Question

A mass is attached to a vertical spring. The mass exhibits simple harmonic motion between points A and B. Which of the following statements are true?Check all that apply.The mass is located midway between points A and B when its potential energy is at maximum.The mass is located at either point A or B when its kinetic energy is at minimum.The mass is located midway between points A and B when its kinetic energy is at maximum.The mass is located at either point A or B when its potential energy is at minimum.

Answer 1

Answer:

The mass is located midway between points A and B when its kinetic energy is at maximum.

The mass is located at either point A or B when its potential energy is at minimum.

Explanation:

The mass is moving by simple harmonic motion. A and B represent the points of maximum displacement of the spring-mass system. The total mechanical energy of the system is sum of elastic potential energy (U) and kinetic energy (K):

$E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2$

where

k is the spring constant

x is the displacement (with respect to the equilibrium position)

m is the mass

v is the speed

Due to the conservation of energy, the total mechanical energy E must be constant. This means that:

- When the displacement (x) is maximum (so, at either A or B), the potential energy is maximum, while the kinetic energy is at minimum

- When the displacement (x) is zero (so, at midway between points A and B), the potential energy is at minimum, while the kinetic energy is at maximum

Therefore, the two correct statements are the last two:

- The mass is located midway between points A and B when its kinetic energy is at maximum.

- The mass is located at either point A or B when its potential energy is at minimum.