AP Physics C T2 U6

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A specially designed spring is stretched from equilibrium to the distances x given in the table above, and the restoring force F is measured and recorded in each case. What is the potential energy of the spring when it is stretched 3 m from equilibrium?

• 81/4 J`

• 81/2 J

• 27 J

• 9/2 J

• 9 J

To stretch a certain nonlinear spring by an amount x requires a force F given by F = 40x – 6x² , where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 2 meters from its equilibrium position?

• 56 J

• 16 J

• 28 J

• 64 J

• 80 J

A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height reached by the ball is most nearly

• 40

• 50

• 10

• 20

• 30

In the system of two blocks and a spring shown above, blocks 1 and 2 are connected by a string that passes over a pulley. The initially unstretched spring connects block 1 to a rigid wall. Block 1 is released from rest, initially slides to the right, and is eventually brought to rest by the spring and by friction on the horizontal surface.

Which of the following is true of the energy of the system during this process?

• The potential energy lost by block 2 is less in magnitude than the potential energy gained by the spring.

• The total mechanical energy of the system is conserved.

• The energy lost to friction is equal to the gain in the potential energy of the spring.

• The potential energy lost by block 2 is greater in magnitude than the potential energy gained by the spring.

• The total mechanical energy of the system increases.

A student pushes a box across a rough horizontal floor. If the amount of work done by the student on the box is 100 J and the amount of energy dissipated by friction is 40 J, what is the change in kinetic energy of the box?

• 0 J

• 60 J

• 140 J

• 100 J

• 40 J

As a particle moves along the x axis it is acted on by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

• BC, AB, CD

• CD, BC, AB

• BC, CD, AB

• AB, BC, CD

• AB, CD, BC

A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its potential energy is 5 J?

• 3.3 J

• 5 J

• 10 J

• 15 J

• 6.7 J

Identical blocks 1 and 2 start from rest at height h and travel down two differently shaped tracks onto identical rough horizontal surfaces, as shown in the figures above. Both tracks are frictionless, and both blocks make a smooth transition onto the rough horizontal surfaces. Block 1 comes to rest at a horizontal distance d₁ from the bottom of the track. Which of the following best describes and explains the horizontal distance d₂ that block 2 travels before coming to rest?

• d₂ = d₁, because the blocks have the same mass

• d₂ < d₁, because block 2 has a lower maximum speed later than block 1

• d₂ > d₁, because the track for block 2 is shorter

• d₂ < d₁, because block 2 reaches its maximum speed later than block 1

• d₂ = d₁, because the blocks start at the same height

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 53° above the horizontal.  The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is:

• 1.6 J

• 2.5 J

• 16 J

• 25 J

• 9.0 J