5.2 Newton's first law (Page 4/8)

University physics volume 1 Page 4 / 8

When does newton’s first law apply to your car?

Newton’s laws can be applied to all physical processes involving force and motion, including something as mundane as driving a car.

(a) Your car is parked outside your house. Does Newton’s first law apply in this situation? Why or why not?

(b) Your car moves at constant velocity down the street. Does Newton’s first law apply in this situation? Why or why not?

Strategy

In (a), we are considering the first part of Newton’s first law, dealing with a body at rest; in (b), we look at the second part of Newton’s first law for a body in motion.

Solution

When your car is parked, all forces on the car must be balanced; the vector sum is 0 N. Thus, the net force is zero, and Newton’s first law applies. The acceleration of the car is zero, and in this case, the velocity is also zero.
When your car is moving at constant velocity down the street, the net force must also be zero according to Newton’s first law. The car’s engine produces a forward force; friction, a force between the road and the tires of the car that opposes forward motion, has exactly the same magnitude as the engine force, producing the net force of zero. The body continues in its state of constant velocity until the net force becomes nonzero. Realize that a net force of zero means that an object is either at rest or moving with constant velocity, that is, it is not accelerating. What do you suppose happens when the car accelerates? We explore this idea in the next section.

Significance

As this example shows, there are two kinds of equilibrium. In (a), the car is at rest; we say it is in static equilibrium . In (b), the forces on the car are balanced, but the car is moving; we say that it is in dynamic equilibrium . (We examine this idea in more detail in Static Equilibrium and Elasticity .) Again, it is possible for two (or more) forces to act on an object yet for the object to move. In addition, a net force of zero cannot produce acceleration.

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Check Your Understanding A skydiver opens his parachute, and shortly thereafter, he is moving at constant velocity. (a) What forces are acting on him? (b) Which force is bigger?

a. His weight acts downward, and the force of air resistance with the parachute acts upward. b. neither; the forces are equal in magnitude

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Engage this simulation to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.

Summary

According to Newton’s first law, there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This law is also known as the law of inertia.
Friction is an external force that causes an object to slow down.
Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object’s mass.
If an object’s velocity relative to a given frame is constant, then the frame is inertial. This means that for an inertial reference frame, Newton’s first law is valid.
Equilibrium is achieved when the forces on a system are balanced.
A net force of zero means that an object is either at rest or moving with constant velocity; that is, it is not accelerating.

Conceptual questions

Taking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames?

(a) A car moving at constant velocity

(b) A car that is accelerating

(d) A space capsule orbiting Earth

(e) An elevator descending uniformly

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A woman was transporting an open box of cupcakes to a school party. The car in front of her stopped suddenly; she applied her brakes immediately. She was wearing her seat belt and suffered no physical harm (just a great deal of embarrassment), but the cupcakes flew into the dashboard and became “smushcakes.” Explain what happened.

The cupcake velocity before the braking action was the same as that of the car. Therefore, the cupcakes were unrestricted bodies in motion, and when the car suddenly stopped, the cupcakes kept moving forward according to Newton’s first law.

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Problems

Two forces of ${\vec{F}}_{1} = \frac{75.0}{\sqrt{2}} (\hat{i} - \hat{j}) N$ and ${\vec{F}}_{2} = \frac{150.0}{\sqrt{2}} (\hat{i} - \hat{j}) N$ act on an object. Find the third force ${\vec{F}}_{3}$ that is needed to balance the first two forces.

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While sliding a couch across a floor, Andrea and Jennifer exert forces ${\vec{F}}_{A}$ and ${\vec{F}}_{J}$ on the couch. Andrea’s force is due north with a magnitude of 130.0 N and Jennifer’s force is $32 °$ east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer’s housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force ${\vec{F}}_{DS}$ should they push so that the couch does not move?

a. ${\vec{F}}_{net} = 95.0 \hat{i} + 283 \hat{j} N$ ; b. 299 N at $71 °$ north of east; c. ${\vec{F}}_{DS} = − (95.0 \hat{i} + 283 \hat{j}) N$

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Source: OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5

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