SHM Quiz

A sphere is connected to a string with negligible mass, as shown, and set into simple harmonic motion by displacing it by a small angle and releasing it from rest. When the sphere is released, it is a height of 2 cm above its lowest position (where the gravitational potential energy of the sphere-Earth system is defined to be zero). Shortly after release, the kinetic energy of the sphere is equal to the gravitational potential energy of the sphere-Earth system. At this instant, the speed of the sphere will be most nearly

• (a) 0 m/s

• (b) 0.20 m/s

• (c) 0.45 m/s

• (d) 0.63 m/s

Answer explanation

Tags

NGSS.HS-PS3-1

Block 1 of mass m and Block 2 of mass 2m are attached to identical horizontal springs. Both blocks are displaced the same distance from equilibrium and released from rest, undergoing simple harmonic motion. Block 1 has maximum kinetic energy K(1, max) and maximum speed v(1, max), and Block 2 has maximum kinetic energy K(2, max) and maximum speed v(2, max). Which of the following correctly compares the maximum kinetic energies and maximum speeds of Block 1 and Block 2?

• (a)

  K(1, max) = K(2, max); v(1, max) = v(2, max)

• (b)

  K(1, max) = K(2, max); v(1, max) > v(2, max)

• (c)

  K(1, max) < K(2, max); v(1, max) = v(2, max)

• (d)

  K(1, max) < K(2, max); v(1, max) > v(2, max)

Answer explanation

(b) is Correct. Because the springs are identical and the springs are compressed by the same amount, they will have the same initial potential energy, and therefore the same total mechanical energy. Because the maximum kinetic energy is equal to the total mechanical energy, both blocks will have the same maximum kinetic energy. The speed is proportional to the kinetic energy and inversely proportional to the mass, as given by v²=2k/m, so Block 1 will have a greater speed because it has a smaller mass.

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

A block is attached to a horizontal spring and is initially at rest at the equilibrium position x=0 m. as shown in Figure 1 . The block is then moved to position x= -A, as shown in Figure 2, and released from rest, undergoing simple harmonic motion. At the instant the block reaches position x= +A, another identical block is dropped onto and sticks to the block, as shown in Figure 3. The two-block-spring system then continues to undergo simple harmonic motion. Which of the following correctly compares the total mechanical energy E(tot,2), of the two-block-spring system after the collision to the total mechanical energy E(tot, 1) of the one-block-spring system before the collision?

• (a)

  E (tot, 2) < E(tot, 1)

• (b)

  E(tot, 2) = E(tot, 1)

• (c)

  E(tot, 1) < E(tot, 2) < 2E(tot, 1)

• (d)

  E (tot, 2) = 2E(tot, 1)

Answer explanation

(b) is Correct. Because the amplitude of oscillation does not change, the total mechanical energy of the two-block-spring system will be the same as that of the one-block-spring system.

Tags

NGSS.HS-PS3-1

A block attached to a horizontal spring undergoes simple harmonic motion. The total mechanical energy of the block-spring system is 2 J. At a particular instant, the block has a kinetic energy of 0.5 J. What is the potential energy of the block-spring system at this instant?

• (a) 0.5 J

• (b) 1.5 J

• (c) 2.0 J

• (d) 2.5 J

Answer explanation

(b) is Correct. The total mechanical energy of the system is constant, therefore the sum of the kinetic and potential energies must be equal to the total mechanical energy

Tags

NGSS.HS-PS3-2

. A block-spring system is undergoing simple harmonic motion. Which of the following statements about the relative values of the maximum kinetic and potential energies of the system is correct?

• a) The maximum kinetic energy is greater than the maximum potential energy.

• b) The maximum kinetic energy is equal to the maximum potential energy.

• c) The maximum kinetic energy is less than the maximum potential energy.

• d) The relative values of the maximum kinetic and potential energies depend on the mass of the block and the spring constant of the spring.

Answer explanation

(b) is Correct. The total mechanical energy of the system is constant. When the kinetic energy is at its maximum value, the potential energy will be zero (because the block will be at the equilibrium position). Similarly, when the potential energy is at its maximum, the kinetic energy will be zero (because the block will be momentarily at rest). Therefore, the maximum energies must be equal to conserve energy

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2