Question

Mark pushes his broken car 140 m down the block to his friend's house. He has to exert a 160 N horizontal force to push the car at a constant speed.

How much thermal energy is created in the tires and road during this short trip?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Concepts and reason

The concepts required to solve this problem are work done and thermal energy.

First, find the work done by the force in moving the car by using the force and displacement. Finally, find the thermal energy created in the tires by conservation of energy.

Fundamentals

The work done by a force in displacing an object by a distance d can be written as follows:

$W = Fd\cos \theta$

Here, F is the force acting on the object, d is the distance, and $\theta$ is the angle between the force and the displacement vector.

The force applied by Mark to move the car is in the direction of the displacement of the car. The angle between force and displacement is zero.

The work done by a force in displacing an object by a distance d can be written as follows:

$W = Fd\cos \theta$

Substitute 0 for $\theta$, 140 m for d, and 160 N for F in the above expression.

$\begin{array}{c}\\W = \left( {160{\rm{ N}}} \right)\left( {140{\rm{ m}}} \right)\cos {0^{\rm{o}}}\\\\ = 22400{\rm{ J}}\\\end{array}$

The thermal energy created between the tires and the road during the motion of the car is equal to the work done by the force on the car.

The thermal energy produced is as follows:

${E_{\rm{t}}} = W$

Substitute 22400 J for W in the above expression.

$\begin{array}{c}\\{E_{\rm{t}}} = 22400{\rm{ J}}\\\\ = 2.2 \times {10^4}{\rm{ J}}\\\end{array}$

Ans:

The thermal energy created is $2.2 \times {10^4}{\rm{ J}}$.