AP Mechanics Unit 3 Multiple Choice Practice

A particle P is located on the x-axis, as shown in the figure. A force exerted on the particle is given by the equation F = kx³, where k = 4 N/m³. How much work is done by the force in moving the particle from x = 2 m to x = 1 m?

• 15 J

• 28 J

• 32 J

• 36 J

• 60 J

For a particular nonlinear spring, the relationship between the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation F = kx². What is the amount of work done by stretching the spring a distance x_o?

• kx_o³

• 1/2 kx_o

• 1/2 kx_o³

• 1/3 kx_o²

• 1/3 kx_o³

Two pucks moving on a frictionless air table are about to collide, as shown. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s. What is the total kinetic energy of the two-puck system before the collision?

• 5.0 J

• 7.0 J

• 10 J

• 11 J

A disc of mass m slides with negligible friction along a flat surface with a velocity v. The disc strikes a wall head-on and bounces back in the opposite direction with a kinetic energy one-fourth of its initial kinetic energy. What is the final velocity of the disc?

• v/4

• v/2

• -v

• -v/2

• -v/4

The graph represents a hypothetical potential energy curve for a particle of mass m. If the potential energy function is given by U(r) = br ^-3/2 + c, where b and c are constants, which of the following is an expression for the force on the particle?

The graph represents a hypothetical potential energy curve for a particle of mass m. If the particle is released from rest at position r₀ , its speed at position 2r₀ is most nearly

A conservative force has the potential energy function U(x), shown by the graph. A particle moving in one dimension under the influence of this force has kinetic energy 1.0 joule when it is at position x₁. Which of the following is a correct statement about the motion of the particle?

• It oscillates with maximum position x₂ and minimum position x₀.

• It moves to the right of x₃ and does not return.

• It moves to the left of x₀ and does not return.

• It comes to rest at either x₀ or x₂.

• It cannot reach either x₀ or x₂.

Two identical massless springs are hung from a horizontal support. A block of mass 1.2 kilograms is suspended from the pair of springs, as shown above. When the block is in equilibrium, each spring is stretched an additional 0.15 meter. The force constant of each spring is most nearly

• 40 N/m

• 48 N/m

• 60 N/m

• 80 N/m

• 96 N/m

A specially designed spring is stretched from equilibrium to the distances x given in the table, 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?

• 9/2 J

• 9 J

• 81/4 J

• 27 J

• 81/2 J

An ideal spring with spring constant k is cut in half. What is the spring constant of either one of the two half springs?

• k/2

• k

• k²

• 2k