Q14DQ - University Physics with Modern Physics

Question

A truck speeding down the highway has a lot of kinetic energy relative to a stopped state trooper but no kinetic energy relative to the truck driver. In these two frames of reference, is the same amount of work required to stop the truck? Explain. 

Step-by-Step Solution

Answer

The amount of work required to stop the truck in both frames of reference is not same.

Step 1: About work-energy theorem

The total work done is given by:

${\mathbf{W}}_{\mathbf{tot}}\mathbf{=}{\mathbf{K}}_{\mathbf{2}}\mathbf{‐}{\mathbf{K}}_{\mathbf{1}}\mathbf{=}\mathbf{∆}\mathbf{K}$ 

When forces act on a particle while it undergoes a displacement, the particle’s kinetic energy changes by an amount equal to the total work done on the particle by all the forces.

Step 2: Explanation of the statement.

A lot of work needs to be done in the frame of reference of the state trooper.

No work is needed to be done in the frame of reference if the driver of the truck is already at rest.

Thus, the same amount of work is not required to stop the driver.