AP PHYSICS
TUESDAY 15.04.07
Week 30
STANDARDS:
P-Problem Solvers
Warm Up
A 2 kg ball with a radius of 0.2 m rolls
down a 5 m ramp. Find its total
kinetic energy at the bottom, its linear
momentum & its angular momentum
Standards: 6B6: A periodic wave repeats as a function
of time and position.
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Learning Goal: SWBAT describe the
motion & energy of a spring for simple
harmonic motion.
Agenda:
1. Warm Up
2. Plan AP Test retake for students who missed it
3. Springs Notes & Guided Practice
Homework
SHM #1
AP PHYSICS
WEDNESDAY 15.04.08
STANDARDS:
D-Disciplined Learners
Standards: 6B6: A periodic wave repeats as a function
of time and position.
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Warm Up
Spring A has a constant of 20 N/m
and Spring B has a constant of 10
N/m. Find the energy and force
required to displace the spring 0.25m
if it is pulled by a 20kg. Which spring
is more rigid?
Learning Goal: SWBAT solve SHM spring
problems in the vertical direction
Agenda:
1. Warm Up
2. Review W#1
3. Plan Make Up AP Practice Test
4. # 17 Vertical SHM in Springs
Homework
W#2
AP PHYSICS
THURSDAY 15.04.08
E-Effective Communicators
Standards: 6B6: A periodic wave repeats as a function
of time and position.
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Warm Up
Spring A has a constant of 20 N/m and
Spring B has a constant of 10 N/m. Find the
energy and force required to displace the
spring 0.25m if it is pulled by a 20kg. Which
spring is more rigid?
Learning Goal: SWBAT review FRQ’s for
AP Torque & angular momentum exam
Agenda:
1. Warm Up
2. Review HW #2
3. Pendulums
4. Take Home Test Due Tomorrow
Homework
W#3
AP PHYSICS
FRIDAY 15.04.10
STANDARDS:
P-Problem Solvers
Standards: 4D net torque changes angular momentum
of system
I –Independent Resilient Individuals
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Warm Up
a. What is the period of simple harmonic
motion of a 800kN/m spring with a 50
kg mass hanging from it?
b. What is the period of the simple
harmonic motion of a 20 m long metal
cable with a 200 kg wrecking ball
attached to the end?
Learning Goal: SWBAT understand the
fundamentals of SHM and solve SHM
problems.
Agenda:
1. Warm Up
2. Turn in Take home test
3. Be ready to turn in Notebook & HW on Monday
4. Simple Harmonic Motion Review
Homework
Finish FRQ’s & SHM Review for
Monday
AP PHYSICS
FRIDAY 15.03.27
Warm Up
NA
STANDARDS:
P-Problem Solvers
Standards: 4D net torque changes
angular momentum of system
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Learning Goal: SWBAT explain each step
of their FRQ with words in addition to
solving the problem.
Agenda:
1. Warm Up
2. Take FRQ quiz
Homework
Prepare for AP Test over Spring
Break
LINEAR VS ROTATIONAL EQUATIONS OF MOTION
Concept
Linear
Position
x
Displacement
Velocity
Acceleration
Equation of Motion #1
Rotational
θ,
Dx = x - x0
Dx
v=
Dt
a=
Dv
Dt
v = v0 + at
x*
q=
r
Dq = q - q0
w=
v
Dq
w=
r
Dt ,
a=
Dw
Dt
a
,a =
r
w = w0 + at
Equation of Motion #2
1
Dx = v0t + at 2
2
Equation of Motion #3
v 2 = v02 + 2aDx w = w0 + 2aDq
1
Dq = w 0t + at 2
2
2
*Note: The x in
rotational
motion means
position on the
circle. More
generally the
equation is
written s=rθ
and in fact all of
the linear and
rotational
motion
equations would
use an s for
displacement in
its most general
form.
2
Extra Credit: Use the equations for rotational position,velocity & acceleration to convert
the Linear Equations of Motion into the Rotational Motion Equations.
#9 CENTER OF MASS LAB ACTIVITY
1. Find the center of mass of a 100 g mass at the 75 cm mark and a
200 g mass at the 25 cm mark. Will there be a net Torque associated
with this center of mass? Calculate the net Torque at the center of
mass.
2. Take a 20g and 40g mass. If the pivot point is at the
50 cm mark on the ruler and the 20g mass is placed at
the 70 cm mark, where should you put the 40g mass to
make the center of mass hit the pivot point. Calculate,
then check your work by testing out your calculated
position.
3. Take a 10 g mass. Place the 10g mass on the 80 cm
mark. Where should you make the pivot point so that it
touches the center of mass and the ruler balances?
Calculate then test with a ruler and masses.
4. A 100 g mass is at the 90cm mark on a ruler that
pivots at the 50 cm mark. A 500 g mass is at the 30 cm
mark on the same ruler. Where would a 200 g mass
need to be placed to make the center of mass hit the
50 cm mark. Calculate then verify.
TAP#8 & #9 & #10 & #11 SEE SHEET
ROTATIONAL MOTION OF TUMBLEBUGGY ACTIVITY
#12
We understand the linear motion of a tumblebuggy, but lets also describe the angular
component of motion on the tumblebuggy.
1) Find the speed of the tumblebuggy.
2) Find the angular speed of each of the tumblebuggy wheels.
3) Find the frequency and period of rotational of the tumblebuggy tires.
4) How many rpm’s does the tumblebuggy produce?
5) Write a paragraph explaining how you might attempt to find the torque produced
by the wheels. Include the information and the devices you would need to use in
order to measure it.
#13 ANGULAR ACCELERATION LAB
You will revisit the motion of objects accelerating down a ramp.
Engage: Golf Ball vs Marble Rotational Motion Racing Match
-Predict: Will a golf ball or a marble contain a greater angular acceleration? Will
their final linear velocities be the same or different?
Test: Your Objective is to compare the angular acceleration and final velocity of a golf
ball vs. the marble.
Object
Mass
(kg)
distanc
e (m)
time1
(s)
time2
(s)
time3(s)
tave(s)
radius (
r)
final
velocity
(m/s)
final
angular
velocity
(rad/s)
linear
acceler
ation
(m/s2)
angular
acceler
ation
(rad/s2)
Marble
Golf Ball
Interpret: What are your results? Do they seem reasonable? Explain the physics in a
paragraph.
#14 ANGULAR ACCELERATION LAB
1a. Predict which dowel has more rotational inertia?
1b. Predict Which ball has more
2. Test Each Prediction
3. Gradually reduce the radius of the circle that the golf and ping pong ball make. Is
it easier or harder to spin? is the rotational inertia bigger or smaller for smaller
radius’s?
4. Find the rotational inertia of each object using the formulas on the back of your
new sheet. I ball on string= mr2
Idowel = ½ mr2
m
Fat Dowel
Skinny Dowel
Ping Pong Ball
Golf Ball
r
#15 ROTATIONAL INERTIA BY ROLLING LAB
Theory: When an object rolls, it has kinetic energy both in its linear (translational) motion and its rotation. The distribution of the mass
about the body can affect how much energy is required to cause the spin. For example, a cart with very small wheels has almost
none of its kinetic energy distributed in rolling whereas a thin hoop has a large share of its mass moving at the radial distance. In the
case of an object rolling down a ramp from rest, the Total Kinetic Energy is equal to the change in gravitational potential energy
ΔU=mgΔh. The total kinetic energy of a body is found by Ktotal=Ktrans+Krot=1/2 mv2+ ½ Iω2
v0=0
d
v=rω
h1
h2
The new symbols, I and ω, are rotational inertia and angular velocity, respectively. Where I is a constant for rigid bodies and
depends on how the mass is distributed, it is usually stated as CmR2 where C is a constant between zero and 1. Angular velocity is
easily found by measuring the objects velocity and converting by the formula V=Rω.
Procedure: Raise a table on one side by putting a block of wood or a book under two of its legs. Allow objects of various shapes and mass
distributions to roll a distance of 1.5 meters across the tilted surface. The change in height is easily measured by comparing h1 to h2 as shown.
Timing the journey allows one to calculate the average translational speed, and from that the angular speed. Vaverage=1/2 (V+V0). The higher
rotational inertias become evident when more energy is in the rotation. This causes a slower translational verlocity and a longer rolling time.
Data: Start by measuring 1.5 m on the table top.
those 1.5 m.
Raise the table with the wood blocks and determine the change the height over
Δh=_________ m
Time the cart as it travels through this distance, fill in the chart
on the next page. *** Repeat your trials until the time value is
reliable.
As you do the trials make sure to predict whether the object will roll
faster or slower than the previous object. DO AT LEAST 4
Objects
mass
Radius
d (m)
hot wheel
1.5
blue cart
1.5
tape
cylinder
1.5
cap cylinder
1.5
solid squish
ball
1.5
ping pong
ball
1.5
marble
1.5
solid foam
disk
1.5
thick dowel
1.5
think dowel
1.5
time (s)
Vave=d/t
Vf=2Vavg
ω=vf/R
Ktotal=
mgΔh
Ktrans=
½ mv2
Krot=
Ktot-Ktrans
Rot. Inertia:
Krot/2ω2
C=
I/(mR2)
Analysis
1. Create a list that Organizes the objects in order of rotational inertia, from largest to smallest.
2. Use conservation of energy to show that neither mass nor radius is needed to predict the final velocity.
3. Is #2 verified by experiment? For example, do both solid cylinders have the same roll time?
4.
Can you understand that a disc is a solid cylinder and that a ring is a hollow cylinder?
5.
Do rings and cylinders have the same fall time? Do disks and rings have the same fall time? #2 & #4 suggest they
shoul.
6.
Expected values for C are 1 ring/hoop/tube, ½=disc/cylinder, 2/5 solid sphere, 2/3=hollow sphere. How well (in
percent) do your values match these expected values?
7.
What would roll down a hill faster, a hard-boiled egg, a fresh egg, or a hollow plastic Easter egg? Explain.
8.
Imagine you are at the store buying foods in cans. Would chicken broth roll down a hill faster than an empty can?
What about pumpkin pie mix (sticky & thick)?
9.
What was cart the fastest object today?
4.
An object that is at rest, not spinning, will not spin unless acted on by an outside torque. Knowing that a torque is a
force that acts at a radius, what force was causing the torque? What made the objects spin? If this force was absent
what would their movement be like?
5.
What are the likely sources of error that could make our measurement unreliable? How well did the experiment work (
see#6) Write a conclusion.
#16 MOTION OF A SPRING NOTES & PRACTICE
& SIMPLE HARMONIC MOTION OF HORIZONTAL
SPRING
F=-kx
Usp=1/2 kx2
Guided Practice: A 2kg ball initially moving at a speed of 2m/s rolls down a ramp 10
meters high. Assume no loss of energy to rotation or fiction. The ball rolls towards
a spring and depresses it 0.5m. Find k, the spring constant of the spring.
#17 SIMPLE HARMONIC MOTION OF VERTICAL
SPRING
F=-kx
Usp=1/2 kx2
T=2π(m/k)1/2
ω=(k/m)1/2
Guided Practice: A 20 N/m spring hangs from a string with a rest position 5 meters
above the ground. A 1kg mass is placed on the spring, then it is stretched an
extra 4 N and undergoes simple harmonic motion.
a. What is the equilibrium position of the mass/spring combination?
b. What is the Amplitude, angular velocity, and period of the wavelike motion of the
wave?
c. What is the total Mechanical Energy of the Spring?
d. What is the maximum height and minimum height of the spring undergoing SHM?
W#2 VERTICAL SPRINGS SHM
A 2-kilogram block is dropped from a height of 0.45 meter above an uncompressed spring, as shown
above. The spring has an elastic constant of 200 newtons per meter and negligible mass. The block
strikes the end of the spring and sticks to it.
a. Determine the speed of the block at the instant it hits the end of the spring
b. Determine the force in the spring when the block reaches the equilibrium position
c. Determine the distance that the spring is compressed at the equilibrium position
d. Determine the speed of the block at the equilibrium position.
e. Determine the resulting amplitude of the oscillation that ensues
f. Is the speed of the block a maximum at the equilibrium position, explain.
g. Determine the period of the simple harmonic motion that ensues
W#3 SHM PENDULUM
A simple pendulum consists of a bob of mass 0.085 kg attached to a string of length 1.5 m. The
pendulum is raised to point Q, which is 0.08 m above its lowest position, and released so that it
oscillates with small amplitude θ between the points P and Q as shown below.
(a) On the figure below, draw free-body
diagrams showing and labeling the forces
acting on the bob in each of the situations
described.
i. When it is at point P
ii. When it is in motion at its lowest position
(b) Calculate the speed v of the bob at its lowest
position.
(c) Calculate the tension in the string when the
bob is passing through its lowest position.
(d) Describe one modification that could be
made to double the period of oscillation.
#18 SHM PENDULUM
It is only Simple Harmonic for 30 degrees or less. It uses small angle approximation.
T=2π(l/g)1/2
Δy=L(1-cosθ)
A A 2kg ball on a 2m is lifted 20 degrees and let go and undergoes simple harmonic
motion.
a. Find the period of the motion
b. Find the maximum velocity of the ball. Where does this happen?
SHM REVIEW #4
A simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. The pendulum is held at
an angle of 30° from the vertical by a light horizontal string attached to a wall, as shown above.
(a) On the figure below, draw a free-body diagram showing and labeling the forces on the bob in the position
shown above.
(b) Calculate the tension in the horizontal string.
(c) The horizontal string is now cut close to the bob, and the pendulum swings down. Calculate the speed
of the
bob at its lowest position.
(d) How long will it take the bob to reach the lowest position for the first time