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Momentum & Impulse

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Momentum & Impulse

Excerpts from

Chapters 9 and 11

- Newton’s 2nd Law of motion can be rewritten by using the definition of acceleration as the change in velocity over the change in time.

- If the change in time is multiplied out of the denominator, we are left with the following:

- The product of force and change in time is called the impulse(symbol is J).
- Impulse is a vector quantity and is measured in Newton-seconds (Ns).

- If a car hits a haystack or the same car hits a wall, momentum is decreased by same impulse – the same products of force and time.
- However, impact force is greater into the wall than it is into the haystack as the haystack extends impact time, lessening the impact force.
- Impact time is the time during which momentum is brought to zero.

- The product of the mass and the velocity is called the momentum (symbol -“rho”) of an object.
- Momentum is also a vector quantity and is measured in kgm/s.
- Note that the units for impulse and momentum appear different, but they are actually the same unit when simplified.

- Momentum can be increasedwith an increase in either mass or in velocity or both.
- Ex: a rolling bowling ball has greater momentum than a tennis ball rolling at the same speed because its mass is greater
- Ex: a racecar going forward at 120 mi/hr has greater momentum than the same size car going 90 mi/hr due to its greater velocity

- If an object is not moving (no matter how big it is), the momentum is equal to zero.

- The impulse-momentum theorem states that the impulse on an object is equal to the object’s final momentum minus the object’s initial momentum.
- Can also be written as:

- Tiger Woods hits a 0.050kg golf ball, giving it a speed of 75m/s. What is the impulse given to the ball?

- Shane hits a stationary 0.12kg hockey puck with a force that lasts for 1.0x10-2s and makes the puck shoot across the ice with a speed of 20.0m/s, scoring a goal for the team. With what force did Shane hit the puck?

- Diana, whose mass is 50.0kg, leaves a ski jump with a velocity of 21.0m/s. What is her momentum as she leaves the ski jump?

- A system is the environment and all of the objects examined in a problem.
- A closed system is a system in which no mass is gained or lost.
- An isolated system is a system in which the net external force is zero… no forces acting outside of the system have an effect inside of it.

- The law of conservation of momentum states that the sum of momentum of any closed, isolated system does not change… or that the sum of the momentum of the objects in that system is constant.

- Mathematically, we can view this as a BEFORE and AFTER situation.
- For any two objects A and B:

- If two objects bounce apart when they collide, it is called an elastic collision and can be written:
- If two objects stick together when they collide, it is called an inelastic collision and can be written:

- Tubby and his twin brother Chubby have a combined mass of 200.0kg and are zooming along in a 100.0kg amusement park bumper car at 10.0m/s. They bump Melinda’s car, which is sitting still. Melinda has a mass of 25.0kg. After the elastic collision, the twins continue ahead with a speed of 4.12m/s. How fast is Melinda’s car bumped across the floor?

Before Collision

After Collision

T&C

Mel

T&C

Mel

- If an 800.kg sports car slows to 13.0m/s to check out an accident scene and the 1200.kg pick-up truck behind him continues traveling at 25.0m/s, with what velocity will the two move if they lock bumpers after a rear-end collision?

Before Collision

After Collision

- What do we mean when we ask people to “conserve water”?
- What do you think it will mean if we say that momentum is conserved?

- Objective:
- Prove that the law of conservation of momentum is true.

- Law of Conservation of Momentum:
- The sum of the momentum of the objects prior to a collision is equal to the sum of the momentum of the objects after a collision.

- Explain how an airbag protects you by making you come to a stop differently than hitting steering wheel.
Try to use the words impulse, force, and time in your answer.

- Impulse is a force applied over an interval of time. In this question, the impulse of hitting the steering wheel and hitting the airbag are the same amount because they both cause you to stop. However, the airbag applies a smaller force to your body over a larger time, therefore keeping you safer.

- Order these objects from the most momentum to the least.
- A bullet shot from a rifle
- An elephant standing still
- A bowling ball rolling
- A fly buzzing by your ear