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Forces Transfer Momentum KEY CONCEPT Forces transfer momentum. BEFORE, you learned NOW, you will learn •A force is a push or a pull • What momentum is • Newton’s laws help to describe • How to calculate momentum and predict motion • How momentum is affected by collisions VOCABULARY EXPLORE Collisions momentum p. 368 What happens when objects collide? collision p. 370 conservation of PROCEDURE MATERIALS momentum p. 371 2 balls of 1 Roll the two balls toward each other on a different masses flat surface. Try to roll them at the same speed. Observe what happens. Experiment by changing the speeds of the two balls. 2 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? 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. VOCABULARY Momentum (moh-MEHN-tuhm) is a measure of mass in motion; Make a magnet word diagram for momentum. 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. 368 Unit 3: Motion and Forces Momentum is similar to inertia. Like inertia, the momentum of an reminder object depends on its mass. Unlike inertia, however, momentum takes Inertia is the resistance into account how fast the object is moving. A wrecking ball that is of an object to changes in its motion. 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 formula, p stands for momentum, m for mass, and v for RESOURCE CENTER velocity. In standard units, the mass of an object is given in kilograms CLASSZONE.COM (kg), and velocity is given in meters per second (m/s). Therefore, the Explore momentum. 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? Calculating Momentum Sample Problem 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 p m/s Check that your units agree: Unit is kg p m/s. Unit of momentum is kg p m/s. Units agree. Answer: p = 3 kg p m/s Practice the Math 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? Chapter 11: Forces 369 Momentum What happens when objects collide? SKILL FOCUS Observing PROCEDURE 1 Set up two parallel rulers separated by one centimeter. Place a line of five MATERIALS marbles, each touching the next, in the groove between the rulers. •2 rulers •8 marbles 2 Roll a marble down the groove so that it collides with the line of marbles, and observe the results. TIME 20 minutes 3 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? Momentum can be transferred from one object to another. If you have ever ridden in a bumper car, you have experienced colli- sions. A collision 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? 370 Unit 3: Motion and Forces 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 reading tip objects that affect one another. As the two objects collide, the velocity A light blue-green arrow and the momentum of each object change. However, as no other shows the momentum of an individual object. forces are acting on the objects, the total momentum of both objects is unchanged by the collision. This is due to the conservation of A dark blue-green arrow momentum. The principle ofconservation of momentum states that shows the total momentum. the total momentum of a system of objects does not change, as long as no outside forces are acting on that system. total momentum total momentum momentum 1 momentum 2 forces in collision momentum 1 momentum 2 1 2 3 Before the collision The momen- During the collision The forces After the collision The momentum tum of the first car is greater than on the two cars are equal and lost by one car was gained by the the momentum of the second car. opposite, as described by Newton’s other car. The total momentum of Their combined momentum is the third law. Momentum is transferred the system remains the same as it total momentum of the system. from one car to the other during was before the collision. the collision. 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 reading tip collision by combining the momenta of the objects. Because momen- The plural of momentum tum is a vector, like force, the direction of motion is important. is momenta. 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 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? Chapter 11: Forces 371 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. In this crash test, momentum is conserved, but some of the energy goes into bending the metal in these two cars. When two cars collide during a crash test, momentum is also conserved during the collision.
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