How does bouncing change momentum

How is this related to the maximum height, the velocity of the ball, and the time? The basic connections are:. We claim that if each bounce rises a fraction of the previous height e. Consider the energy. It can be expressed mathematically as follows:. An example of potential energy is a book resting on the edge of a table.

If you were to nudge it off the edge of the table the book would fall to the floor and make a loud noise. This is an expression of kinetic energy. Kinetic energy is the energy an object has because of its motion ; any object that is moving has kinetic energy.

The falling book in this example is an illustration of kinetic energy. The kinetic energy depends on both mass and velocity and can be expressed mathematically as follows:. The amount of momentum an object has depends both on its mass and how fast it is going.

For example, a heavier object going the same speed as a lighter object would have greater momentum. Sometimes, when objects collide into each other, momentum can be transferred from one object to another. There are two types of collisions that relate to momentum: elastic and inelastic. In a closed system, which means that there are no external forces acting on the objects that collide, both types of collisions follow the Law of Conservation of Momentum, which states "the total amount of momentum before a collision is equal to the total amount of momentum after a collision.

Watching a billiards game is an ideal place to observe ball collisions. In an elastic collision , not only is momentum is conserved, but also kinetic energy.

The total kinetic energy of the system which includes the objects that collide is the same before and after the collision. An example of an elastic collision would be a super-bouncy ball. If you were to drop it, it would bounce all the way back up to the original height at which it was dropped.

Another elastic collision example can be seen while playing a game of pool. Watch a moving cue ball hit a resting pool ball. At impact, the cue ball stops, but transfers all of its momentum and kinetic energy to the other ball, resulting in the hit ball rolling with the initial speed of the cue ball. In an inelastic collision , momentum is conserved, but the total kinetic energy of the system is not conserved.

When the collision occurs, some kinetic energy is transferred to another kind of energy such as heat or internal energy. A dropped ball of clay demonstrates an extremely inelastic collision. It does not bounce at all and loses its kinetic energy. Instead, all the energy goes into deforming the ball into a flat blob. In the real world, there are no purely elastic or inelastic collisions. Even though rubber balls, pool balls when hitting each other , and ping-pong balls may be assumed extremely elastic, there is still some bit of inelasticity in their collisions.

If there were not, rubber balls would bounce forever. The degree to which something is elastic or inelastic is usually found experimentally. The following demonstration shows momentum in action for an elastic collision. This demonstration is difficult to get right the first time, so practice a few times before presenting it to the class.

First, bounce the ping-pong ball on the floor by dropping it from shoulder height. This works best on a tile floor. If your classroom is carpeted, bounce the balls onto a cinder block or a large brick placed on the carpet. Have a student volunteer mark on the board how high it bounced. Next, drop the golf ball from the same height and mark how high it bounced. Then, hold the golf ball and the ping-pong ball together, with the ping-pong ball directly on top of the golf ball.

Drop them both and watch as the ping-pong ball bounces as high as 10 feet. For a conservation of momentum demonstration, a ping-pong ball is held on top of a golf ball and they are dropped together. The trick to what happens is momentum from the golf ball transfers to the ping-pong ball.

When the golf ball strikes the floor, it bounces up and collides with the ping-pong ball. This action transfers the greater momentum of the golf ball to the ping-pong ball, which responds by rising faster and higher.

And, since the golf ball transfers much of its momentum to the ping-pong ball, the golf ball hardly bounces up at all. This demonstration illustrates conservation of momentum , which states that momentum may be transferred from one object to another, but the total momentum must stay the same.

Another way to look to understand collisions is through Newton's 3rd Law, which tells us that "for every action, there is an equal and opposite reaction". When the golf ball hits the floor, the force exerted on the floor by the golf ball is equal and opposite to the force exerted on the golf ball by the floor.

This causes the golf ball to bounce and move upwards. When the golf ball collides with the ping-pong ball, the force exerted on the ping-pong ball by the golf ball is equal and opposite to the force exerted on the golf ball by the ping-pong ball.

As we know, the golf ball due to its larger weight has more momentum than the ping-pong ball, so it transfers momentum to the ping-pong ball, and so the ping-pong ball goes higher in this scenario than if it was dropped alone no collision.

Remember, based on the Law of Conservation of Momentum, after the collision between the golf ball and the ping-pong ball, the total momentum of the system is conserved. This means that if you added the momentum of the two balls before the collision and added the momentum of the two balls after the collision, the total would be the same.

Engineers consider momentum when designing vehicles for safety. In a head-on collision, the front end of a car is designed to crumple, making the collision inelastic.

It takes energy to crumple the front of the car and this is what absorbs some of the impact. This makes the crash less severe for anyone that is in the car. Instead of absorbing the full force of the crash, the passengers are cushioned by the inelastic collision. Note: This "cushion" is not as comfortable as a pillow, but it will save lives during accidents. Engineers also consider momentum when designing brakes for vehicles.

The acceleration is greatest in case B. Acceleration depends on velocity change and the velocity change is greatest in case B as stated above. The momentum change is greatest in case B. Momentum change depends on velocity change and the velocity change is greatest in case B as stated above. The impulse is greatest in case B. Impulse equals momentum change and the momentum change is greatest in case B as stated above.

The velocity change is greatest in case A. The acceleration is greatest in case A. Acceleration depends on velocity change and the velocity change is greatest in case A as stated above. The momentum change is greatest in case A. Momentum change depends on velocity change and the velocity change is greatest in case A as stated above. The impulse is greatest in case A. Impulse equals momentum change and the momentum change is greatest in case A as stated above.

In each case the initial velocity is the same. In case B, the object rebounds in the opposite direction with a greater speed than in case A. Observe that each of the collisions above involve the rebound of a ball off a wall. Observe that the greater the rebound effect , the greater the acceleration, momentum change, and impulse.

A rebound is a special type of collision involving a direction change in addition to a speed change. The result of the direction change is a large velocity change. On occasions in a rebound collision, an object will maintain the same or nearly the same speed as it had before the collision. Collisions in which objects rebound with the same speed and thus, the same momentum and kinetic energy as they had prior to the collision are known as elastic collisions. In general, elastic collisions are characterized by a large velocity change, a large momentum change, a large impulse, and a large force.

Use the impulse-momentum change principle to fill in the blanks in the following rows of the table. As you do, keep these three major truths in mind:. Force N. Time s. Mass kg. See Answer N. See Answer 0. See Answer 25 kg. There are a few observations that can be made in the above table that relate to the computational nature of the impulse-momentum change theorem. First, observe that the answers in the table above reveal that the third and fourth columns are always equal; that is, the impulse is always equal to the momentum change.

Observe also that if any two of the first three columns are known, then the remaining column can be computed. Knowing two of these three quantities allows us to compute the third quantity. And finally, observe that knowing any two of the last three columns allows us to compute the remaining column.

There are also a few observations that can be made that relate to the qualitative nature of the impulse-momentum change theorem. An examination of rows 1 and 2 show that force and time are inversely proportional; for the same mass and velocity change, a tenfold increase in the time of impact corresponds to a tenfold decrease in the force of impact. An examination of rows 1 and 3 show that mass and force are directly proportional; for the same time and velocity change, a fivefold increase in the mass corresponds to a fivefold increase in the force required to stop that mass.

Finally, an examination of rows 3 and 4 illustrate that mass and velocity change are inversely proportional; for the same force and time, a twofold decrease in the mass corresponds to a twofold increase in the velocity change. Express your understanding of the impulse-momentum change theorem by answering the following questions. Click the button to view the answers. Which cart 1 or 2 has the greatest acceleration? See Answer Cart 2 has the greatest acceleration.

Recall that acceleration depends on force and mass. They each have the same mass, yet cart 2 has the greater force. See Answer The impulse is the same for each cart. See Answer The momentum change is the same for each cart.

Momentum change equals the impulse; if each cart has the same impulse, then it would follow that they have the same momentum change. In a physics demonstration, two identical balloons A and B are propelled across the room on horizontal guide wires. The motion diagrams depicting the relative position of the balloons at time intervals of 0. See Answer Balloon B has the greatest acceleration.

See Answer Balloon B has the greatest final velocity.