A mass is suspended vertically from an ideal spring. When the action in this pro

Question

A mass is suspended vertically from an ideal spring. When the action in this problem begins, the mass has been lifted upwards so that the spring is much less extended than when the mass is simply hanging, at rest, from the end of the spring. The mass is then released; it falls and stretches the spring and ends up vibrating up and down about the equilibrium position (the position where the total force on the mass is zero).

(a) The acceleration of the mass (as well as the net force on the mass) is greatest in magnitude and is directed upward when

the spring is least extended (i.e. the mass is at the upper endpoint of the motion).the spring is most extended (i.e. the mass is at the lower endpoint of the motion).     the mass is somewhere between the equilibrium position and the lower endpoint of the motion.the mass is passing the equilibrium position.

(b) The speed of the mass is greatest when

the spring is most extended (i.e. the mass is at the lower endpoint of the motion).the mass is passing the equilibrium position.     the mass is somewhere between the equilibrium position and the lower endpoint of the motion.the spring is least extended (i.e. the mass is at the upper endpoint of the motion).

(c) The acceleration of the mass is zero when

the mass is passing the equilibrium position.the spring is least extended (i.e. the mass is at the upper endpoint of the motion).     the mass is somewhere between the equilibrium position and the lower endpoint of the motion.the spring is most extended (i.e. the mass is at the lower endpoint of the motion).

(d) The acceleration of the mass (as well as the net force on the mass) is greatest in magnitude and directed downward when

the mass is passing the equilibrium position.the spring is most extended (i.e. the mass is at the lower endpoint of the motion).     the spring is least extended (i.e. the mass is at the upper endpoint of the motion).the mass is somewhere between the equilibrium position and the lower endpoint of the motion.

Explanation / Answer

The correct answers are as follows:

(a)

the spring is most extended (i.e. the mass is at the lower endpoint of the motion).

(b)

the mass is passing the equilibrium position.

(c)

the mass is passing the equilibrium position.

(d)

the spring is least extended (i.e. the mass is at the upper endpoint of the motion).

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