Unit 5 Momentum Impulse Impulse Changes Momentum Bouncing Conservation of Momentum Collisions

Momentum = mass x velocity Momentum: Inertia in motion - or - mass in motion . Carries the notion of both mass (inertia) and velocity (motion) Momentum = mass x velocity (momentum is in the same direction as the velocity) Momentum = mv Or Momentum = mass x speed (if you don’t care about the direction) Momentum is a vector!! A 20 kg object moving at 10 m/s has a momentum of Something massive moving fast carries a lot of momentum Something REALLY massive moving not so fast carries a lot of momentum. Something with little mass doesn’t carry much momentum unless it goes fast. Video: Definition of Momentum

Practice Problem:  Calculate the momentum of a 11.35kg wagon rolling down a hill at 12m/s. Calculate the velocity of a baseball with a momentum of 20kgm/s and a mass of 5kg.

Impulse Given that … Momentum = mv If velocity changes, momentum changes, and acceleration (either + or –) occurs But we know: for acceleration to occur, a force has to be applied. If a given force is applied over a longer time, more acceleration occurs. IMPULSE is a measure of how much force is applied for how much time, and it’s equal to the change in momentum. Impulse = Force x time Or Impulse = F x t A force applied over time will change the momentum of an object:

Impulse Problems What is the change in velocity of a .35 Kg air track cart if you exert a force of 1.2 N on it for 3 seconds? A rocket engine exerts a force of 500 N on a space probe (in outer space!) for 5 seconds. The probe speeds up from rest to a speed of 21 m/s. What is its mass?

Impulse examples Follow through increases the time of collision and the impulse                       I small large

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Impulse changes Momentum A greater impulse exerted on an object A greater change in momentum OR Impulse = Change in momentum OR Greek symbol “Delta” Means “the change in…” Impulse = Δ(mv) Impulse can be exerted on an object to either INCREASE or DECREASE its momentum.

Case 1: Increasing Momentum Examples: Hitting a golf ball: Apply the greatest force possible for the longest time possible. Accelerates the ball from 0 to high speed in a very short time. The impulse of the bat decelerates the ball and accelerates it in the opposite direction very quickly. Baseball and bat: Video: Changing Momentum – Follow Through

Case 2: Decreasing Momentum It takes an impulse to change momentum, and Remember … Impulse = F x t If you want to stop something’s motion, you can apply a LOT of force over a short time, Or, you can apply a little force over a longer time. Remember, things BREAK if you apply a lot of force to them.

Case 3: Decreasing Momentum over a Short Time If the boxer moves away from the punch, he extends the time and decreases the force while stopping the punch. If he moves toward the punch, he decreases the time and increases the force The airbag extends the time over which the impulse is exerted and decreases the force. Hitting the bricks with a sharp karate blow very quickly maximizes the force exerted on the bricks and helps to break them.

Bouncing Think about a bouncing ball: Total Impulse = 2mv After it leaves the ground: Speed = v Momentum = mv Before it hits the ground: Speed = v Momentum = mv At the moment it hits the ground: Speed = 0 Momentum = 0 Impulse needed to accelerate the ball upwoard = mv Impulse needed to stop the ball = mv Total Impulse = 2mv Important point: It only takes an impulse of mv to stop the ball. It takes twice that much (2mv) to make it bounce) (Maybe why basketballs don’t bounce so well on gravel) Video: Definition of Momentum

Other Bouncing Examples From book: Pendulum and block Pelton Wheel Flower Pot on Head Also: Pool Ball off a cushion (linked to applet) (Ignore the rotational motion for now)

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Conservation of Momentum If no net external force (same as saying “no net impulse”) acts on a system, the system’s momentum cannot change. Momentum = 0 before the shot And after the shot Cannon’s momentum Shell’s momentum (equal and opposite) Cart and bricks applet After the bricks fall on the cart, the momentum of the cart-brick system will still be the same.

Collisions Net momentum before collision = net momentum after collision 2 billiard balls collide head on momentum is zero before and after Elastic collisions - No kinetic energy lost to heat, etc 1 billiard balls collide with a stationary one momentum is the same before and after 2 billiard balls moving in the same direction collide momentum is the same before and after Upon collision, the cars stick together The total mass moves slower, but the momentum of the 2 cars together is the same as the momentum of the system before the collision. Inelastic collisions - Some kinetic energy lost to heat, etc

More Complicated Collisions Colliding at an angle: The momentum vectors of car A and B add together to give the resultant momentum of the system. Momentum of car A Resultant Momentum The ”exploding object”: Momentum of car A The firecracker is initially falling After the explosion, the momenta of the pieces add. The total momentum of the “system” of pieces is the same as the original momentum of the firecracker.