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Linear Momentum

Linear Momentum. why is more force needed to stop a train than a car if both travel at the same speed? why does a little tiny bullet have so much force on impact? how do you steer a satellite or shuttle in space?. Momentum (p)  a term which describes the product of mass and velocity.

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Linear Momentum

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  1. Linear Momentum why is more force needed to stop a train than a car if both travel at the same speed? why does a little tiny bullet have so much force on impact? how do you steer a satellite or shuttle in space?

  2. Momentum (p) a term which describes the product of mass and velocity • changing momentum depends upon changing either mass or velocity • the train is harder to stop than the car because its larger mass means a greater change in momentum • a bullet has a tremendous impact because its change in speed upon impact is extremely large- hence a large change in momentum

  3. Momentum depends directly upon mass and directly upon velocity: units: kg • m/s p = mv A change in momentum usually means a change in velocity. A change in momentum will only occur if a force acts upon the object and changes its velocity (it accelerates the object!)

  4. = m∆v ∆t F = ma therefore: F∆t = m∆v Impulse produces a change in momentum In order to change the momentum of an object, a force must be exerted on it for a given period of time!

  5. A 1400 kg car traveling in the positive direction takes 10.5 seconds to slow from 25.0 meters per second to 12.0 meters per second. What is the average force on the car during this time? A cue stick applies an average force of 66 N to a stationary 0.17 kg cue ball for 0.0012 s. What is the magnitude of the impulse on the cue ball?

  6. A government agency estimated that air bags have saved over 14,000 lives as of April 2004 in the United States. (They also stated that air bags have been confirmed as killing 242 people, and they stress that seat belts are estimated to save 11,000 lives a year.) Assume that a car crashes and has come to a stop when the air bag inflates, causing a 75.0 kg person moving forward at 15.0 m/s to stop moving in 0.0250 seconds. (a) What is the magnitude of the person's impulse? (b) What is the magnitude of the average force the airbag exerts on the person?

  7. Law of Conservation of Momentum the total (vector sum) momentum of two (or more) objects before a collision will be the same as after the collision! • a collision simply means a force acted over a relatively short period of time! an explosion would be a collision! There are two types of collisions: • Inelastic- kinetic energy is not conserved • Elastic- kinetic energy is conserved

  8. A 1.20 kg cart heading east at .50 m/s collides head on with a 1.60 kg cart heading west at .70 m/s and they lock together. What is the velocity of the two carts afterward? pbefore = pafter m1 = 1.20 kg m1v1 + m2v2 = (m1 + m2)v v1 = .50 m/s (1.20 kg)(.50 m/s)+(1.60 kg)(-.70 m/s) m2 = 1.60 kg = (1.20 kg + 1.60 kg)v v2 = -.70 m/s .60 + (-1.12) = 2.80v v = ? v = -.19 m/s Is this collision elastic? or .19 m/s West

  9. An 6.00 kg bowling ball traveling at 2.00 m/s collides with an 8.00 kg ball that is at rest. After the collision, the 6.00 kg ball is reduced in speed to .500 m/s. What is the speed of the other ball after? p = p’ m1 = 6.00 kg v1 = 2.00 m/s m1v1 + m2v2 = m1v1 + m2v2 m2 = 8.00 kg (6.00 kg)(2.00 m/s) + 0 = v2 = 0 (6.00 kg)(.500 m/s) + (8.00 kg)(v2) v1 = .500 m/s v2 = 12.0 - 3.00 =1.13 m/s v2= ? Elastic? 8.00

  10. A car of 1200 kg heading east at 25.0 m/s collides with a second car of 1800 kg that is heading north at 21.0 m/s. The cars stick together after the collision. What is the velocity of the cars after the collision? Remember that momentum is a vector and is conserved in both x and y directions!

  11. A little red wagon with a mass of 75.0 kg is rolling along when a 210.0 kg mail sack is dropped into the wagon. The wagon and the mail sack continue to roll along at 1.37 m/s. What was the speed of the little red wagon before the mail sack was dropped on it? A bowling ball of mass 6.0 kg is traveling at 4.0 m/s when it collides with an 8.0 kg ball. After the collision, the second ball accelerates to 4.75 m/s and the first is traveling 1.0 m/s opposite of its initial direction. What was the velocity of the second ball initially?

  12. Is the previous collision an elastic or inelastic collision? While on a space walk, a 75.0 kg astronaut, initially at rest relative to the shuttle, throws a hammer with a speed of 4.00 m/s. If the mass of the hammer is 3.00 kg, what is the resulting velocity of the astronaut? A second astronaut, mass 85.5 kg, initially at rest, catches the thrown hammer. What is his resultant velocity?

  13. A .300 kg dynamics cart traveling at .650 m/s collides with a second, identical cart at rest. They stick together after the collision. Find their velocity after and find how much kinetic energy was lost during the collision. An 86.0 kg running back heading north at 9.00 m/s is hit head on by a 92.0 kg linebacker going south at 6.00 m/s. Assume the linebacker wraps up well and find their velocity immediately after they collide.

  14. A 925 kg car traveling straight east at 24.0 m/s is broad-sided by a pick up truck of mass 1250 kg traveling north at 15.5 m/s. After the collision, the car has a velocity of 19.5 m/s at 18.0˚ East of North. What is the velocity of the truck after the collision?

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