A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is:

Question

Quizplus · Accepted Answer

Using conservation of energy, we can find the maximum compression of the spring. Initially, the block has kinetic energy of (1/2)mv^2 = (1/2)(0.5 kg)(2 m/s)^2 = 1 J. When the spring is fully compressed, all of the block's energy is stored as potential energy in the spring. That is, (1/2)kx^2 = 1 J, where k is the spring constant and x is the compression of the spring. Solving for x, we get x = sqrt(2/k) = sqrt(2/800) = 0.05 m = 5 cm. Therefore, the maximum spring compression is 5 cm.

A 05-Kg Block Slides Along a Horizontal Frictionless Surface at 2