Momentum – Impulse Collisions

Momentum Inertia  Objects at rest or Objects in motion The concept of inertia in motion is called Momentum Which one is harder to stop? A large truck or a small car? momentum = mass x velocity momentum = m ∙ v

How long this force acts, it is also important. Impulse Changes Momentum If momentum changes  mass, velocity or both change If velocity changes  We have acceleration What causes acceleration?  Force The greater the Force acting on an object  the greater its change in velocity  the greater its change in momentum How long this force acts, it is also important. The quantity of force x time interval is called impulse impulse = F ∙ t impulse = change in momentum  F ∙ t = m ∙ v F ∙ t = m ∙ v

Review Questions Distinguish between mass and momentum. Which is inertia and which is inertia in motion? Which has the greater mass, a heavy truck at rest or a rolling skateboard? Which has the greater momentum? When the force of impact on an object is extended in time, does the impulse increase or decrease? Does impulse equal momentum or a change in momentum? In a car crash, why is it advantegeous for an occupant to extend the time during which the collition takes place? If the time of impact in a collision is extended by four times, how much does the force of impact change? Why is it advantageous for a boxer to ride with the punch? Why should he avoid moving into an oncoming punch?

Bouncing Impulses are greater when an object bounces. The impulse to bring an object to stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop. Pelton Wheel                                                                                 Curved blades prolong contact with water: Impulse = F Dt Greater impulse means greater change in momentum of the wheel.  

Conservation of Momentum Newton’s second Law: To accelerate an object, a net force must be applied on it To change the momentum of an object, exert an impulse on it.                                                                                    Momentum Before = 0 ------------- Momentum After = 0 ------------- After firing, the opposite momenta cancel.     In the absence of an external force, the momentum of a system remains unchanged. momentum (before) = momentum (after)

Collisions In the absence of external forces, the net momentum of both objects before collision, equal the net momentum of both objects after collision net momentum (before collision) = net momentum (after collision) Elastic Collisions: When objects collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision    

net m ∙ v (before) = net m ∙ v (after) Inelastic Collisions: Momentum conservation holds true even when coliding objects become distorded and generate heat during collision. Whenever colliding objects become tangled or coupled together, a totally inelastic collision occurs. net momentum (before collision) = net momentum (after collision) net m ∙ v (before) = net m ∙ v (after) Diesel: m = 8000 kg, v = 5 km/h / Wagon: m = 2000kg, v = 0 km/h     8000 kg ∙ 5 km/h + 2000 kg ∙0 km/h = 10,000 kg ∙ 4 km/h

net momentum (before collision) = net momentum (after collision) Elastic Collisions: net momentum (before collision) = net momentum (after collision) Car "Rear-Ends" Truck -  Elastic Truck "Rear-Ends" Car -  Elastic    

Inelastic Collisions: net momentum (before collision) = net momentum (after collision) Car "Rear-Ends" Truck -  Inelastic Truck "Rear-Ends" Car -  Inelastic    

net momentum (before collision) = net momentum (after collision) Problem Solving: Consider a 8 kg fish that swims toward and swallows a 2 kg fish that is at rest. If the larger fish swims at 5 km/h, what is the velocity immediately after lunch? net momentum (before collision) = net momentum (after collision)    

Momentum Vectors Momentum is conserved even when interacting objects don’t move along the same straight line. Momentum, like the quantities velocity and force, has both direction and magnitude. It is a vector quantity. net momentum (before collision) = net momentum (after collision)    

Review Questions Why is more impulse delivered during a collision when bouncing occurs than during one when it doesn’t? Why is the Pelton Wheel an improvement over paddle wheels with flat blades? In terms of momentum conservation, why does a cannon recoil when fired? What does it mean to say that momentum is conserved? Distinguish between an elastic and an inelastic collision. Imagine that you are hovering next to the space shuttle in an Earth orbit. Your buddy of equal mass, who is moving at 4 km/h with respect to the shuttle, bumps into you. If he holds onto you, how fast do you both move with respect to the ship?