Transcript Momentum
Physics Chapter 6 Impulse and Momentum Momentum • Momentum depends on… – Mass – Velocity – Momentum = Mass x Velocity • The property of momentum… – Variable: p – Unit: kg m s – Scalar or Vector? – Equation: p = mv Example #1 Which has more momentum, a 1-ton car moving at 100 km/h or a 2-ton truck moving at 50 km/h? Example #2 How fast would a 18 kg kid on a tricycle have to go in order to have the same momentum as a 55 kg car traveling at 25 m/s? Impulse • Momentum can change. Most often, the mass of an object remains the same, while the velocity changes. • Dp = mDv • Dv acceleration a = Dv/t Dv=at • Dp = mDv becomes Dp = m x a x t • Dp = Force x time = Ft F • This is called Impulse – I = Ft Example #3 If a baseball bat applies a 22-N force to a baseball for 0.13 s, what is the impulse experienced by the ball? Impulse & Momentum • Impulse equals a change in momentum • I = Dp • Variations Ft = mDv Ft = mvf – mvi I = mDv I = mvf – mvi Ft = Dp Example #4 What is the impulse needed to stop a 10kg bowling ball moving at 6 m/s? Example #5 A car crashes into a wall at 25 m/s and is brought to a rest in 0.1 s. Calculate the average force exerted on a 75-kg test dummy by the seat belt. Impulse & Momentum Increasing Momentum mDv = Ft Increase the time to increase the velocity • Examples: – Follow through in sports • • • • Basketball shoot Baseball hit Soccer kick Golf swing – Long-range cannons have long barrels Impulse & Momentum Decreasing Force mDv = Ft Increase the time to decrease the Force • Examples: – Catching • Egg toss • Water balloon • Football – – – – – – – Cars: Crumple Zones & Air Bags Roll with the punches Mighty Ducks Jumping and landing (sprung floors) Running Shoes Any padding Bungee Jumping Problems • Review Questions 1-11, 13 • Exercises 1-4, 6, 9, 10 • Problems 1, 2, 5 Conservation of Momentum • Newton’s Second Law… – If we want an object to accelerate, we must apply a force. • Impulse and Momentum… – If we want a change in momentum, we must apply an impulse. • In both cases, the force or impulse must be exerted on the object or any system of objects by something external. Conservation of Momentum • If we define the system to include all the objects we want to study… all forces become internal; there can be no impulse; no impulse means no change in momentum! • When a physical quantity remains unchanged during a process, that quantity is said to be… CONSERVED. Collisions • Momentum is conserved Momentum before = Momentum after • Three types of collisions… – Elastic objects rebound off each other without lasting deformation. – Inelastic objects are deformed by the collision; think car crashes. – Perfectly inelastic both objects stick together Example #1a The blue car is moving at 10 m/s, with a mass m. The orange car, also mass m, is at rest. If the freight cars are coupled together by the collision, what is their combined velocity? v = 10 m/s v=? v=0 Example #1b If the freight cars in the previous example do not couple and experience an elastic collision, what is the velocity of the orange car? v = 10 m/s v=? v=0 v=0 Example #2 Two trucks with equal masses, m, experience a head on collision. After collision, the coupled wreck remains at the point of impact with zero momentum. If the green truck was moving at 10 m/s, how fast was the red truck moving? v = 10 m/s v=? v=0 Example #3 A 3 kg object traveling at 5 m/sec collides head-on with a 2 kg object that is traveling at 2 m/sec in the opposite direction. What is the velocity of the second object after the collision if the first object is moving at 1 m/sec? Problems • Review Questions 18-23 • Exercises 13, 21 • Problems 6-10