VOCABULARY
momentum p. 64 collision p. 66 conservation of
momentum p. 67
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 transfer momentum.
MATERIALS
2 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 at the same speed that you threw the tennis ball? The wall would most likely break apart. Why would a wrecking ball have a different effect on 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 the tennis ball because the wrecking ball has more mass. However, you could increase the momentum of the tennis ball by throwing it faster.
Momentum
VOCABULARYMake 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 by changing 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 the balls 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?
2 1
Momentum is similar to inertia. Like inertia, the momentum of an object depends on its mass. Unlike inertia, however, momentum takes into account how fast the object is moving. A wrecking ball that is moving very slowly, for example, has less momentum than a fast- moving wrecking ball. With less momentum, the slower-moving wrecking 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 · velocity p = mv
In this equation, p stands for momentum, m for mass, and v for velocity. In standard units, the mass of an object is given in kilograms (kg), and velocity is given in meters per second (m/s). Therefore, the unit 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—it has 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 speed instead of velocity in the formula as long as you do not need to know the direction of motion. As you will read later, it is important to know the direction of the momentum when you are working with more than one object.
check your reading
How do an object’s mass and velocity affect its momentum?
RESOURCE CENTER
CLASSZONE.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 kgp 2 m/s Calculate and simplify: p = 3 kgp m/s
Check that your units agree: Unit is kgp m/s.
Unit of momentum is kgp m/s. Units agree.
Answer: p = 3 kgp m/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?
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 contact exchange energy and momentum. As another car bumps into the back of yours, the force pushes your car forward. Some of the momentum of the car behind you is transferred to your car. At the same time, the car behind you slows because of the reaction force from your car. You gain momentum from the collision, and the other car loses momen- tum. The action and reaction forces in collisions are one way in which objects 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 ball toward each other so that they collide. Not only will the speed of the tennis ball change, but the direction of its motion will change as it bounces back. The bowling ball, however, will simply slow down. Even though the forces acting on the two balls are the same, the tennis ball will 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 five marbles, 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 of marbles. 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?
3 2 1
Momentum Momentum
SKILL FOCUS
Observing
MATERIALS
• 2 rulers
• 8 marbles
TIME
20 minutes
reading tip
A light blue-green arrow shows the momentum of an individual object.
A dark blue-green arrow shows the total momentum.
Momentum is conserved.
During a collision between two objects, each object exerts a force on the other. The colliding objects make up a system—a collection of objects that affect one another. As the two objects collide, the velocity and the momentum of each object change. However, as no other forces are acting on the objects, the total momentum of both objects is unchanged by the collision. This is due to the conservation of
momentum. The principle of states that
the total momentum of a system of objects does not change, as long as no outside forces are acting on that system.
How much an object’s momentum changes when a force is applied depends on the size of the force and how long that force is applied. Remember Newton’s third law—during a collision, two objects are acted upon by equal and opposite forces for the same length of time. This means that the objects receive equal and opposite changes in momentum, and the total momentum does not change.
You can find the total momentum of a system of objects before a collision 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 opposite directions, subtract one momentum from the other. Then use the principle of conservation of momentum and the equation for momentum 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 momentum conservation
Before the collisionThe momen- tum of the first car is greater than the momentum of the second car.
Their combined momentum is the total momentum of the system.
During the collisionThe forces on the two cars are equal and opposite, as described by Newton’s third law. Momentum is transferred from one car to the other during the collision.
After the collisionThe momentum lost by one car was gained by the other car. The total momentum of the system remains the same as it was before the collision.
1 2 3
total momentum
momentum 2 momentum 1
total momentum
momentum 2 momentum 1
forces in collision
reading tip
The plural of momentum is momenta.
Two Types of Collisions
When bumper cars collide, they bounce off each other. Most of the force goes into changing the motion of the cars. The two bumper cars travel separately after the collision, just as they did before the collision.
The combined momentum of both cars after the collision is the same as 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 total momentum of both cars together is the same as the total momentum of both cars before the collision. Before the crash shown in the photo- graph, the yellow car had a certain momentum, and the blue car had no momentum. After the crash, the two cars move together with a combined momentum equal to the momentum the yellow car had before the collision.
check your reading
Compare collisions in which objects separate with collisions in
which objects stick together.
Momentum and Newton’s Third Law
Collisions are not the only events in which momentum is conserved.
In fact, momentum is conserved whenever the only forces acting on objects are action/reaction force pairs. Conservation of momentum is really just another way of looking at Newton’s third law.
In this crash test, momentum is conserved, but some of the energy goes into bending the metal in these two cars.
When a firefighter turns on a hose, water comes out of the nozzle in one direction, and the hose moves back in the opposite direction. You can explain why by using Newton’s third law. The water is forced out of the hose. A reaction force pushes the hose backward. You can also use the principle of conservation of momentum to explain why the hose moves backward:
• Before the firefighter turns on the water, the hose and the water are not in motion, so the hose/water system has no momentum.
• Once the water is turned on, the water has momentum 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 is pushed backward. However, the action and reaction force pair acting on the hose and the water are not usually the only forces acting on the hose/water system, as shown in the photograph above. There the firefighters are holding the hose steady.
The force the firefighters apply is called an outside force because it is not being applied by the hose or the water. When there is an outside force on a system, momentum is not conserved. Because the firefighters hold the hose, the hose does not move backward, even though the water has a forward momentum.
check your reading
Under what condition is momentum not conserved? What part
of the paragraph above tells you?
KEY CONCEPTS
1. How does increasing the speed of an object change its momentum?
2. A car and a truck are traveling at the same speed. Which has more momentum? Why?
3. Give two examples showing the conservation of momen- tum. Give one example where momentum is not conserved.
CRITICAL THINKING
4. Predict A performing dolphin speeds through the water and hits a rubber ball originally at rest. Describe what happens to the velocities of the dolphin and the ball.
5. Calculate A 50 kg person is running at 2 m/s. What is the person’s momentum?
CHALLENGE
6. Apply A moving train car bumps into another train car with the same mass. After the collision, the two cars are cou- pled and move off together.
How does the final speed of the two train cars compare with the initial speed of the moving train cars before the collision?
Firefighters must apply a force to the water hose to prevent it from flying backward when the water comes out.
