Question

One end of an ideal spring having spring constant 100n/m is converted to a block of mass 4 kg

Answer 1

We need to know the spring compression coefficient, often denoted as k. Once we know that, this problem is simply a conservation of energy problem.

First, find the block’s initial energy, from motion or height or springs - in this case, the block’s only energy comes from its motion, or its kinetic energy. The formula for kinetic energy is 0.5 * (mass) * (velocity)^2. That gives us 1 joule of energy.

Next, we need to find any change in energy, due to work or friction. Since the question doesn’t say so, we can assume there is no energy lost to friction or any energy added due to work.

Finally, we know that all the initial energy from the block’s kinetic energy is converted into spring potential energy. The formula for spring potential energy looks very similar to the formula for kinetic energy: 0.5 * (spring constant) * (change in position of spring) ^ 2.

Equating everything, 1 joule = 0.5 * (spring constant) * (change in position) ^ 2. We’re looking for the change in position, so that would be the square root of (2/spring constant).