Question

A 10- kg ball starting from rest rolls down a 5 m tall smooth hill from one person to another person who is standing at the bottom of the hill with a big spring whose constant is 100 N/m. How far does the spring compress in order to stop the ball

Answer 1

Answer: 3.13 m

Explanation:

Given

mas of the ball is m=10 kg

The ball rolls down a vertical distance of 5 m

Spring constant of spring is $k=100\ N/m$

Here, the potential energy of the ball converted into kinetic energy which in turn converts into elastic potential energy

$\Rightarrow mgh=\frac{1}{2}kx^2\quad [\text{x=compression in the spring}]\\\\\Rightarrow 10\times 9.8\times 5=\frac{1}{2}\cdot 100\cdot x^2\\\Rightarrow x=\sqrt{9.8}\\\Rightarrow x=3.13\ m$

Thus, the spring compresses by 3.13 m.