasts to the
other planet. Once in motion, it will stay in constant motion until it hits the other planet (in many cases years).
The 1st law is also called the Law of Inertia
Interia: The tendency for an object to resist a change in motion.
Inertia is directly related to Mass. Bigger Mass = More Inertia
This is an easy concept. For example, take two rocks, one boulder, and one pebble. Which one is harder to
kick? Obviously, the boubler is MUCH harder to kick, it has more mass, so it wants to stay are rest more than
the little pebble.
Again, lets say that boulder is rolling down the road. How hard would it be to stop? Very hard compared to the
pebble. Since it has such a large mass, once in motion it will stay in motion.
Example: Sliding a book across a desk. You apply a force to start it in motion. According to the 1st law, it
should stay in motion. Why doesn’t it? Because friction from the surface of the desk applies an unbalanced
force, which causes it to slow down. What if we slid it on ice? There is less friction, so it would travel further.
 Wrap-up of 1st law: Law of Inertia
So, if an object is at rest, one must apply a force to overcome the objects inertia in order to get it to move.
If an object is moving, one must apply a force to overcome the objects inertia in order to stop it’s motion.
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Newton’s 2nd Law
(demos: hovering globe, cart with increasing mass)
The 2nd law deals with unbalanced forces.
According to 1st law, if forces are balanced, there will not be any acceleration (no change in motion)
(do hovering globe)
Balanced forces:
A = 0 m/s2
Two cases:
If V = 0, the object will stay at rest
or if V ± 0, the object will stay in constant motion
(like a projectile in the X direction)
According to the 1st law, if forces are Unbalanced, the object will accelerate (change in motion)
Unbalanced forces:
A ± 0 m/s2
Newton experimented with unbalanced forces and found a relationship:
a proportional 1/m
and
a proportional Fnet
a prop 1/m - makes common sense, a larger mass has more inertia, therefore it won’t change motion as fast (a
will be less)
a prop F - makes common sense also, a larger force, larger disturbance, will cause a bigger change in motion.
(do demo with cart varying masses)
Newton combined the two proportions: A prop F/m - turn prop sign to = sign (add constant) constant = 1.
a = F/m - Newton’s 2nd law. Often we see it written as F = ma
Newton’s 3rd Law:
(rope “tug of war” with force readers demo)
For every action force there is an equal but opposite reaction force.
What this means is forces ALWAYS come in pairs.
This may sound counter intuative, but action/reaction pairs are easily seen in nature.
Swimmer in water – swimmer pushes arms back, water pushes person foreward
Birds – Wings push air down, air pushes bird up
Car – the wheels spin, pushing Backward on the road. Road pushes foreward on the car
Walking – You push backward on the ground, ground pushes you foreward.
Jumping – You push DOWN on ground, ground pushes you upward.
Student sitting on chair - Gravity pushes person down, chair pushes back up on person
Notice all of these reaction forces are OPPOSITE in direction. If measured, they are also EQUAL in
magnitude.
Just because the forces are equal, doesn’t mean the accelerations are equal:
Example:
Moon in orbit – Moon pulls on Earth, Earth pulls back on moon
The two forces are equal. However, the moons mass is MUCH smaller, so by newtons 2nd law, the acceleration
of the moon falling toward earth is MUCH grater. So the moon orbits the earth, not vice versa
(skateboard demo: raft/boat example)
This is a really important law, and the basis for constructing “FREE BODY DIAGRAMS” Diagrams used to
solve a variety of force/motion problems.
(Look at a horse and cart example:)
A FREEBODY DIAGRAM only shows the forces acting ON the object. They don’t show any forces that
are NOT acting on the object.
Example: (Fan Sail Demo)
Freebody Diagrams & problem solving
In order to sucessfully do “Newton’s laws “ problems, you should first construct a free body diagram of the
situation. This makes solving the problem much easier.
Steps:
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Draw a freebody diagram of situation
Write a equations for total force in the X directoin and the Y direction.
Write down knowns and unknowns
Pick appropriate equation(s).
Substitute/ Sovle for appropriate variable
Plug in #’s and solve
By using freebody diagrams, we can do many applicatoins of newtons laws. Two notable ones are Friction and
Tension.
Friction:
Application of Newton’s laws:
A good example of where we use freebody diagrams is friction.
Friction: A force that resists motion when two objects are in contact (floor and object you are dragging).
Friction always acts in the opposite direction of motion.
Friction is NOT a conservative force. This means the energy used
during the frictional force cannot go back into the object, the energy is
used in sound, heat, light, etc… that is given off to the environment.
What causes friction?
If we look on the microscopic level, even a smooth surface appears
rugged. The two surfaces that are in contact rub against each other, the
microscopic peaks and valleys catch one another.
There are also other reasons for friction, even if the objects are
perfectly smooth, interactions with the electrons will cause friction.
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There are two types of Friction: Static and Kinetic
Static Friction (Fs) – The friction that needs to be overcome in order to start an object in motion
(Friction of a stationary object)
If you apply a small force to an object, it will not move. You need to apply enough force to overcome
its static friction.
Kinetic Friction (Fk)- The firction that needs to be overcome in order to keep an object in motion.
(Friction of a moving object)
Static friction is ALWAYS greater than Kinetic friction.
The reason why related to newton’s 1st law of motion.
An object at rest wants to stay at rest, so one needs to apply an
extra force to overcome it’s inertia
An object in motion wants to stay in motion, so one does not
need ot apply an extra force to keep it moving.
So, in the presence of friction, once an object starts moving, it requires less force to keep it moving.
How do we measure friction?
What causes two surfaces to push on each other? Gravity.
Gravity pushes down, and the Normal force from the surface pushes
back up.
Therefore, the Normal force is the root cause of friction.
Fk is proportional to (Fn)
To get proportion to an equal sign,
Fk = (constant)(Fn)
The constant is a number that tells how much friction a surface has. For example, Ice has a small constant,
while Rubber has a large constant.
This constant is called the Coefficient of friction. The symbol is µ - mu – it is unitless
For kinetic friction, the coefficent of friction si µk
For static friction, the coefficent of friction si µs
So, the equation for kinetic friction is Fk = µk Fn
For static friction, the equation is Fs = µs Fn
Again, µs is always greater than µk
*** Coefficients can not be greater than 1. 1 is the maximum friction.
Some common values of coefficients of kinetic and static friction:
Surfaces
µ
µ
(static) (kinetic)
Steel on steel
0.74
0.57
Glass on glass
0.94
0.40
Metal on Metal
(lubricated)
0.15
0.06
Ice on ice
0.10
0.03
Teflon on Teflon
0.04
0.04
Tire on concrete
1.00
0.80
Tire on wet road
0.60
0.40
Tire on snow
0.30
0.20
Synovial Fluid (joints)
0.01
0.003
Solving Friction problems:
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It is important to first draw a freebody diagram of the situation
Next, pull out your 2 freebody equations
Solve the equations for the appropriate variables
Do substitutions for friction and gravity if necessary
Hints:
Usually you need to find FN, use your freebody equation in the Y direction to find it.
Remember, any time you are looking for Force of Gravity (the weight) Fg, Fg = m ag
Examples:
1.) A 15 kg object is being dragged with a force of 70 N at a constant rate along a level surface. What is the
coefficient of kinetic friction between this object and the ground?
2.) A 15 kg object is being dragged with a force of 70 N at an angle of 30 degrees a constant rate along a
level surface. What is the coefficient of kinetic friction between this object and the ground?
3.) Draw a freebody diagram of the following situation in order to determine the force applied in the x
direction. An object of mass 10 kg is accelerating at a rate of .2m/s2 along a level surface along the x
direction. k =.2
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Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it.
The direction of the force of tension is parallel to the string, away from the object exerting the stretching force.
So if an object hangs from a rope due to gravity, the gravitational force on the object points downward, and
there is an equal tension force in the rope point upward, making the net force on the object equal to zero.
Ftot = Fa – Ft = ma
Tensile Strength - measures the stress required to pull something such as rope, wire, or a structural beam to the
point where it breaks.
Tension:
Equilibirum Probelms – Sum of all forces = 0 , No Acceleration
Key to solving. Break the tensions into the X and Y components, then solve.
Examples:
The weight of the sign is 42.4 N.
The tension is 30.0 N and the angle is 45 degrees. Thus,
sine (45 degrees) = (Fvert) / (30.0 N).
The proper use of algebra leads to the equation:
Fvert = (30.0 N) • sine (45 degrees) = 21.2 N
Each cable pulls upward with 21.2 N of force. Thus, the sign must weigh
twice this - 42.4 N
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The tension is 980 Newtons.
Since the mass is 50 kg, the weight is 490 N. Since there is only one
"upward-pulling" cable, it must supply all the upward force. This cable
pulls upwards with approximately 490 N of force. Thus,
sine (30 degrees) = (490 N ) / (Ftens).
Proper use of algebra leads to the equation
Ftens = (490 N) / [ sine 30 (degrees) ] = 980 N.
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The tension is 346 Newtons.
Since the mass is 50.0 kg, the weight is 490 N. Each cable must
pull upwards with 245 N of force.
Thus, sine (45 degrees) = (245 N ) / (Ftens).
Proper use of algebra leads to the equation
Ftens = (245 N) / [sine (45 degrees)] = 346 N.
Inclined Planes:
If we look at an inclined plane, and draw a freebody diagram of
An object sliding down it, we get the following illustration:
Notice, Fg is straight, all the others are crooked. Instead of using
trig twice to rotate the FN and Fk, we can take a short cut and
rotate the X and Y axis.
Now, if we look at the diagram, only Fg is crooked. We just
have to use trig for Fg.
Lets make a triangle and solve Fgx and Fgy
Notice Fgy is perpendicular to the plane hyp of the inclined plane,
and Fgx is parallel to the hyp of the inclined plane. This means
the inclined plane triangle and the Fg triangle is a similar triangle,
which also means the two thetas are the same (as shown in the
diagram)
From our Fg diagram, we can use trig:
Fgx = Fg sin θ
Fgy = Fg cos θ
Now that we know Fgx and Fgy we can redraw our
original freebody diagram using Fgx and Fgy, so now all
of the force vectors are aligned with the X and Y axis.
Once we have this diagram set up, and the equations for
Fgx and Fgy, we can now write a freebody equation for
the X and Y directions, and solve for what the problems
ask for.
Special Case:
If we have an inclined plane, set at a low angle, the object will not move, friction will hold it back.
Now, if we raise the angle of the inclined plane, to a high angle, the object will accelerate down, Fgx will
be greater than Fk.
What if we change the angle so it is between the two above cases, where the angle is small enough so that
it doesn’t accelerate, but large enough so that is moves. This means Fgx = Fk, and the object will travel
at a constant velocity.
This is a special angle. There is only 1 angle, a threshold angle, in which the object will just start sliding
at a constant velocity. Any higher, it accelerates, and lower it stops.
At this special angle, Fgx = Fk
Example:
What is the maximum angle a plane can be tilted so that it does not move?
Solution: If we think carefully about this problem, we actually want to find the angle at which the object
just starts to move, that threshold angle. Anything before that angle, and the object will not move.
Draw your diagram:
Write your freebody equations:
X: Fgx – Fk = 0  Fgx = Fk (there is no acceleration)
Y: Fn –Fgy = 0  Fn = Fgy
Look at X equation:
Fg sin θ =
µkFn
Fg sin θ = µk Fg cos θ
Fg’s cancel out…
sin θ = µk cos θ
We are looking for theta, so put thetas on one side:
sin θ / cos θ = µk
In Trig, sin/cos = tan , therefore:
Tan θ = µk
This is the equation for the threshold angle, the angle at which a stationary object will just start to move.
Any higher angle, the object accelerates, and lower angle the object stops.
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