# An object, of mass m, moving at speed, V*, makes contact with a spring, of spring constant, k,...

## Question:

An object, of mass m, moving at speed, V*, makes contact with a spring, of spring constant, k, that slows it down. Determine the work done by the spring force at the moment the object comes to a stop.

## Work done and Energy:

Work done can be defined as the change of energy of the object. When the object is at motion it has some kinetic energy, and when the spring slows down the object then there is some change in the kinetic energy that changes in the energy is equal to the work done by the spring force.

## Answer and Explanation:

The object has an initial speed {eq}V {/eq} and mass {eq}m {/eq}, hence kinetic energy of the object is {eq}E_i=\dfrac12mv^2 {/eq}

and finally, the object comes to rest, therefore final kinetic energy of the object is {eq}E_f=0 {/eq}.

Hence the change in the kinetic energy or the work done by the spring force is \begin{align} &W=\Delta E=E_i-E_f\\ &W=\dfrac12mV^2-0\\ &\color{red}{W=\dfrac12mV^2} \end{align}