5.3 Newton's second law  (Page 3/8)

What acceleration can a person produce when pushing a lawn mower?

Suppose that the net external force (push minus friction) exerted on a lawn mower is 51 N (about 11 lb.) parallel to the ground ( [link] ). The mass of the mower is 24 kg. What is its acceleration?

Strategy

This problem involves only motion in the horizontal direction; we are also given the net force, indicated by the single vector, but we can suppress the vector nature and concentrate on applying Newton’s second law. Since $F_{\text{net}}$ and m are given, the acceleration can be calculated directly from Newton’s second law as $F_{\text{net}}=ma.$

Solution

The magnitude of the acceleration a is $a=F_{\text{net}}\text{/}m$ . Entering known values gives

Substituting the unit of kilograms times meters per square second for newtons yields

Significance

The direction of the acceleration is the same direction as that of the net force, which is parallel to the ground. This is a result of the vector relationship expressed in Newton’s second law, that is, the vector representing net force is the scalar multiple of the acceleration vector. There is no information given in this example about the individual external forces acting on the system, but we can say something about their relative magnitudes. For example, the force exerted by the person pushing the mower must be greater than the friction opposing the motion (since we know the mower moved forward), and the vertical forces must cancel because no acceleration occurs in the vertical direction (the mower is moving only horizontally). The acceleration found is small enough to be reasonable for a person pushing a mower. Such an effort would not last too long, because the person’s top speed would soon be reached.

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Which force is bigger?

(a) The car shown in [link] is moving at a constant speed. Which force is bigger, ${\overrightarrow{F}}_{\text{engine}}$ or ${\overrightarrow{F}}_{\text{friction}}$ ? Explain.

(b) The same car is now accelerating to the right. Which force is bigger, ${\overrightarrow{F}}_{\text{engine}}$ or ${\overrightarrow{F}}_{\text{friction}}?$ Explain.

Strategy

We must consider Newton’s first and second laws to analyze the situation. We need to decide which law applies; this, in turn, will tell us about the relationship between the forces.

Solution

1. The forces are equal. According to Newton’s first law, if the net force is zero, the velocity is constant.
2. In this case, ${\overrightarrow{F}}_{\text{engine}}$ must be larger than ${\overrightarrow{F}}_{\text{friction}}.$ According to Newton’s second law, a net force is required to cause acceleration.

Significance

These questions may seem trivial, but they are commonly answered incorrectly. For a car or any other object to move, it must be accelerated from rest to the desired speed; this requires that the engine force be greater than the friction force. Once the car is moving at constant velocity, the net force must be zero; otherwise, the car will accelerate (gain speed). To solve problems involving Newton’s laws, we must understand whether to apply Newton’s first law (where ${\displaystyle \sum \overrightarrow{F}}=\overrightarrow{0}$ ) or Newton’s second law (where ${\displaystyle \sum \overrightarrow{F}}$ is not zero). This will be apparent as you see more examples and attempt to solve problems on your own.

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