368 Unit 3: Motion and Forces

VOCABULARY

momentum p. 368collision p. 370conservation of

momentum p. 371

BEFORE, you learned

• A force is a push or a pull• Newton’s laws help to describe

and predict motion

NOW, you will learn

• What momentum is• How to calculate momentum• How momentum is affected

by collisions

KEY CONCEPT

Forces transfermomentum.

MATERIALS2 balls of

different masses

Objects in motion have momentum.If you throw a tennis ball at a wall, it will bounce back toward you.What would happen if you could throw a wrecking ball at the wall atthe same speed that you threw the tennis ball? The wall would mostlikely break apart. Why would a wrecking ball have a different effecton the wall than the tennis ball?

A moving object has a property that is called momentum.(moh-MEHN-tuhm) is a measure of mass in motion;

the momentum of an object is the product of its mass and its velocity.At the same velocity, the wrecking ball has more momentum than thetennis ball because the wrecking ball has more mass. However, youcould increase the momentum of the tennis ball by throwing it faster.

MomentumVOCABULARYMake a magnet word diagram for momentum.

EXPLORE Collisions

What happens when objects collide?

PROCEDURE

Roll the two balls toward each other on a flat surface. Try to roll them at the same speed. Observe what happens. Experiment bychanging the speeds of the two balls.

Leave one ball at rest, and roll the other ball so that it hits the first ball. Observe what happens. Then repeat the experiment with theballs switched.

WHAT DO YOU THINK? • How did varying the speed of the balls affect the

motion of the balls after the collision?• What happened when one ball was at rest? Why

did switching the two balls affect the outcome?

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Chapter 11: Forces 369

Momentum is similar to inertia. Like inertia, the momentum of anobject depends on its mass. Unlike inertia, however, momentum takesinto account how fast the object is moving. A wrecking ball that ismoving very slowly, for example, has less momentum than a fast-moving wrecking ball. With less momentum, the slower-movingwrecking ball would not be able to do as much damage to the wall.

To calculate an object’s momentum, you can use the following formula:

momentum = mass · velocityp = mv

In this formula, p stands for momentum, m for mass, and v forvelocity. In standard units, the mass of an object is given in kilograms(kg), and velocity is given in meters per second (m/s). Therefore, theunit of momentum is the kilogram-meter per second (kg p m/s).Notice that the unit of momentum combines mass, length, and time.

Like force, velocity, and acceleration, momentum is a vector—ithas both a size and a direction. The direction of an object’s momen-tum is the same as the direction of its velocity. You can use speedinstead of velocity in the formula as long as you do not need to knowthe direction of motion. As you will read later, it is important to knowthe direction of the momentum when you are working with morethan one object.

check your reading How do an object’s mass and velocity affect its momentum?

RESOURCE CENTERCLASSZONE.COM

Explore momentum.

reminder

Inertia is the resistance of an object to changes in its motion.

Sample Problem

Practice the Math

Calculating Momentum

What is the momentum of a 1.5 kg ball moving at 2 m/s?

What do you know? mass = 1.5 kg, velocity = 2 m/s

What do you want to find out? momentum

Write the formula: p = mv

Substitute into the formula: p = 1.5 kg p 2 m/s

Calculate and simplify: p = 3 kg pm/s

Check that your units agree: Unit is kg pm/s.

Unit of momentum is kg pm/s. Units agree.

Answer: p = 3 kg pm/s

1. A 3 kg ball is moving with a velocity of 1 m/s. What is the ball’s momentum?

2. What is the momentum of a 0.5 kg ball moving 0.5 m/s?

370 Unit 3: Motion and Forces

Momentum can be transferred from one object to another.

If you have ever ridden in a bumper car, you have experienced colli-sions. A is a situation in which two objects in close contactexchange energy and momentum. As another car bumps into the backof yours, the force pushes your car forward. Some of the momentumof the car behind you is transferred to your car. At the same time, thecar behind you slows because of the reaction force from your car. Yougain momentum from the collision, and the other car loses momen-tum. The action and reaction forces in collisions are one way in whichobjects transfer momentum.

If two objects involved in a collision have very different masses,the one with less mass has a greater change in velocity. For example,consider what happens if you roll a tennis ball and a bowling balltoward each other so that they collide. Not only will the speed of thetennis ball change, but the direction of its motion will change as itbounces back. The bowling ball, however, will simply slow down. Eventhough the forces acting on the two balls are the same, the tennis ballwill be accelerated more during the collision because it has less mass.

check your reading How can a collision affect the momentum of an object?

collision

What happens when objects collide?PROCEDURE

Set up two parallel rulers separated by one centimeter. Place a line of fivemarbles, each touching the next, in the groove between the rulers.

Roll a marble down the groove so that it collides with the line of marbles,and observe the results.

Repeat your experiment by rolling two and then three marbles at the line ofmarbles. Observe the results.

WHAT DO YOU THINK?• What did you observe when you rolled the marbles?

• Why do you think the marbles moved the way they did?

CHALLENGE Use your answers to write a hypothesis explaining your observations. Design your own marble experiment to test this hypothesis. Do your results support your hypothesis?

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MomentumMomentumSKILL FOCUSObserving

MATERIALS• 2 rulers• 8 marbles

TIME20 minutes

Chapter 11: Forces 371

reading tip

A light blue-green arrowshows the momentum of an individual object.

A dark blue-green arrowshows the total momentum.

Momentum is conserved.During a collision between two objects, each object exerts a force onthe other. The colliding objects make up a system—a collection ofobjects that affect one another. As the two objects collide, the velocityand the momentum of each object change. However, as no otherforces are acting on the objects, the total momentum of both objectsis unchanged by the collision. This is due to the conservation ofmomentum. The principle of states thatthe total momentum of a system of objects does not change, as longas no outside forces are acting on that system.

How much an object’s momentum changes when a force isapplied depends on the size of the force and how long that force isapplied. Remember Newton’s third law—during a collision, twoobjects are acted upon by equal and opposite forces for the samelength of time. This means that the objects receive equal and oppositechanges in momentum, and the total momentum does not change.

You can find the total momentum of a system of objects before acollision by combining the momenta of the objects. Because momen-tum is a vector, like force, the direction of motion is important.To find the total momentum of objects moving in the same direction,add the momenta of the objects. For two objects traveling in oppositedirections, subtract one momentum from the other. Then use theprinciple of conservation of momentum and the formula for momen-tum to predict how the objects will move after they collide.

check your reading What is meant by “conservation of momentum”? What questions do you have about the application of this principle?

of momentumconservation

Before the collision The momen-tum of the first car is greater thanthe momentum of the second car.Their combined momentum is thetotal momentum of the system.

During the collision The forceson the two cars are equal andopposite, as described by Newton’sthird law. Momentum is transferredfrom one car to the other duringthe collision.

After the collision The momentumlost by one car was gained by theother car. The total momentum ofthe system remains the same as itwas before the collision.

1 2 3

total momentum

momentum 2momentum 1

total momentum

momentum 2momentum 1forces in collision

reading tip

The plural of momentumis momenta.

372 Unit 3: Motion and Forces

Two Types of CollisionsWhen bumper cars collide, they bounce off each other. Most of theforce goes into changing the motion of the cars. The two bumper carstravel separately after the collision, just as they did before the collision.The combined momentum of both cars after the collision is the sameas the combined momentum of both cars before the collision.

When two cars collide during a crash test, momentum is also conserved during the collision. Unlike the bumper cars, however,which separate, the two cars shown in the photograph above stick and move together after the collision. Even in this case, the totalmomentum of both cars together is the same as the total momentumof both cars before the collision. Before the crash shown in the photo-graph, the yellow car had a certain momentum, and the blue car hadno momentum. After the crash, the two cars move together with acombined momentum equal to the momentum the yellow car hadbefore the collision.

check your reading Compare collisions in which objects separate with collisions inwhich objects stick together.

Momentum and Newton’s Third LawCollisions are not the only events in which momentum is conserved.In fact, momentum is conserved whenever the only forces acting onobjects are action/reaction force pairs. Conservation of momentum isreally just another way of looking at Newton’s third law.

In this crash test, momentum is conserved,but some of the energygoes into bending themetal in these two cars.

When a firefighter turns on a hose, watercomes out of the nozzle in one direction, and thehose moves back in the opposite direction. Youcan explain why by using Newton’s third law. Thewater is forced out of the hose. A reaction forcepushes the hose backward. You can also use theprinciple of conservation of momentum toexplain why the hose moves backward:

• Before the firefighter turns on the water, thehose and the water are not in motion, so thehose/water system has no momentum.

• Once the water is turned on, the water hasmomentum in the forward direction.

• For the total momentum of the hose and the water to stay the same, the hose must have an equal amount of momentum in the opposite direction. The hose moves backward.

If the hose and the water are not acted on by any other forces,momentum is conserved. Water is pushed forward, and the hose ispushed backward. However, the action and reaction force pair actingon the hose and the water are not usually the only forces acting on the hose/water system, as shown in the photograph above. There thefirefighters are holding the hose steady.

The force the firefighters apply is called an outside force because itis not being applied by the hose or the water. When there is an outsideforce on a system, momentum is not conserved. Because the firefightershold the hose, the hose does not move backward, even though thewater has a forward momentum.

check your reading Under what condition is momentum not conserved? What partof the paragraph above tells you?

KEY CONCEPTS1. How does increasing the

speed of an object change itsmomentum?

2. A car and a truck are travelingat the same speed. Which hasmore momentum? Why?

3. Give two examples showingthe conservation of momen-tum. Give one example wheremomentum is not conserved.

CRITICAL THINKING4. Predict A performing dolphin

speeds through the water andhits a rubber ball originally atrest. Describe what happens tothe velocities of the dolphinand the ball.

5. Calculate A 50 kg person isrunning at 2 m/s. What is theperson’s momentum?

CHALLENGE6. Apply A moving train car

bumps into another train carwith the same mass. After thecollision, the two cars are cou-pled and move off together.How does the final speed ofthe two train cars comparewith the initial speed of themoving train cars before thecollision?

Chapter 11: Forces 373

Firefighters must apply aforce to the water hose to prevent it from flyingbackward when the watercomes out.