Ch.9 Momentum and Its Conservation
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Transcript of Ch.9 Momentum and Its Conservation
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Ch.9 Momentum and Its Conservation
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9.1 Impulse and Momentum• Momentum (p): the product of the mass (m) of
an object and its velocity (v)p = mv
An object has a greater momentum if:1. it has a greater mass2. it has a greater velocity
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Example Problem
• A 5 kg hockey puck has a momentum of 10 kg* m/s. What is the speed of the hockey puck?
• A ball has a momentum of 50 kg*m/s and is thrown at a speed of 10 m/s, what is the ball’s mass?
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Impulse• Impulse: Force times change in time – Impulse = FΔt – Is the result of force acting on an object over time• Greater force = Greater impulse• Greater time = Greater impulse
Which would have a greater impulse, one person pushing a car, or 3 people pushing a car?
Which would have a greater impulse, pushing the car for 2 seconds, or pushing the car for 30 seconds?
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Impulse-Momentum Relationship• The greater the impulse, the greater the change in
momentum.
Impulse = change in momentum FΔt = mΔv
Impulse and the change in momentum are ALWAYS linked!
Furthermore, Δv = v2 – v1 so the impulse-momentum theorem says we can write the equation as follows'
FΔt = p2 – p1
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Would you rather…• Drive your car into a brick wall, or into a pile of hay?
WHY?
– Both would have the same change in momentum to bring your car to a stop…BUT:• The brick wall has a greater force over a smaller period of time• The hay has a smaller force over a greater period of time
Change in momentum = Ft Change in momentum = Ft
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Impulse-Momentum Relationship in Sports
Dancers like to have a wooden floor with some “give,” which increases the time of impact whenever a dancer lands. This reduces the chance of injury.
Boxers “ride” or “roll” with punches to reduce the force during impact by moving with the punch.
A karate expert can break a stack of bricks by reducing the time that the hand is in contact with the bricks, which increases the force.
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Example Problem
• A 5.0-kg ball has a velocity of 10 m/s downward just before it strikes the ground and bounces up with a velocity of 10 m/s upward. What is the change in momentum of the ball?
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Example Problem pg. 203
• A 2200-kg sport utility vehicle traveling at 94 km/h (26 m/s) can be stopped in 21 s by gently applying the brakes, in 5.5 s in a panic stop, or in 0.22 s if it hits a concrete wall. What average force is exerted on the vehicle in each of these stops?
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Sec. 9.2 Conservation of Momentum• Law of Conservation of Momentum:– In the absence of an external force, the momentum of
a system remains unchanged.
The momentum gained by the cannonball, is equal and opposite to the momentum gained by the cannon. So the system has not gained or lost momentum.
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Conservation of MomentumCollisions
• Elastic Collision: A collision in which colliding objects rebound without lasting deformation or generation of heat– Ex: molecules of gas, billiard ball
• Inelastic Collision: A collision in which colliding objects become distorted, generate heat, and possibly stick together.– Ex: One car hitting another
Net Momentum before collision = Net Momentum after collision
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Elastic or Inelastic?
Inelastic
Elastic or Inelastic?
ElasticIf the problem does not state object stick together or it’s an inelastic collision always assume an ELASTIC collision occurred.
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Guide to solving ANY collision problem
• DRAW A PICTURE• USE The Law of Conservation of Momentum
Total Momentum Before Collision = Total Momentum After Collision
pbefore = pafter
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Example Problem pg. 209
• A 2275-kg car going 28 m/s rear-ends an 875-kg compact car going 16 m/s on ice in the same direction. The two cars stick together. How fast does the wreckage move immediately after the collision?
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Example Problem
• A 10.0-kg cart moving to the right with a speed of 2.0 m/s has a head-on collision with a 15.0-kg cart that is initially moving to the left with a speed of 5 m/s. After the collision, the 10.0-kg cart is moving to the left with a speed of 2.0 m/s, what is the final velocity of the 15.0-kg cart?
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Example Problem pg. 212
• An astronaut at rest in space fires a thruster pistol that expels 35 g of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing the pistol?
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2- Dimensional Collisions
The Law of Conservation of Momentum
still applies
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Example Problem pg. 215
• A 2.00-kg ball, A, is moving at a speed of 5.00 m/s. It collides with a stationary ball, B, of the same mass. After the collision, A moves off in a direction of 30.0 degrees to the left of its original direction. Ball B moves off in a direction 90.0 degrees to right of ball A’s final direction. How fast are they moving after the collision?
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Angular Momentum
• The product of a rotating object’s moment of inertia and angular speed about the same axis.
L= mvr (for a point mass)• Conservation of Angular Momentum = the net
external torque acting on an object or objects is zero, the angular moment of the object does not change
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Angular Momentum Demo
• http://youtu.be/WnS2d24HCK0