Key Termsinertianet forceequilibrium

InertiaA hovercraft, such as the one in Figure 2.1, glides along the surface of the water on a cushion of air. A common misconception is that an object on which no force is acting will always be at rest. This situation is not always the case. If the hovercraft shown in Figure 2.1 is moving at a constant velocity, then there is no net force acting on it. To see why this is the case, consider how a block will slide on different surfaces.

First, imagine a block on a deep, thick carpet. If you apply a force by pushing the block, the block will begin sliding, but soon after you remove the force, the block will come to rest. Next, imagine pushing the same block across a smooth, waxed floor. When you push with the same force, the block will slide much farther before coming to rest. In fact, a block sliding on a perfectly smooth surface would slide forever in the absence of an applied force.

In the 1630s, Galileo concluded correctly that it is an object’s nature to maintain its state of motion or rest. Note that an object on which no force is acting is not necessarily at rest; the object could also be moving with a constant velocity. This concept was further developed by Newton in 1687 and has come to be known as Newton’s first law of motion.

Newton’s First Law

An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a

straight line) unless the object experiences a net external force.

Inertia is the tendency of an object not to accelerate. Newton’s first law is often referred to as the law of inertia because it states that in the absence of a net force, a body will preserve its state of motion. In other words, Newton’s first law says that when the net external force on an object is zero, the object’s acceleration (or the change in the object’s velocity) is zero.

Newton’s First Law Main Ideas

Explain the relationship between the motion of an object and the net external force acting on the object.

Determine the net external force on an object.

Calculate the force required to bring an object into equilibrium.

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Hovercraft on Air A hovercraft floats on a cushion of air above the water. Air provides less resistance to motion than water does.

Figure 2.1

inertia the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction

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PHYSICSSpec. Number PH 99 PE C04-002-002-ABoston Graphics, Inc.617.523.1333

resistanceF

gravityF

forwardF

ground-on-carF

The sum of forces acting on an object is the net force.Consider a car traveling at a constant velocity. Newton’s first law tells us that the net external force on the car must be equal to zero. However, Figure 2.2 shows that many forces act on a car in motion. The vector Fforward represents the forward force of the road on the tires. The vector Fresistance, which acts in the opposite direction, is due partly to friction between the road surface and tires and is due partly to air resistance. The vector Fgravity represents the downward gravitational force on the car, and the vector Fground-on-car represents the upward force that the road exerts on the car.

To understand how a car under the influence of so many forces can maintain a constant velocity, you must understand the distinction between external force and net external force. An external force is a single force that acts on an object as a result of the interaction between the object and its environment. All four forces in Figure 2.2 are external forces acting on the car. The net force is the vector sum of all forces acting on an object.

When many forces act on an object, it may move in a particular direction with a particular velocity and acceleration. The net force is the force, which when acting alone, produces exactly the same change in motion. When all external forces acting on an object are known, the net force can be found by using the methods for finding resultant vectors. Although four forces are acting on the car in Figure 2.2, the car will main-tain a constant velocity if the vector sum of these forces is equal to zero.

Mass is a measure of inertia.Imagine a basketball and a bowling ball at rest side by side on the ground. Newton’s first law states that both balls remain at rest as long as no net external force acts on them. Now, imagine supplying a net force by pushing each ball. If the two are pushed with equal force, the basketball will accelerate more than the bowling ball. The bowling ball experiences a smaller acceleration because it has more inertia than the basketball.

As the example of the bowling ball and the basketball shows, the inertia of an object is proportional to the object’s mass. The greater the mass of a body, the less the body accelerates under an applied force. Similarly, a light object undergoes a larger acceleration than does a heavy object under the same force. Therefore, mass, which is a measure of the amount of matter in an object, is also a measure of the inertia of an object.

net force a single force whose external effects on a rigid body are the same as the effects of several actual forces acting on the body

Net Force Although several forces are acting on this car, the vector sum of the forces is zero, so the car moves at a constant velocity.

Figure 2.2

InertIa

Place a small ball on the rear end of a skateboard or cart. Push the skateboard across the floor and into a wall. You may need to either hold the ball in place while push-ing the skateboard up to speed or accelerate the skateboard slowly so that friction holds the ball

in place. Observe what happens to the ball when the skateboard hits the wall. Can you explain your observation in terms of inertia? Repeat the procedure using balls with different masses, and compare the results.

MATerIAlsskateboard or cart•

toy balls with various masses•

sAFeTy Perform this experiment away from walls and furniture that can be damaged.

Chapter 4124

Determining Net Force

Sample Problem B Derek leaves his physics book on top of a drafting table that is inclined at a 35° angle. The free-body diagram at right shows the forces acting on the book. Find the net force acting on the book.

AnAlyze Define the problem, and identify the variables.Given: Fgravity-on-book=Fg=22N

Ffriction =Ff=11NFtable-on-book=Ft=18N

Unknown: Fnet=?Select a coordinate system, and apply it to the free-body diagram.

Choosethex-axisparalleltoandthey-axisperpendiculartotheinclineofthetable,asshownin(a).Thiscoordinatesystemisthemostconvenientbecauseonlyoneforce

needstoberesolvedintoxandycomponents.

PlAn Find the x and y components of all vectors.Drawasketch,asshownin(b),tohelpfindthecomponentsofthevectorFg.Theangleθisequalto180°-90°-35°=55°.

cosθ=Fg, x

_Fg

sinθ=Fg, y

_Fg

Fg,x=Fgcosθ Fg,y=Fgsinθ

Fg,x=(22N)(cos55°)=13N Fg,y=(22N)(sin55°)=18N

Addbothcomponentstothefree-bodydiagram,asshownin(c).

solve Find the net force in both the x and y directions.Diagram(d)showsanotherfree-bodydiagramofthebook,nowwithforcesactingonlyalongthex-andy-axes.

Forthexdirection: Fortheydirection:

ƩFx=Fg,x-Ff ƩFy=Ft-Fg,y

ƩFx=13N-11N=2N ƩFy=18N-18N=0N

Find the net force.Addthenetforcesinthexandydirectionstogetherasvectorstofindthetotalnetforce.Inthiscase,Fnet=2 Ninthe+xdirection,asshownin(e).Thus,thebookacceleratesdowntheincline.

checkyourwork

Theboxshouldacceleratedowntheincline,sotheanswerisreasonable.

Continued

35°

11 N

18 N

18 N

13 N

22 N

11 N13 N

18 N

18 N

= 2 NFnet

= 18 Ntable-on-book F

= 22 Ngravity-on-book F

= 11 NfrictionF

11 N 18 N

22 N

TSI GraphicsHRW • Holt Physics

PH99PE-C04-002-007-A

Tips and TricksTo simplify the problem, always choose the coordinate system in which as many forces as possible lie on the x- and y-axes.

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(b)

(c)

(d)

(e)

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Determining Net Force (continued)

1. A man is pulling on his dog with a force of 70.0 N directed at an angle of +30.0° to the horizontal. Find the x and y components of this force.

2. A gust of wind blows an apple from a tree. As the apple falls, the gravitational force on the apple is 2.25 N downward, and the force of the wind on the apple is 1.05 N to the right. Find the magnitude and direction of the net force on the apple.

3. The wind exerts a force of 452 N north on a sailboat, while the water exerts a force of 325 N west on the sailboat. Find the magnitude and direction of the net force on the sailboat.

Astronaut Workouts

G ravity helps to keep bones strong. Loss of bone density is a serious outcome of time spent in space. Astronauts routinely exercise on treadmills

to counteract the effects of microgravity on their skeletal systems. But is it possible to increase the value of their workouts by increasing their mass? And does it matter if they run or walk?

A team of scientists recruited runners to help find out. The runners used treadmills that measured the net force on their legs, or ground reaction force, while they ran and walked. The runners’ inertia was changed by adding masses to a weighted vest. A spring system supported them as they exercised. Although the spring system did not simulate weightless conditions, it kept their weight the same even as their inertia was changed by the added mass. This mimicked the situation in Earth orbit, where a change in mass does not result in a change in weight.

The scientists were surprised to discover that ground reaction force did not increase with mass while the subjects were running. Ground reaction force did increase with mass while the subjects were walking. But overall, ground reaction force for running was still greater. So astronauts still need to run, not walk—and they can’t shorten their workouts by carrying more mass.

Tips and TricksIf there is a net force in both the x and y directions, use vector addition to find the total net force.

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Reviewing Main Ideas

1. If a car is traveling westward with a constant velocity of 20 m/s, what is the net force acting on the car?

2. If a car is accelerating downhill under a net force of 3674 N, what addi-tional force would cause the car to have a constant velocity?

3. The sensor in the torso of a crash-test dummy records the magnitude and direction of the net force acting on the dummy. If the dummy is thrown forward with a force of 130.0 N while simultaneously being hit from the side with a force of 4500.0 N, what force will the sensor report?

4. What force will the seat belt have to exert on the dummy in item 3 to hold the dummy in the seat?

Critical Thinking

5. Can an object be in equilibrium if only one force acts on the object?

equilibriumObjects that are either at rest or moving with constant velocity are said to be in equilibrium. Newton’s first law describes objects in equilibrium, whether they are at rest or moving with a constant velocity. Newton’s first law states one condition that must be true for equilibrium: the net force acting on a body in equilibrium must be equal to zero.

The net force on the fishing bob in Figure 2.3(a) is equal to zero because the bob is at rest. Imagine that a fish bites the bait, as shown in Figure 2.3(b). Because a net force is acting on the line, the bob accelerates toward the hooked fish.

Now, consider a different scenario. Suppose that at the instant the fish begins pulling on the line, the person reacts by applying a force to the bob that is equal and opposite to the force exerted by the fish. In this case, the net force on the bob remains zero, as shown in Figure 2.3(c), and the bob remains at rest. In this example, the bob is at rest while in equilib-rium, but an object can also be in equilibrium while moving at a constant velocity.

An object is in equilibrium when the vector sum of the forces acting on the object is equal to zero. To determine whether a body is in equilibrium, find the net force, as shown in Sample Problem B. If the net force is zero, the body is in equilibrium. If there is a net force, a second force equal and opposite to this net force will put the body in equilibrium.

equilibrium the state in which the net force on an object is zero

Forces on a Fishing line (a) The bob on this fishing line is at rest. (b) When the bob is acted on by a net force, it accelerates. (c) If an equal and opposite force is applied, the net force remains zero.

Figure 2.3

(a)

(b) (c)

Forces and the Laws of Motion 127

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