Question

Consider the acceleration of a car on dry pavement, if there is no slipping. The axle moves at speed v, and the outside of the tire moves at a speed$\mathbf{}\mathit{v}$ relative to the axle. The instantaneous velocity of the bottom of the tire is zero. How much work is done by the force exerted on the tire by the road? What is the source of the energy that increases the car’s translational kinetic energy?

Short answer

The work done by the force exerted on the tire by the road is 0Joule.The internal energy of the car cause speeding a car and this will result ingaining translational kinetic energy.

Step-by-step solution

Identification of given data 

• The speed of a car outside of the is $v_{out}=v$

• The instantaneous velocity of the bottom of the tire is $v_{bot}=0$

Concept of the work done by the force

The work done by the force is determined by the multiplication of force and displacement.

Determination of the work done by the force

The work done by the force can be calculated as,

The motion of tires of a car is pure rolling. Therefore, the work done the road friction on the tires will be 0.Hence, the work done by the force exerted on the tire by the road is 0 Joule.

The engine of a car gives power to the wheel. The increase in the car's kinetic energy comes from the internal energy of the car, this will result in gaining translational kinetic energy.