Question

A student has the idea that the total work done on an object is equal to its final kinetic energy. Is this idea true always, sometimes, or never? If it is sometimes true, under what circumstances? If it is always or never true, explain why.

Short answer

Thetotal work done on an object is equal to its final kinetic energy only if the object moves on the ground with zero initial speed.

Step-by-step solution

Energy conservation principle 

Based on the energy conservation principle, the total work done on an object is equal to the total energy associated with the object.

In the formula,

$\begin{array}{l}\mathbf{W}\mathbf{=}\mathbf{\Delta KE}\mathbf{+}\mathbf{\Delta PE}\\ \mathbf{W}\mathbf{=}\left({\mathrm{KE}}_f-{\mathrm{KE}}_i\right)\mathbf{+}\mathbf{\Delta PE}\end{array}$

Here, W is the total work done, $\mathbf{∆}\mathbf{KE}$is the change in the kinetic energy, $\mathbf{∆}\mathbf{PE}$is the change in the potential energy, ${\mathbf{KE}}_{\mathbf{i}}$is the initial kinetic energy, and${\mathbf{KE}}_{\mathbf{f}}$ is the final kinetic energy of the object.

The total work done on an object

For an object, moving on the ground and starting from the rest

$\mathrm{\Delta PE}=0$and ${\text{KE}}_i=0$.

Then, the total work done on an object is given by the following:

$\begin{array}{l}\mathrm{W}=\left({\mathrm{KE}}_{\mathrm{f}}-0\right)+0\\ \mathrm{W}={\mathrm{KE}}_{\mathrm{f}}\end{array}$

Hence, the total work done on an object is equal to its final kinetic energy only if the object moves on the ground with zero initial speed.