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):
[tex]E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2[/tex]
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.
