Chapter 7 – Momentum Inertia in motion!!! An object in motion will stay in motion until a force acts to stop it. Momentum = mass x velocity (kg * m/s) p = mv Does an object at rest have momentum???

If a car and truck are moving at the same speed, which one has more momentum? When would a car have a greater momentum than a truck?

Force Changes Momentum For momentum of an object to change, either the mass or velocity or both changes. force = velocity = momentum When would the mass change?

Impulse Changes Momentum How long a force acts is also important. Force and Time are important in changing momentum impulse = Force x time interval impulse = F x t What would we measure impulse in? N. s

Impulse = change in momentum Ft = (mv) Impulse is a vector quantity Case 1: When would you want to increase momentum?? *pulling a sling shot back, driving a golf ball, swinging a bat

Let’s look at the forces involved with impulses Hitting a golf ball: a golf club exerts zero force until it comes in contact; then the force increases rapidly as the ball becomes distorted; then the force diminishes as the ball comes up to speed and returns to its original shape. We call the force on the ball the impact force.

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Another scenario Case 2 – Decreasing Momentum When would you want to decrease momentum and minimize the force of something? m v => F t vs. m v => F t

Other Examples Bending your knees when you jump off something Moving away from a punch rather than towards it Landing on carpet rather concrete Safety net for circus acrobats

Bouncing Impulses are greater when an object bounces. Why? The impulse required to bring an object to stop and then “throw it back again” is greater than the impulse required to just bring it to a stop

. Think of a karate expert breaking boards – they deliver a force in a short amount of time and let their hand bounce back which yields twice the impulse to the target.

Internal vs. External Forces If you’re sitting inside your car pushing on the dashboard, will the car move? Internal force If you’re standing outside a car pushing on it, will the car move? External force

*Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged. m 1 v 1 = m 2 v 2 How does this go along with Newton’s Laws of Motion?

Examples Cannon and cannonball – look at the mass and velocity of each = momentum A dropped rock in free fall The rock falls to Earth, as Earth “moves up” to the rock with equal and opposite momentum. Momentum is conserved.

Collisions!!! When objects collide in the absence of external forces, the net momentum of both objects before collision equals the net momentum of objects after collision Net momentum before collision = Net momentum after collision

Elastic Collisions 3 types A moving object striking a ball at rest A head-on collision between two moving objects A collision of two objects moving in the same direction Look at the vector arrows. Objects are not deformed and heat is not generated. Two objects ‘bounce’ off each other Almost all energy is transferred from the first object to the second object

Elastic Collison Example A car's bumper works by using this principle to prevent damage. In a low speed collision, the kinetic energy is small enough that the bumper can deform and then bounce back, transferring all the energy directly back into motion. Almost no energy is converted into heat or damage to the body of the car, as it would in an inelastic collision. However, car bumpers are often made to collapse if the speed is high enough, and not use the benefits of an elastic collision. The rational is that if you are going to collide with something at a high speed, it is better to allow the kinetic energy to crumple the bumper in an inelastic collision than let the bumper shake you around as your car bounces in an elastic collision. Making their bumpers this way benefits the car companies: they get to sell you a new bumper, and you can't sue them for whiplash.

Inelastic Collisions Momentum becomes shared in some way, but is still conserved. Colliding objects become distorted and generate heat during collision. Look at the freight train in Fig 7.10 on page 95 (net mv) before = (net mv) after (m)(4 m/s) + (m)(0 m/s) = (2kg)(v after ) 4kg*m/s = (2kg) V after V after = ???

Air track collisions – elastic and inelastic collisions rison/Flash/ClassMechanics/AirTrack/AirT rack.html rison/Flash/ClassMechanics/AirTrack/AirT rack.html

Recoil Collisions