AP PHYSICS 1 UNIT 4 PRACTICE TEST NAME_________________________________

FREE RESPONSE PROBLEMS – Put all answers on this test. Show your work for partial credit.

Circle or box your answers. Include the correct units and the correct number of significant

figures in your answers!

1. A spring that can be assumed to be ideal hangs from a

stand, as shown at right. You wish to determine

experimentally the spring constant 𝑘 of the spring.

(a) What additional, commonly available equipment

would you need?

(b) What measurements would you make?

(c) How would 𝑘 be determined from these measurements?

(d) Assume the spring constant is determined to be 500 N/m. A 2.0-kg mass is attached to

the lower end of the spring and released from rest. Find the farthest distance the spring is

stretched as the mass drops.

(e) Suppose the spring is now used in a spring scale that is limited to a maximum value of

25 N, but you would like to weight an object of mass 𝑀 that weighs more than 25 N. You must use commonly available equipment and the spring scale to determine the weight of

the object without breaking the scale. Draw a clear diagram that shows one way that

the equipment you choose could be used with the spring scale to determine the weight

of the object, and explain how you would make the determination.

2. A block is initially at position 𝑥 = 0 and in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position 𝑥 = 0 to 𝑥 = −𝐷. The block is then released. At 𝑥 = 0 the block enters a rough part of the track and eventually comes to rest at position 𝑥 = 3𝐷. The coefficient of kinetic friction between the block and the rough track is 𝜇.

(a) On the axes below, sketch and label graphs of the kinetic energy 𝐾 of the block as a function of the position of the block between 𝑥 = −𝐷 and 𝑥 = 3𝐷. You do not need to calculate values for the vertical axis.

(b) On the same axes above, sketch and label a graph of the potential energy 𝑈 of the block-spring system as a function of the position of the block between 𝑥 = −𝐷 and 𝑥 = 3𝐷. You do not need to calculate values for the vertical axis, but use the same vertical scale

that you used for the kinetic energy.

The spring is now compressed twice as much, to 𝑥 = −2𝐷. A student is asked to predict the final position of the block. The student reasons that since the spring is compressed

twice as much as before, the block will have twice as much energy when it leaves the

spring, so it will slide twice as far along the track, stopping at position 𝑥 = 6𝐷.

(c) Which aspects of the student’s reasoning, if any, are correct? Explain how you arrived

at your answer.

(d) Which aspects of the student’s reasoning, if any, are incorrect? Explain how you

arrived at your answer.

(e) Use quantitative reasoning, including equations as needed, to develop an expression

for the new final position of the block. Express your answer in terms of 𝐷.

(f) Use your reasoning in (e) to justify your answers to (c) and (d) – explain how the correct

and incorrect aspects of the student’s reasoning identified in (c) and (d) are confirmed

by your mathematical relationships in part (e).

3. 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 at right. 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.

The person swings two

times, each time

letting go of the rope

at a different point.

(a) On the first swing, the person lets go of the rope when first arriving at point 𝐶. Draw a solid line on the diagram above to represent the trajectory of the center of mass after the

person releases the rope.

(b) On the second swing, the person lets go of the rope at point 𝐷. Draw a dotted line on the diagram above to represent the trajectory of the center of mass after the person

releases the rope.

(c) 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

ins at point 𝐴 relative to when the person is at the surface of the water.

(d) 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.

(e) Suppose 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.

(f) If the person does not let go of the rope, how does the person’s kinetic energy 𝐾𝑐 at point 𝐶 compare with the person’s kinetic energy 𝐾𝐵 at point B?

_____𝐾𝑐 > 𝐾𝑏 _____𝐾𝑐 < 𝐾𝑏 _____𝐾𝑐 = 𝐾𝑏

Provide a physical explanation to justify your answer.