Physics

Physics

Problem

A block of mass 0.50 kg0.50\,\text{kg} is released from rest at a point 0.40 m0.40\,\text{m} above the upper end of a light vertical spring fixed to the ground. The spring has force constant 200 N m−1200\,\text{N\,m}^{-1}. Neglecting any energy losses, calculate the maximum compression produced in the spring before the block momentarily comes to rest.
Intuitive explanation

This is an energy conservation problem where you track how gravitational potential energy converts into both elastic potential energy and changes in height. The key insight is that at maximum compression, all the block's initial potential energy (measured from the ground) has been converted into the spring's elastic potential energy—so you can set up one equation with mghtotal=12kx2mgh_{\text{total}} = \frac{1}{2}kx^2, where htotalh_{\text{total}} includes both the initial drop and the compression distance itself.

Intuitive explanation

This is an energy conservation problem where you track how gravitational potential energy converts into both elastic potential energy and changes in height. The key insight is that at maximum compression, all the block's initial potential energy (measured from the ground) has been converted into the spring's elastic potential energy—so you can set up one equation with mghtotal=12kx2mgh_{\text{total}} = \frac{1}{2}kx^2, where htotalh_{\text{total}} includes both the initial drop and the compression distance itself.

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