Two cars travel at the same speed, so that they move 105 km in one hour. One car, a sleek

Question

sports car, has a motor that delivers only 35 kW of power at this speed. The other car
needs its motor to produce 65 kW to move the car this fast. The difference is caused by air
resistance.
a. For each car, list the external horizontal forces exerted on it, and give the cause of each
force. Compare their magnitudes.
b. By Newton’s third law, the car exerts forces on the ground and the air. What are their directions?
c. Calculate the magnitude of the forward frictional force exerted by each car.
d. The car engines did work. Where did the energy come from?

Answer 1

a. The external horizontal forces exerted on each car are:
1) Frictional force from the ground which propels the car forward, caused by the contact between the tires and the ground.
2) Air resistance (drag force), which acts in the opposite direction of the car's motion, caused by the interaction between the car and air molecules.

The magnitudes of the frictional force and air resistance for each car are different due to their different power requirements (35 kW for the sports car and 65 kW for the other car).

b. By Newton's third law, the car exerts an equal and opposite force on the ground and the air. The directions of these forces are:
1) The force exerted on the ground by the car is in the opposite direction of the frictional force (backward).
2) The force exerted on the air by the car is in the opposite direction of the air resistance (forward).

c. To calculate the magnitude of the forward frictional force exerted by each car, we will use the following equation:

Power = Force × Velocity

For the sports car:
35,000 W (35 kW) = Force × (105,000 m / 3,600 s)
Force = 35,000 × 3,600 / 105,000
Force ≈ 1,200 N

For the other car:
65,000 W (65 kW) = Force × (105,000 m / 3,600 s)
Force = 65,000 × 3,600 / 105,000
Force ≈ 2,240 N

Hence, the forward frictional force exerted by the sports car is about 1,200 N and by the other car is about 2,240 N.

d. The energy required for the car engines to do work came from the fuel (for example, gasoline) that the engines burned. The chemical energy stored in the fuel was converted into mechanical work to propel the cars forward.