Pushing a Stalled Car

Example 1 Pushing a Stalled Car

Two people are pushing a stalled car, as Figure 4.5a indicates. The mass of the car is 1850 kg. One person applies a force of 275 N to the car, while the other applies a force of 395 N. Both forces act in the same direction. A third force of 560 N also acts on the car, but in a direction opposite to that in which the people are pushing. This force arises because of friction and the extent to which the pavement opposes the motion of the tires. Find the acceleration of the car.

Figure 4.5

(a)

Two people push a stalled car. A force created by friction and the pavement opposes their efforts.

(b)

A free-body diagram that shows the horizontal forces acting on the car.

Problem-solving insight

A free-body diagram is very helpful when applying Newton's second law. Always start a problem by drawing the free-body diagram.

Reasoning According to Newton's second law, the acceleration is the net force divided by the mass of the car. To determine the net force, we use the free-body diagram in Figure 4.5b. In this diagram, the car is represented as a dot, and its motion is along the +x axis. The diagram makes it clear that the forces all act along one direction. Therefore, they can be added as colinear vectors to obtain the net force.

Solution From Equation 4.1, the acceleration is a = (ΣF)/m. The net force is

The acceleration can now be obtained:


	(4.1)

The plus sign indicates that the acceleration points along the +x axis, in the same direction as the net force.

Problem-solving insight

The direction of the acceleration is always the same as the direction of the net force.