Collisions and Momentum
Momentum
The concept of momentum is often used in sports. An announcer might say, "The Pittsburgh Penguins really have some momentum going into the fourth quarter!" or a newspaper headline might read, "The Pittsburgh Penguins pick up momentum!" What this means is that the team is sticking together and moving ahead as a whole rather than playing as individuals and not getting anywhere. In the engineering and physics world, momentum refers to the quality of motion that an object has, and it depends on the mass and velocity of the object:
Momentum = mass x velocity
So, if the Pittsburgh Penguins were all skating together in a close group at a fast speed, they would have a lot of momentum, physically.
Think about the difference between a ping-pong ball and a golf ball. Although they are about the same size, the golf ball is heavier. If you threw each ball the same speed, the golf ball would have greater momentum. This becomes painfully obvious with an example. Have you ever played "dodge ball" or a similar game? Would you rather play with the ping-pong ball or the golf ball? Which ball would hurt more? Yes the golf ball. The reason it would hurt more is because it would have substantially more momentum than a ping-pong ball. In this case, more momentum is due to the greater mass (weight) of the golf ball, and the momentum of the golf ball would translate into a big bruise on your leg!
Types of Collisions
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 moving 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.
An elastic collision follows 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." In addition, the total kinetic energy of the system (all the objects that collide) is conserved during an elastic collision. An elastic collision example might involve a super-bouncy ball; if you were to drop it, it would bounce all the way back up to the original height from which it was dropped. Another elastic collision example may be observed in 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 to the other ball, resulting in the hit ball rolling with the initial speed of the cue ball.
In an inelastic collision, the total momentum of the system is conserved, but the total kinetic energy of the system is not conserved. Instead, the 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.
Types of Collisions
In an inelastic collision, the total momentum of the system is conserved, but the total kinetic energy of the system is not conserved. Instead, the 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. Rubber balls, pool balls (hitting each other), and ping-pong balls may be assumed extremely elastic, but 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 dependent on the material of the object.
Collisions
Many sports incorporate collisions and momentum as part of game play. Can you think of some? Certain sports rely primarily on elastic collisions that conserve momentum, such as pool or billiards, while others use inelastic collisions to make the game more challenging. What would happen if a baseball and a bat had an elastic collision like a golf ball and club?
Another way to understand collisions is through Newton's 3rd Law, which tells us that "for every action, there is an equal and opposite reaction". When a cue ball collides with another pool ball, the cue ball exerts a force on the stationary pool ball in the direction that the cue ball is traveling, while the stationary pool ball exerts an equal and opposite force on the cue ball. This is the reason that after the cue ball collides with a stationary pool ball, it sometimes moves in a new direction, sometimes leading to a "scratch". Understanding Newton's 3rd Law, momentum and elastic and inelastic collisions provides a new understanding of our physical world that is full of motion and collisions.
Engineering Connection
Sports engineering is becoming a popular specialty field of study. Some engineers dedicate their research to understanding collisions between balls and bats; others study the effects of a golf ball colliding with the head of a golf club. Mechanical engineers consider momentum and collisions when designing vehicles. Learning how the human body and equipment interacts with the ball during impact or how the human body interacts with the inside of a car during a crash, helps engineers design better sports equipment and safer vehicles.
Bouncing Balls Activity:
Now you will have a chance to examine how different balls react when colliding with different surfaces, and see the difference between elastic and inelastic collisions. You will also learn how to calculate momentum, and understand the principle of conservation of momentum.
Before you get started. Think of the answers to the following questions:
Click on the following document to get started on the Activity for today:
Bouncing Balls Investigation Directions
Use the mass determined in step 1. In this example, use .05 kilograms for the mass. Next, determine the velocity of the object when it hits the ground. Velocity of a falling object can be described as:
where g is gravity (9.81 m/s2) and h is height (1 m).
Momentum = .05 kilograms x 4.43 meters/second = .222 kg•m/s.
Note: All the balls will have the same velocity because any object dropped from the same height will fall at the same constant rate due to gravity. So, for this activity, the velocity is: 4.43 m/s.
Review: Tell Someone What you Learned Today.
Once you finish Bouncing Balls Investigation, identify which balls had the best elastic collisions on each surface. Do you think elastic collisions are more determined by the surface or the momentum? Tell someone your thoughts.
Extension: Use what you have learned from this presentation to solve the following Challenge Question.
Calculate which case has the greater momentum.
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