Question

A spring (k= 100 N/m) that is initially compressed launches a solid small toy ball of mass 0.250 kg from rest along a horizontal surface as shown. the ball does not slip ( meaning it is moving to the right and also rolling) as it moves to the right. If the balls final linear speed is 6.8 m/s find the initial compression distance of the spring

Answer 1

Given data:

The mass of the ball is m=0.25 kg.

The spring constant is k=100 N/m.

The speed of the ball is v=6.8 m/s.

The amount of energy stored in the spring in the form of elastic potential energy will equal to the kinetic energy of the ball. It can be applied as,

$\begin{gathered} PE=KE \\ \frac{1}{2}kx^2=\frac{1}{2}mv^2 \end{gathered}$

Here, x is the compression in the spring.

Substitute the given values in above equation,

$\begin{gathered} \frac{1}{2}(100)x^2=\frac{1}{2}(0.25)(6.8)^2 \\ x=0.34\text{ m} \end{gathered}$

Thus, the initial compression of the spring is 0.34 m.