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Chapter 6

Chapter 6. Momentum and Collisions. Momentum, p . Momentum & Impulse Video (6 min) Definition: P = mv a vector quantity: Has a direction and a magnitude The same direction as the velocity + v → +P ‒ v → ‒ P Unit: kg · m /s. Impulse, ∆p = J.

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Chapter 6

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  1. Chapter 6 Momentum and Collisions

  2. Momentum, p • Momentum & Impulse Video (6 min) • Definition: P = mv • a vector quantity: Has a direction and a magnitude • The same direction as the velocity • + v → +P • ‒ v → ‒P • Unit: kg·m/s

  3. Impulse, ∆p = J • the change in momentum of a body, caused by a force exerted over a time interval • Impulse = pf – pi =∆p = J • A vector quanitity • Unit: kg·m/s=N·s

  4. Sample 6A, Pg 209 A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck? *Remember to include the direction!!

  5. Relating impulse to Force

  6. Impulse-momentum Theorem • If you want to change the momentum of an object, a force must be applied to it for a time duration. • For the same amount of momentum change, longer the time, less force required

  7. Impulse determination from Force vs. Time graph

  8. Example A 2200-kg car traveling at 94km/hr is stopped in 21 s. • What is the momentum when its velocity is 94km/hr? • What is the momentum when it stops? (c) What is the impulse? (d) What is the average force exerted?

  9. Example, Pg 211 A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the magnitude of the force exerted on the car during the collision.

  10. Example A 0.174-kg softball is pitched horizontally at 26.0 m/s. The ball moves in the opposite direction at 38.0 m/s after it is hit by the bat. • Draw arrows showing the ball’s momentum before and after the bat hits it. • What is the change in momentum of the ball? • What is the impulse delivered by the bat? • If the bat and softball are in contact for 0.80 ms, what is the average force that the bat exerts on the ball?

  11. p, J, and F • P = mv • J = Δp = m(vf – vi) = m Δv =FΔt

  12. Sample Problem 6C, Pg 212 A 2250 kg car traveling to the west is slowed down uniformly from 20.0 m/s to 5.00 m/s in 4.00 s. (a) What constant force acted on the car during this time? (b) How far in distance did the car travel during the acceleration?

  13. Conservation of Momentum • The momentum of a closed or isolated system remains constant • A closed system can exchange heat and work (for example, energy), but not matter, with its surroundings. • An isolated system cannot exchange any of heat, work, or matter with the surroundings. • An open system can exchange all of heat, work and matter • To use this law, the mass in a system must not change

  14. Problem-solving strategies • Define the system • must be closed or isolated • Draw the diagram • View the system before and after an event • Use the conservation of momentum • The total momentum before the event = The total momentum after the event • Assign the correct sign for the direction of velocity • Advantage over the conservation of energy • Check if the answer is reasonable

  15. Example, Pg 218 A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?

  16. Examples • A 1875-kg car going 23 m/s rear-ends a 1025-kg compact car going 17 m/s in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

  17. Using Momentum in Space An astronaut at rest in space fires a thruster pistol that expel 35 g of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing the pistol?

  18. Collisions • Inelastic collision • Objects do not maintain the original shape • Kinetic energy is NOT conserved – lost to other types of energy • Perfectly inelastic • Two objects collide and become one object • m1v1,i +m2v2,i = (m1+m2)vf • Elastic collision • Objects maintain the original shape • m1v1,i +m2v2,i = m1V1,f+m2V2,f • Kinetic energy is conserved (KE = ½ mv2)

  19. Example, Pg 223 A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?

  20. Example, pg 225 Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The mass of the second ball is 0.250 kg, and it has an initial velocity of 3.00 m/s to the left. (a) What is the final velocity of the composite ball of clay after the collision? (b) What is the decrease in kinetic energy during the collision?

  21. Example, Pg 228 A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-0n collision with a 0.030 kg shooter marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. What is the velocity of the 0.030 kg marble after the collision?

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