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AP Physics 1: Review Packet 04
Problem 1: Each part shows a set of energy bar graphs that are in sequence. Explain a situation where the
energy of a system could be represented by that sequence of bar graphs. Draw a diagram to help your
explanation. As you explain the energy transformations, reference the diagrams using (1), (2), etc. If the total
energy of the system changes, explain what external force does work to change the energy of the system. Note
that KT represents translational kinetic energy, Ug represents gravitational potential energy, and US represents
the potential energy of a spring.
Diagram
(a)

(1)

(2)
(3)
Diagram
(b)

(1)

(2)
(3)
Diagram
(c)

(1)

(2)
(3)
04-1
Diagram
(d)

(1)
(2)
(Repeat 1 and 2 over and over)
Diagram
(e)

(1)
(2)
(Repeat 1 and 2 over and over)
Diagram
(f)

(1)

(2)
(3)
(1, then 2, then 3, then 2, then 1, then 2, then 3, then 2, then 1, then 2, …)
Diagram
(g)

(1)

(2)
(3)
04-2
Problem 2: A student wishes to determine the spring constant k
of the spring inside of a marble launcher. The student builds the
experimental set-up shown in the diagram, where the marble
launcher will project the ball horizontally after the spring is
compressed a distance x. The student measures the spring
compression x for five trials, and for each trial the student also
measures the horizontal distance D that the ball travels once it
becomes a projectile. The student also measures the height from
which the ball is launched to be H = 0.8 m and the mass of the
ball to be 0.03 kg. Use g = 9.8 m/s2.
(a) Write two equations that relate D and H to the initial speed of the ball as it becomes a projectile and the time
that the ball is a projectile.
(b) Write a conservation of energy equation that relates the initial speed of the ball as it exits the launcher to the
compression of the spring.
(c) Combine all three equations into a single expression that relates D, x, g, H, and k.
(d) What quantities should be graphed in order to yield a straight-line relationship to the data? What would the
slope represent?
(e) Fill in the blank data table with those quantities that need to be graphed and plot the quantities on the grid
below. Label each axis with symbol, units, and an appropriate scale. Draw a best-fit line.
Spring
Comp.
x (m)
Horiz.
Dist.
D (m)
0.10
1.24
0.10
1.24
0.15
1.90
0.15
1.90
0.20
2.61
0.20
2.61
0.25
3.14
0.25
3.14
0.30
3.84
0.30
3.84
04-3
(f) From your best-fit line, determine the spring constant of the marble launcher.
To get a different measurement of the spring constant, the student removes the spring from the marble launcher
and hangs it vertically. The student hangs different amounts of mass on the spring and measures the length of
the spring when the objects are in equilibrium.
(g) Select two quantities that can be graphed such that the slope of the line is the spring constant. Fill in the
second data table with those values. Graph those quantities.
Hanging
Mass
m (kg)
Spring
Length
L (m)
0.2
0.163
0.4
0.231
0.6
0.300
0.8
0.359
1.0
0.428
(h) State this new measurement of the spring constant. Calculate a percent error from your two spring constant
measurements.
(i) Explain what the intercept of your graph represents.
04-4
Work, Energy, and Power Review
IMPORTANT QUANTITIES
Name
Symbol
Units
Work
J
W
Kinetic
Energy
K
J
Potential
Energy
(Spring)
Us
J
IMPORTANT EQUATIONS
Name
Basic Equation
W  Fx||
K  12 mv 2 
p2
2m
U s  12 kx 2
Name
Energy
Potential
Energy
(Gravity)
Symbol
E
Units
J
Basic Equation
None
Ug
J
U g  mgh
Power
P
W
P
Equation
Given?
Work done by Friction
(also energy lost to
friction)
W f  Ff x
No
Conservation of Energy
Ki  Ui  K f  U f
No
Power in terms of Force
and Velocity
P  Fv||
Yes
IMPORTANT GRAPHS
Name
Graph (Shape)
Energy
time
Notes
Friction takes some energy out of the
system. Note that energy lost to friction
becomes heat, so sometimes this is
referred to as thermal energy.
The sum of all different energies before
equals the sum of all different energies
after. These could be kinetic, potential,
thermal, etc. energies.
Note that dot products imply that you are
multiplying the two vectors and the
“cosine of the angle between them”.
Notes
The area under a force vs. displacement graph is
work.
Force vs. Displacement
(Could be anything)
IMPORTANT CONCEPTS
 NO WORK IS DONE IF FORCE IS PERPENDICULAR TO AN OBJECTS MOTION!!!
 USE ENERGY EQUATIONS IF YOU ARE ASKED FOR VELOCITY IN TERMS OF POSITION, OR
POSITION IN TERMS OF VELOCITY!
 Note that the equations W  Fx|| and P  Fv|| are equivalent to W  F|| x and P  F|| v and W  Fx cos 




and P  Fv cos  . Cosine does the job of finding the parallel component for you.
Work is a transfer of energy from one form to another. If energy goes from kinetic to potential, potential to
kinetic, kinetic to thermal, kinetic to another object’s kinetic, etc., work was done.
A force does positive work if the force is in the same direction as displacement. Likewise a force does
negative work if the force is opposite displacement.
A force does positive work if the potential energy related to that force decreases. Likewise, a force does
negative work if the potential energy related to that force decreases.
A force does positive work if the kinetic energy of the object increases.

Potential energy increases if an object is forced to do “the opposite of what it wants to do.” Likewise,
potential energy decreases if an object is allowed to do “what it wants to do.”
o Objects want to fall down. So raising an object up increases its potential energy.
o Springs don’t like to be stretched or compressed. Therefore, compressing or stretching a spring (away
from its equilibrium position) increases its potential energy.
o Objects in space want to attract each other due to gravity. Therefore, moving objects apart in space
increases their potential energy.
o Like charges want to move away from each other. Therefore, pushing like charges near each other
increases their potential energy.
o Opposite charges want to move toward each other. Therefore, pulling opposite charges apart increases
their potential energy.
o Like poles of magnets want to move away from each other. Therefore, pushing like poles near each
other increases their potential energy.
o Opposite poles of magnets want to move toward each other. Therefore, pulling opposite poles apart
increases their potential energy.
Example:
I lift a book from a low shelf to a high shelf. I do positive work because the force I exert (up) is in the same
direction as displacement (up), and my potential energy decreases because I had to burn calories to lift the book.
On the other hand, gravity did negative work because the force of gravity (down) was opposite the direction as
displacement (up), and gravitational potential energy increased.
NO WORK IS DONE ON AN OBJECT IN ANY UNIFORM CIRCULAR MOTION (the speed doesn’t
change, so no work is done because no energy is transferred). THIS INCLUDES A CHARGE CIRCLING IN
A MAGNETIC FIELD OR A PLANET IN CIRCULAR ORBIT.
Big concept: Use energy whenever are given a position and asked
for a velocity, OR given a velocity and asked for a position.
Example: A block is released from rest at the top of the
incline (point A) as shown.
If the incline is frictionless, how fast does the block
move at point B?
Potential energy becomes kinetic energy
mgh  12 mv 2  v  2 gh  210 15 = 17.3 m/s
If the incline has a coefficient of friction 0.11, what is
the speed at point B?
P.E. becomes K.E. AND energy lost to friction
mgh  12 mv 2  F f x (where F f  FN  mg cos  )
mgh  12 mv 2  mgx cos 

v  2 gh  2gx cos   21015  20.111025 20
25
v = 16 m/s
If the incline and horizontal plane have a coefficient
of friction of 0.11, what is the distance x traveled
along the horizontal surface to point C?
The speed at the bottom is v = 16 m/s from
before. All of this kinetic energy becomes
energy lost to friction:
2
1
2 mv  mgx (no cosine because this is flat)
1
2
162  0.1110x
 x = 116 m