Question

A 0.400kg ball is dropped from a height of 3.00m onto a spring with a spring constant of 600.N/m. How much does the spring compress if the ball comes to a stop.0.313m0.098m0.0392m0.198m

Answer 1

Given data

*The given mass of the ball is m = 0.400 kg

*The given height is h = 3.00 m

*The given spring constant is k = 600.0 N/m

*The value for the acceleration due to the gravity is

`g=9.8\text{ m/s\textasciicircum{}2}`

The expression for the spring compresses at a distance is given by the conservation of energy as

`\begin{gathered} U_s=U_p \\ \text{mgh}=(1)/(2)kx^2 \\ x=\sqrt[]{(2mgh)/(k)} \end{gathered}`

Substitute the values in the above expression as

`\begin{gathered} x=\sqrt[]{(2*0.400*9.8*3.00)/(600.0)} \\ =0.198\text{ m} \end{gathered}`