Notes Chapter 8 Momentum Objectives: Define momentum. (8.1) Define impulse and describe how it affects momentum. (8.2) Explain why an impulse is greater when an object bounces than when the same object comes to a sudden stop. (8.3) State the law of conservation of momentum. (8.4) Distinguish between an elastic collision and an inelastic collision. (8.5) Given an example of how the vector nature of momentum affects the law of conservation of momentum. (8.6)

8.1 Momentum Inertia in motion. A measure of how difficult it is to change the motion of an object in motion. A moving object can have a large momentum of it has a large mass, speed, or both. A vector quantity. What are the units for momentum?

Question Can you think of a case where a roller skate and a truck will have the same momentum? Answer: Skate would have to have a much greater speed, as many times as great as the truck mass is greater than the skate.

8.2 Impulse Changes Momentum For an object, momentum changes when velocity changes, an acceleration occurs. What causes acceleration?....Force The change in momentum depends on the force that acts and the length of time it acts. The greater the impulse exerted on an object, the greater will be the change in momentum.

Increasing momentum Maximum change in momentum can be achieved if maximum force is applied for as long as it can be applied. In baseball and golf, swing really hard and follow through. Average force

Decreasing momentum If you increase the contact time—time which your momentum is decreased—the force is decreased. The product of force and time remains the same. Double the time, force is decreased to half. Opposite is true if contact time is decreased. Force increases.

Questions When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard floor? Explain. The boxer in Figure 8.6 is able to make the impact time five times longer by “riding” with the punch. How many times will the force of impact be reduced? Answers: Impulse will be the same in both cases as would the change in the momentum of the dish. However, the carpet would increase the contact time, thereby decreasing the force on the dish and saving it from breaking. It will be reduced by 5 times (1/5F).

8.3 Bouncing Impulses are greater when a bounce occurs. Book example of flower pot on head. The impulse required to stop and then to “throw it back again” is greater than the impulse required to simply bring the object to a stop.

8.4 Conservation of Momentum Momentum of system cannot change unless acted on by an external force. Law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged. If all forces acting on the system are internal, the net momentum of the system remains the same. Recall that momentum is a vector quantity—has both magnitude and direction.

In the case of the cannon firing a cannonball, the action and reaction force are internal. The forward momentum (mv) of the cannon ball is the same as the backwards momentum of the cannon (-mv). Cannon and cannonball both start at rest, i.e. zero momentum. Though both have a momentum after firing, the net momentum is ZERO, i.e. they cancel out.

Questions Newton’s second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs? Newton’s third second law states that the force a cannon exerts on a cannonball is equal and opposite to the force the cannonball exerts on the cannon. Does it follow that the impulse the cannon exerts on the cannonball is equal and opposite to the impulse the cannonball exerts on the cannon? Answers: Yes, because no acceleration means that no change occurs in velocity or in momentum (mass x velocity). Another line of reasoning is simply to imply that no net force means there is no net impulse and thus no change on momentum. Yes, because the cannon acts on the cannonball and the cannonball reacts on the cannon during the same time interval. Since time is equal and the forces are equal and opposite, the impulses, Ft, are also equal and opposite. Impulse is a vector quantity and can be canceled.

8.5 Collisions Whenever objects collide in the absence of external forces, the net momentum of the objects before the collision equals the net momentum of both objects after the collision.

Elastic collision – collision in which colliding objects rebound w/o lasting deformation or heat generation.

Car Rear Ends Truck Truck Rear Ends Car Car and Truck in Head-on Collision

Inelastic collision – a collision in which colliding objects become tangled or coupled together and/or generate heat during a collision.

Car Rear Ends Truck Truck Rear Ends Car Car and Truck in Head-on Collision

Final note on collisions: Perfectly elastic collision are NOT common in the everyday world. Some heat is generated This has implications when we cover energy. Energy is conserved in a perfectly elastic collision Not so in inelastic collisions because heat is lost from the system. (More on this later.) At the atomic level, charged particles (ions) exhibit perfectly elastic collisions.

8.6 Momentum Vectors The vector sum of the momenta is the same before and after a collision.

Example Problem 1 A car of mass 1100 kg moves at 24 m/s. What braking force is needed to bring the car to a halt in 20 s?

Example Problem 2 An 80. kg astronaut carrying a 20. kg tool kit is initially drifting toward a stationary rocket ship at a speed of 2.0 m/s. If she throws the toolkit toward the ship with a speed of 6.0 m/s, what is her final velocity (speed and direction)?

Example Problem 3

Example Problem 4 Data just before a perfectly elastic collision if provided in the illustration above. If the velocity of the truck after the collusion is 10. m/s, what is the velocity of the car after the collision?