Chapter 6 Momentum and Collisions

6.1 Momentum and Impulse Linear Momentum After a bowling ball strikes the pins, its speed and direction change. So does the speed and direction of the pins. Newton’s laws can be used to calculate the motion of the ball after it hits the pins. The force and duration of a collision between objects affects the motion of both.

Momentum is mass times velocity The momentum of an object is simply its mass times its velocity. Momentum is represented by the symbol “p”. Momentum is a vector quality. It is expressed as kilograms times meters per second (kg . m/s)

video The faster you move, the more momentum you will have. This is why it is harder to stop when you are moving faster than when going slower. An object that is heavier but traveling at the same speed as another, will have more momentum. Light objects traveling at great speeds can have a lot of momentum like hailstones! video

Practice A Momentum 5.6 x 104 kg . m/s to the east or 56,000 A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck? p = mv Answer 5.6 x 104 kg . m/s to the east or 56,000

A change in momentum takes force and time It takes more force to stop a ball that is moving quickly than one that is moving slowly. Think about catching a fast ball versus one that is moving slowly. Think about how much force is needed to stop a train versus a car. video

Practice B Force and Impulse A 1400 kg car moving eastward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision.  Answer     7.0 x 104 N to the east or 70,000 N

Stopping times and distance depend on the impulse-momentum theorem Highway safety engineers use the impulse-momentum theorem to determine stopping distances and safe following distances for vehicles. A truck hauling bricks can have twice the mass of an empty truck. Therefore, it will have twice the momentum. Having the same type of brakes, the heavier truck will take twice the distance to stop. video

Practice C Stopping Distance A 2240 kg car traveling west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is 8410 N to the east? How far does the car travel during the deceleration? Answer Answer       4.00 s -50.0 m

Force is reduced when the time interval of an impact is increased The impulse-momentum theorem is used to design safety equipment. This equipment is able to reduce the force exerted on the human body during collisions. The falling girl in this photo has the same momentum whether she hits the ground or the mat. The mat however changes her momentum over a longer period of time.

When an egg falls on a hard surface, it comes to rest in a short period of time. If it lands on a pillow, its momentum is changed over a longer period of time. By applying a small force to the egg over a longer period of time, the change in momentum is still the same, the results very different.

Questions 1. The momentum of an object is simply its mass times its _________. 2. An object that is heavier but traveling at the same speed as another, will have more ________ 3. It takes more ______ to stop a ball that is moving quickly than one that is moving slowly. 4. By applying a small force to a falling egg over a longer period of ______, the change in momentum is still the same, the results very different. velocity momentum force time

6.2 Conservation of Momentum Momentum is Conserved Now we will consider the momentum of two or more objects interacting. Below ball A is moving towards a stationary ball, B. Once they collide, ball A becomes stationary and ball B continues at the velocity A was at. This collision caused all of ball A’s momentum to go to B. Lets see how this looks with numbers…

The total momentum of each ball remains constant. This is known as the law of conservation of momentum. The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

Momentum is conserved in collisions Total momentum is conserved in a system. Any additional objects added will interact the same, conserving the momentum. At this point, however, frictional forces have been disregarded.

Momentum is conserved for objects pushing away from each other Momentum is also conserved when two objects at rest push away from each other. They move in opposite directions with equal momentum. video

Practice D Conservation of Momentum A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto a dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right what is the final velocity of the boat? Because v1 and v2 are 0 m/s, we can cancel out…  Answer       4.2 m/s to the left

Newton’s third law leads to conservation of momentum Consider two bumper cars with velocities of v1i and v2i. After they collide their velocities become v1f and v2f. The impulse-momentum theorem FΔt = Δp describes their change in momentum. Newton’s third law tells us the force acting on these cars is equal and opposite.

How can this be if both are conserved? To simplify, if the momentum of one object increases then the momentum of the other decreases. How can this be if both are conserved? Answer; this only occurs because the direction changes, the magnitude stays the same it is only equal but opposite.  

Forces in real collisions are not constant during the collision In real collisions the forces may vary in time in a complicated way. During the collision, the forces are equal and opposite in magnitude. In solving impulse problems, we use average force over time.

Questions 1. T / F Momentum is not conserved in collisions. 2 Questions 1. T / F Momentum is not conserved in collisions. 2. T / F Momentum is conserved for objects pushing away from each other. 3. If the momentum of one object increases then the momentum of the other __________. 4. T / F Forces in real collisions are not constant during the collision. false true decreases true

6.3 Elastic and Inelastic Collisions Total momentum remains constant in any type of collision. However, the total kinetic energy is generally not conserved. This is because some kinetic energy is converted to internal energy when the objects deform.

Perfect inelastic collisions can be analyzed in terms of momentum video Perfect inelastic collisions can be analyzed in terms of momentum When two football players, collide and move as one mass, this is known as a perfectly inelastic collision. Perfectly inelastic collisions are easy to analyze in terms of momentum because they essentially become one object afterwards. Their final mass is equal to their combined mass.

Practice E Perfect Inelastic Collisions A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s before the collision, what is the velocity of the two after? m1 = 1850 m2 = 975 v1 = 0 m/s v2 = 22.0 m/s  answer     7.59 m/s

Kinetic energy is not conserved in inelastic collisions Total kinetic energy is not conserved with an inelastic collision. Some of the energy is lost to sound and to internal energy as the objects deform. Elastic collisions allow the objects to return to their original shape. With inelastic they stay deformed.

Practice F Kinetic Energy in Perfectly Inelastic Collisions Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The second has a mass of 0.250 kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision? 

Unknown: ∆KE = KEf – KEi = ? Since our collision is perfectly inelastic, they will stay and travel together as one object. We must solve for vf first. m1 = 0.500 kg v1 = to the right = 4.00 m/s m2 = 0.250 kg v2 = to the left = - 3.00 m/s  Answer KEi = ½(0.500 kg)(4.00 m/s)2 + ½(0.250 kg)(-3.00)2 = 5.12 J KEf = ½(0.500 kg + 0.250 kg)(1.67 m/s)2 = 1.05 J KEf – KEi = 1.05 J – 5.12 J = ( - ) indicates energy lost     1.67 m/s to the right -4.07 J

Elastic Collisions Video In an elastic collision, two objects collide and then return to their original shape. No kinetic energy is lost in this process. In the other collisions we have learned about, momentum was the only thing that was conserved. Elastic collisions are the only type that both are conserved. Video

Most collisions are neither elastic nor perfectly inelastic In real life there really is no such thing as perfectly elastic or inelastic. In most collisions, some of the kinetic energy is converted to into sound, such as two billiard balls clicking as they hit. So any collision that produces sound can not be perfectly elastic.

Kinetic energy is conserved in elastic collisions The two soccer balls below are colliding but at different velocities. During the collision, the impulse will be equal but the momentum of each ball will change. After the collision the slower ball will reverse direction and then travel at the velocity of the faster ball.

In the case of a golf ball being hit, the ball accelerates from a velocity of zero and the club is slowed due to the impulse during contact. The momentum is conserved. Since this is an elastic collision, the kinetic energy is conserved as well.

Summary This table summarizes out three type of collisions

Practice G Elastic Collisions Two marbles are colliding as shown above. What will the velocity and direction of the 0.030 kg marble be after the collision? v1f = -0.315 m/s  Answer       0.090 m/s to the right

Questions 1. Total __________ remains constant in any type of collision. 2. T / F Total kinetic energy is conserved with an inelastic collision. 3. Elastic collisions allow the objects to return to their original shape. With inelastic they stay _____ 4. Of the three types of collisions, _______ is the only one where momentum and kinetic energy are conserved. momentum false deformed elastic

Elastic or Inelastic?

Elastic or Inelastic?

Elastic or Inelastic?

Elastic or Inelastic?

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