Shm Springs

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?

• 0.5 J

• 1.5 J

• 2.0 J

• 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-PS3-1

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?

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

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

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

• 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

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-PS3-2

How does the stretch (displacement) of a spring affect the force the spring applies?

• The force is directly proportional to the displacement

• The force is inversely proportional to the displacement

• The force is independent of the displacement

• The force is equal to the displacement

What is simple harmonic motion? What type of objects undergo SHM?

• SHM is periodic motion, and objects like pendulums and springs undergo SHM

• SHM is random motion, and objects like pendulums and springs undergo SHM

• SHM is periodic motion, and objects like cars and planes undergo SHM

• SHM is random motion, and objects like cars and planes undergo SHM

Spring A has a spring constant of 20 N/m. Spring B has a spring constant of 100 N/m. What is different about the springs?

• Spring B is stiffer than Spring A

• Spring A is stiffer than Spring B

• Both springs have the same stiffness

• Spring A is longer than Spring B

What factors affect the period of a spring? Period of a pendulum?

• The mass and spring constant affect the period of a spring; the length and gravity affect the period of a pendulum

• The mass and length affect the period of a spring; the spring constant and gravity affect the period of a pendulum

• The mass and gravity affect the period of a spring; the length and spring constant affect the period of a pendulum

• The mass and spring constant affect the period of a spring; the length and mass affect the period of a pendulum

A mass attached to a spring is oscillating with simple harmonic motion. If the spring constant is 50 N/m and the mass is 2 kg, what is the angular frequency of the oscillation?

A spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the potential energy stored in the spring?

• A) 0.5 J

• B) 1 J

• C) 2 J

• D) 4 J

Tags

NGSS.HS-PS3-2

Which of the following describes the motion of a mass-spring system in simple harmonic motion?

• A) The acceleration is constant.

• B) The velocity is constant.

• C) The acceleration is proportional to the displacement and opposite in direction.

• D) The velocity is proportional to the displacement and opposite in direction.

Tags

NGSS.HS-PS2-1