(AP P1) Quiz 4.2

A block of mass 0.10 kg is attached and secured to one end of a spring with spring constant 50 N/m. 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  $x=-0.04$ m. When uncompressed, the end of the spring that is attached to the block is at a position of  $x=0.00$ m. 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  $x=-0.02$ m 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 0.01 J

A ball is dropped from rest and falls to the floor. The initial gravitational potential energy of the ball-Earth-floor system is 10 J. The ball then bounces back up to a height where the gravitational potential energy is 7 J. What was the mechanical energy of the ball-Earth-floor system the instant the ball left the floor?

• 0 J

• 3 J

• 7 J

• 10 J

A block on a horizontal surface of negligible friction is placed in contact with an ideal spring, as shown above. The block is moved to the left so that the spring is compressed a distance $x$ from equilibrium and then released from rest. The block has kinetic energy  $K_1$  when it separates from the spring. When the spring is compressed a distance  $2x$  and the block is released from rest, the kinetic energy of the block when it separates from the spring is

•  $K_1$  

•  $\sqrt{2}K_1$  

•  $2K_1$  

•  $4K_1$  

A nonrotating spherical planet with no atmosphere has mass  $M$  and radius  $R$ . A projectile of mass  $m$  is launched radially from the surface of the planet with initial speed  $v=\sqrt{\frac{GM}{2R}}$ . The potential energy of the projectile-planet system, as a function of the projectile's distance  $r$  from the center of the planet, is given by  $U=-G\frac{Mm}{r}$ . The greatest distance from the center of the planet that the projectile reaches is 

• infinity

•  $R$  

•  $\frac{7}{5}R$  

•  $\frac{4}{3}R$  

A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the total mechanical energy of the Earth-book system?

• The total mechanical energy is unchanged, because there is no change in the book’s kinetic energy as it is lowered to the table.

• The total mechanical energy is unchanged, because no work is done on the Earth-book system while the book is lowered.

• The total mechanical energy decreases, because the person does positive work on the book by exerting a force that opposes the gravitational force.

• The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.

A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above a floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce?

• 0.30 m

• 0.90 m

• 1.2 m

• 1.5 m

A sled slides down a hill with friction between the sled and hill but negligible air resistance. Which of the following must be correct about the resulting change in energy of the sled-Earth system?

• The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.

• The gravitational potential energy decreases and the kinetic energy is constant.

• The decrease in the gravitational potential energy is equal to the increase in kinetic energy.

• The gravitational potential energy and the kinetic energy must both decrease.

An inclined track is secured to a table. The height of the highest point of the track above the tabletop is $h_1$ . The height from the tabletop to the floor is  $h_2$ . A block of mass  $M$  is released from rest and slides down the track such that all frictional forces are considered to be negligible. The block leaves the track horizontally and strikes the ground at a distance  $D$  from the edge of the track as shown. Which of the following statements are correct about the scenario? Select two answers

• If the block is released from a height  $2h_1$  the block will land at a distance  $2D$  away from the end of the track.

• If the block’s mass is increased to  $2M$  , the block will land at a distance  $2D$   away from the edge of the track.

• The total mechanical energy of the system containing only the block increases from the moment of release to the moment it strikes the ground.

• The total mechanical energy of the block-Earth system remains constant.

An object initially at rest falls from a height  $H$  until it reaches the ground. Two of the following energy bar charts represent the kinetic energy  $K$   and gravitational potential energy  $U_g$  of the object-Earth system at two positions. The first position is when the object is initially released, and the second position is when the object is halfway between its release point and the ground. Which two charts could represent the mechanical energy of the object-Earth system? Select two answers.

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A 2 kg object is released from rest near and above Earth’s surface such that the object-Earth system’s gravitational potential energy as a function of time is shown in the graph. Which of the following graphs represents the kinetic energy of the object as a function of time? Assume all frictional forces are considered to be negligible.

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