AP PHYSICS 1
Test Booklet
Final Exam Extra Credit
1.
A 0.50 kg cart moves on a straight horizontal track. The graph of velocity vx versus time t for the cart is given
below.
a. Indicate every time t for which the cart is at rest.
b. Indicate every time interval for which the speed (magnitude of velocity) of the cart is increasing.
c. Determine the horizontal position x of the cart at t = 9.0 s if the cart is located at x = 2.0 m at t = 0.
d. On the axes below, sketch the acceleration a versus time t graph for the motion of the cart from t = 0 to t
= 25 s.
e. From t = 25 s until the cart reaches the end of the track, the cart continues with constant horizontal
velocity. The cart leaves the end of the track and hits the floor, which is 0.40 m below the track.
Neglecting air resistance, determine each of the following.
i. The time from when the cart leaves the track until it first hits the floor
AP Physics 1
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Test Booklet
Final Exam Extra Credit
ii. The horizontal distance from the end of the track to the point at which the cart first hits the floor
iii. The kinetic energy of the cart immediately before it hits the floor
2.
A child pulls a 15 kg sled containing a 5.0 kg dog along a straight path on a horizontal surface. He exerts a force
of 55 N on the sled at an angle of 20º above the horizontal, as shown in the figure above. The coefficient of
friction between the sled and the surface is 0.22.
(a) On the dot below that represents the sled-dog system, draw and label a free-body diagram for the system as it
is pulled along the surface.
(b) Calculate the normal force of the surface on the system.
(c) Calculate the acceleration of the system.
(d) Calculate the work done by the child’s pulling force as the system moves a distance of 7.0 m.
(e) At some later time, the dog rolls off the side of the sled. The child continues to pull with the same force. On the
axes below, sketch a graph of speed u versus time t for the sled. Include both the sled’s travel with and without the
dog on the sled. Clearly indicate with the symbol tr the time at which the dog rolls off.
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AP Physics 1
Test Booklet
Final Exam Extra Credit
3.
A coin C of mass 0.0050 kg is placed on a horizontal disk at a distance of 0.14 m from the center, as shown above.
The disk rotates at a constant rate in a counterclockwise direction as seen from above. The coin does not slip, and
the time it takes for the coin to make a complete revolution is 1.5 s.
a. The figure below shows the disk and coin as viewed from above. Draw and label vectors on the figure
below to show the instantaneous acceleration and linear velocity vectors for the coin when it is at the
position shown.
b. Determine the linear speed of the coin.
c. The rate of rotation of the disk is gradually increased. The coefficient of static friction between the coin
and the disk is 0.50. Determine the linear speed of the coin when it just begins to slip.
d. If the experiment in part (c) were repeated with a second, identical coin glued to the top of the first coin,
how would this affect the answer to part (c) ? Explain your reasoning.
AP Physics 1
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Test Booklet
Final Exam Extra Credit
4.
Block A of mass 2.0 kg is pulled along a horizontal table by a force of 15 N, which is applied by a light string that
passes over a light frictionless pulley, as shown above. The coefficient of kinetic friction between the block and
the surface is 0.25.
(a) On the dot below, which represents the block, draw and label the forces (not components) that act on the block
as it is pulled across the table.
(b) Calculate the magnitude of the acceleration of the block.
The applied force is removed. Block B of mass 1.5 kg is now attached to the string, as shown above. The system is
released from rest so that the 1.5 kg box descends and the 2.0 kg block is again pulled across the table.
(c) Calculate the acceleration of the 1.5 kg block as it descends.
(d) Calculate the tension in the string connecting the two blocks.
(e) Calculate the distance that the 1.5 kg block descends in 0.40 s.
(f) If this system is set up in a laboratory and the acceleration of the 1.5 kg block is experimentally determined, the
experimental value is found to be smaller than the value calculated above. If the given value for the coefficient of
friction is correct and air resistance is negligible, explain briefly, but specifically, why the experimental value of
the acceleration is smaller.
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AP Physics 1
Test Booklet
Final Exam Extra Credit
5.
A spacecraft of mass m is in a clockwise circular orbit of radius R around Earth, as shown in the figure above.
The mass of Earth is ME.
a. In the figure below, draw and label the forces (not components) that act on the spacecraft. Each force
must be represented by a distinct arrow starting on, and pointing away from, the spacecraft.
b.
i. Derive an equation for the orbital period T of the spacecraft in terms of m, ME, R, and physical
constants, as appropriate. If you need to draw anything other than what you have shown in part
(a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).
ii. A second spacecraft of mass 2m is placed in a circular orbit with the same radius R. Is the
orbital period of the second spacecraft greater than, less than, or equal to the orbital period of
the first spacecraft?
____Greater than ____Less than ____Equal to
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Test Booklet
Final Exam Extra Credit
Briefly explain your reasoning.
c. The first spacecraft is moved into a new circular orbit that has a radius greater than R, as shown in the
figure below.
Is the speed of the spacecraft in the new orbit greater than, less than, or equal to the original speed?
____Greater than ____Less than ____Equal to
Briefly explain your reasoning.
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AP Physics 1
Test Booklet
Final Exam Extra Credit
6.
You are assigned to do some calculations for a movie stunt that involves a car on a straight road. The road,
pictured above, has a hill that rises 8.0 m above the flat region. The top of the hill is a circular arc of radius 20 m.
You need to determine whether a car traveling under certain conditions will lose contact with the road at the top of
the hill. There is a stop sign 50 m from the beginning of the hill. You are to assume that a car of mass 1600 kg
accelerates uniformly from rest at the stop sign, has a speed of when it reaches the beginning of the hill, and then
coasts with the engine off. Assume energy losses due to friction and air resistance are negligible.
a. Calculate the magnitude of the acceleration of the car during the first 50 m.
b. Calculate the time it takes the car to reach the beginning of the hill
c. Calculate the magnitude of the net force required to accelerate the car during the first 50 m.
d. On the dot below that represents the car, draw and label the forces (not components) that act on the car at
the top of the hill if it travels over the hill without losing contact.
e. Calculate the minimum speed the car must have at the top of the hill to momentarily lose contact with the
road. If you need to draw anything other than what you have shown in part (d) to assist in your solution,
use the space below. Do NOT add anything to the figure in part (d).
f. Calculate the speed the car must have at the beginning of the hill in order to have the speed at the top of
the hill you calculated in part (e).
AP Physics 1
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Test Booklet
Final Exam Extra Credit
7.
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
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AP Physics 1
Test Booklet
Final Exam Extra Credit
8.
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 figures below, draw free-body diagrams showing and labeling the forces acting on the bob in each
of the situations described.
b. Calculate the speed u 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.
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Test Booklet
Final Exam Extra Credit
9.
A box is being pushed at constant speed up an inclined plane to a vertical height of 3.0 m above the ground, as
shown in the figure above. The person exerts a force parallel to the plane. The mass m of the box is 50 kg, and the
coefficient of kinetic friction km between the box and the plane is 0.30.
(a) On the dot below that represents the box, draw and label the forces (not components) acting on the box.
(b) Calculate the normal force of the plane on the box. If you need to draw anything other than what you have
shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).
(c) Calculate the component of the force of gravity acting on the box that is parallel to the plane.
(d) Calculate the friction force between the plane and the box.
(e) Calculate the force applied by the person on the box.
(f) Calculate the work done by the person pushing the box, assuming the box is raised to the vertical height of 3.0
m.
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AP Physics 1
Test Booklet
Final Exam Extra Credit
10.
Starting from rest at point A, a 50 kg person swings along a circular arc from a rope attached to a tree branch over
a lake, as shown in the figure above. Point D is at the same height as point A. The distance from the point of
attachment to the center of mass of the person is 6.4 m. Ignore air resistance and the mass and elasticity of the
rope.
(a) The person swings two times, each time letting go of the rope at a different point.
i. On the first swing, the person lets go of the rope when first arriving at point C. Draw a solid line to represent the
trajectory of the center of mass after the person releases the rope.
ii. A second time, the person lets go of the rope at point D. Draw a dashed line to represent the trajectory of the
center of mass after the person releases the rope.
(b) The center of mass of the person standing on the platform is at point A, 4.1 m above the surface of the water.
Calculate the gravitational potential energy when the person is at point A relative to when the person is at the
surface of the water.
(c) The center of mass of the person at point B, the lowest point along the arc, is 2.4 m above the surface of the
water. Calculate the person’s speed at point B.
(d) Suppose that the person swings from the rope a third time, letting go of the rope at point B. Calculate R, the
horizontal distance moved from where the person releases the rope at point B to where the person hits the water.
(e) If the person does not let go of the rope, how does the magnitude of the person’s momentum pC at point C
compare with the magnitude of the person’s momentum pB at point B ?
____ pC > pB ____ pC < pB ____ pC = pB
Provide a physical explanation to justify your answer.
AP Physics 1
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Test Booklet
Final Exam Extra Credit
11.
A 0.40 kg object moves in a straight line under the action of a net force. The graph above shows the velocity as a
function of time for the object during a 25 s interval. At time t = 0, the object is at the position x = 0.
(a) On the grid below, sketch a graph of the acceleration as a function of time for the object. Label the scale for the
acceleration.
(b) Calculate the position of the object at t = 5.0 s.
(c) On which segment of the graph is the net force acting on the object zero?
____ A ____ B ____ C
Justify your answer.
(d) Calculate the net force on the object during the first 3.0 s of the motion.
(e) Calculate the amount of work done on the object by the net force during the first 15 s of the motion.
(f) For the interval t = 15 s to t = 25 s, is the work done on the object by the net force positive, negative, or zero?
____ Positive ____ Negative ____ Zero
Justify your answer.
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AP Physics 1