AP Physics 1 First Semester

An amusement park ride has two identical carriages that revolve around the center of the ride’s axle, as shown in the figure. Both carts travel at a constant tangential speed at all points along the circular path. At what position is the total mechanical energy of the cart-cart-Earth system at its maximum value?

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• The total energy of the Earth-Ferris wheel ride is constant.

Objects X and Y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, creating an Atwood’s machine, as shown in the figure. The objects are initially at rest, and the mass of Object Y is greater than the mass of Object X. As Object Y falls, how does the gravitational potential energy of the Object X-Object Y-Earth system change? All frictional forces are considered to be negligible.

• The gravitational potential energy increases because the center of mass of Object X and Object Y moves upward.

• The gravitational potential energy increases because the center of mass of Object X and Object Y moves downward.

• The gravitational potential energy decreases because the center of mass of Object X and Object Y moves upward.

• The gravitational potential energy decreases because the center of mass of Object X and Object Y moves downward.

A block of mass 0.10kg is attached and secured to one end of a spring with spring constant 50Nm. The other end of the spring is secured to a wall. The block is pushed against the spring, which compresses the spring to a position of x=−0.04m. When uncompressed, the end of the spring that is attached to the block is at a position of x=0.00m . The block-spring system is then released from rest, and the block travels along a horizontal, rough track. A motion sensor is placed so that it measures the velocity of the object as it slides along the track. A graph of total mechanical energy of the block-spring system as a function of position is shown. Which of the following statements about the block-spring system are true? Select two answers.

• The force exerted on the block by the spring at x =−0.02 mm is 1 N.

• The block has maximum speed at x =0.00 m.

• The block has half the initial spring potential energy at x = −0.025 m.

• The work done by friction as the block travels from x = −0.04 m to x == −0.02 m is 0.01J.

A block on a horizontal surface is placed in contact with a light spring with spring constant k, as shown in Figure 1. When the block is moved to the left so that the spring is compressed a distance d from its equilibrium length, the potential energy stored in the spring-block system is Em . When a second block of mass 2m is placed on the same surface and the spring is compressed a distance 2d, as shown in Figure 2, how much potential energy is stored in the spring compared to the original potential energy Em ? All frictional forces are considered to be negligible.

• 1/2 Em

• Em

• 2 Em

• 4 Em

Consider a system of two objects and Earth. Object X and object Y are held together by a light string as shown in the figure. MY is larger than MX. The two-object system is released from rest in the orientation shown in the figure at a height H above Earth’s surface. The change in the kinetic energy of the system from when it is released to the instant it hits the ground is most nearly

• MYgH

• MXgH

• (MY−MX)gH

• (MY+MX)gH

A block of mass M is sliding with an initial speed vi along a horizontal surface with negligible friction. A constant force of magnitude FA is exerted on the object at an upward angle of 60∘ from the horizontal, causing the object to speed up. If the block remains in contact with the floor, what is the change in the block’s kinetic energy as it moves a horizontal distance Δx ?

• 1/2FAΔx

• FAΔx

• 1/2M(vi)^2+1/2FAΔx

• 1/2M(vi)^2+FAΔx

A block of mass m is launched by a spring of negligible mass along a horizontal surface of negligible friction. The spring constant of the spring is k. The spring is initially compressed a distance x0. The block is released from rest. Some time after the block is released and travels in the direction shown in the figure, the spring compression is xf. Which of the following mathematical calculations can a student use to determine the speed vf of the block at this new position?

• 1/2k(x0)^2 = 1/2m(vf)^2 Solve for vf.

• 1/2k(x0)^2 = 1/2k(xf)^2 + 1/2m(vf)^2 Solve for vf.

• F∥d = 1/2mΔv^2 and F∥=kx0 . Solve for Δv.

• Fdcosθ = 1/2mΔv^2 and F=kx0 . Solve for Δv.

A block of mass M is released from rest and slides down an incline, as shown in the figure. The length D of the incline is 0.8  m and the angle of the incline, θ, is 37°. A graph of the speed v as a function of time t of the block as it descends the incline is shown. How could a student use the graph and the information provided to determine whether the block-Earth system is an open system or a closed system?

• Use the known mass of the block and the final velocity of the block after 0.5 s to determine the final kinetic energy of the block.

• Use the known length of the incline and the known angle that the incline makes with the horizontal to determine the height above the ground at which the block is released. Use this height and the object’s known mass to determine the initial gravitational potential energy of the block-Earth system.

• Use the known mass of the block and the initial velocity of the block at 0.0 s to determine the initial kinetic energy of the block. Compare it with final kinetic energy of the block that can be found as described above.

• Determine final kinetic energy as described above and compare it with the initial gravitational potential energy of the block-Earth system as described above.

A planet moves in an elliptical orbit around a star, as shown in the diagram. Which of the following is true as the planet moves from position 1 to position 2?

• The planet loses kinetic energy due to negative gravitational work; thus, the total energy in the planet-star system decreases.

• The planet’s kinetic energy increases due to positive gravitational work; thus, the total energy in the planet-star system increases.

• Kinetic energy decreases and gravitational potential energy increases, but the total energy in the planet-star system stays constant.

• Potential energy decreases and kinetic energy increases, but the total energy in the planet-star system stays constant.

A block of mass M=0.10kg is attached to one end of a spring with spring constant k=100Nm . The other end of the spring is attached to a fixed wall. The block is pushed against the spring, compressing it a distance x=0.04m . The block is then released from rest, and the block-spring system travels along a horizontal, rough track. Data collected from a motion detector are used to create a graph of the kinetic energy K and spring potential energy Us of the system as a function of the block's position as the spring expands. How can the student determine the amount of mechanical energy dissipated by friction as the spring expanded to its natural spring length?

• Use Fd with F equal to the distance the spring is compressed. Then multiply the value by the spring constant of the spring. Then multiply this value by d equal to the total displacement of the center of mass of the block.

• Subtract the final kinetic energy of the block-spring system from the initial spring potential energy stored within the block-spring system.

• Use 1/2kx^2 with k equal to 100Nm and x equal to the maximum compression of the spring.

• Use the value of the kinetic energy of the block-spring system when the block is at a position of 0 m.