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

Step-by-step 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=(1)/(2)kx^2\quad [\text{x=compression in the spring}]\\\\\Rightarrow 10* 9.8* 5=(1)/(2)\cdot 100\cdot x^2\\\Rightarrow x=√(9.8)\\\Rightarrow x=3.13\ m`

Thus, the spring compresses by 3.13 m.