Chapter 6: Momentum and Collisions

Objectives Understand the concept of momentum. Use the impulse-momentum theorem to solve problems. Understand how time and force are related in collisions.

Momentum momentum: inertia in motion; the product of mass and velocity p = m · v How much momentum does a 2750 kg Hummer H2 moving at 31 m/s possess? Note: momentum is a vector; units are kg·m/s

Impulse Changes Momentum Newton actually wrote his second law in this form: SF · Dt = m · Dv The quantity SF·Dt is called impulse. The quantity m·Dv represents a change in momentum. Thus, an impulse causes a change in momentum SF SF · Dt = m · Dv = Dp “impulse-momentum theorem”

Impulse Problem A 1750 kg car traveling at 21 m/s hits a concrete wall and stops in 0.62 s. What is the Dp? How much impulse is applied to the car? How much force does the wall apply to the car? What would be the force applied to the car if you used the brakes and took 4.5 seconds to stop?

Impulse Problem The face of a golf club applies an average force of 5300 N to a 49 gram golf ball. The ball leaves the clubface with a speed of 44 m/s. How much time is the ball in contact with the clubface? SF · Dt = m · Dv SF

Bouncing Which collision involves more force: a ball bouncing off a wall or a ball sticking to a wall? Why? The ball bouncing because there is a greater Dv. SF · Dt = m · Dv so SF ~ Dv

Highway Safety and Impulse Water-filled highway barricades increase the time it takes to stop a car. Why is this safer? They reduce the force of impact! SF = (m · Dv) / Dt Seatbelts and airbags also increase the stopping time and reduce the force of impact.

Objectives Understand the concept of conservation of momentum. Understand why momentum is conserved in an interaction. Be able to solve problems involving collisions.

Conservation of Momentum conservation of momentum: in any interaction (such as a collision) the total combined momentum of the objects remains unchanged (as long as no external forces are present). system: all of the objects involved in an interaction

Conservation of Momentum system Conservation of Momentum ma·vai + mb·vbi = Spi mb ma vai vbi Dp = -SF · Dt -SF +SF Dp = +SF · Dt Dt DpTOTAL = ( -SF·Dt ) + ( +SF·Dt ) = 0 ma·vaf + mb·vbf = Spf mb ma S pi = S pf vaf vbf Law of Conservation of Momentum: ma·vai + mb·vbi = ma·vaf + mb·vbf

Types of Collisions elastic: objects collide without being permanently deformed and without releasing heat or sound ma·vai + mb·vbi = ma·vaf + mb·vbf perfectly inelastic: objects become tangled or combined together ma·vai + mb·vbi = (ma+ mb) ·vf

Conservation of Momentum Problem A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.6 m/s. How fast does the target ball move? Assume all motion is in one dimension. ma·vai + mb·vbi = ma·vaf + mb·vbf

Conservation of Momentum Problem Victor, who has a mass of 85 kg, is trying to make a “get-away” in his 23-kg canoe. As he is leaving the dock at 1.3 m/s, Dakota jumps into the canoe and sits down. If Dakota has a mass of 64 kg and she jumps at a speed of 2.7 m/s, what is the final speed of the the canoe and its passengers?

Conservation of Momentum in Two-Dimensions Collisions in 2-D involve vectors. paf ma initial ma mb final Spi mb pbf

Equal Mass Collision A cue ball (m = 0.16 kg) rolling at 4.0 m/s hits a stationary eight ball of the same mass. If the cue ball travels 25o above its original path and the eight ball travels 65o below the original path, what is the speed of each ball after the collision?

Unequal Mass Collision A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.8 m/s and travels at a 15o angle above its original path. What is the speed of the target ball it travels at a 75o below the original path?

Slingshot Manuever NASA has made use of conservation of momentum on numerous missions. The spacecraft substantially increased its momentum (as speed) and Jupiter lost the same amount of momentum, but because Jupiter is so massive, its overall speed remained virtually unchanged. Jupiter S pi = S pf The spacecraft is pulled toward Jupiter by gravity, but as Jupiter moves along its orbit, the spacecraft just misses colliding with the planet and continues it trip.