Simple Harmonic Motion of a Block Attached to a Spring in Free Fall Scenario
What is the subsequent motion of the block relative to the freely falling elevator when the elevator cable snaps?
When the elevator cable snaps, what is the amplitude of the motion of the block attached to the spring?
Subsequent Motion of the Block Attached to the Spring:
The block attached to the spring will oscillate in simple harmonic motion when the elevator cable snaps. The gravitational force on the block and the elevator cancel each other out, resulting in oscillation.
Amplitude of the Motion:
The amplitude of this motion, however, is zero, due to the effect of free fall on the forces involved.
When the elevator cable snaps, the block attached to the spring will be in a state of free fall along with the elevator. The gravitational force acting on the block is balanced by the force on the elevator, creating the appearance of temporary weightlessness. As a result, the block will oscillate up and down in simple harmonic motion with a period determined by its mass and the force constant of the spring.
The amplitude of the motion refers to the maximum displacement of the block when the spring is at its maximum compression or extension. According to Hooke's law, which correlates the force exerted by a spring with its displacement, the amplitude of the motion should be calculated based on the equilibrium position of the spring. However, in this scenario of free fall, the displacement, or amplitude, is zero due to the cancellation effect of gravity on the spring and block.