Momentum

What is momentum? Momentum is the quantity of motion. If an object is in motion, it has momentum Mass in motion Momentum is dependent on 2 things: –How much “stuff” is moving, Mass, measured in kg –How fast the stuff is moving, Velocity, measured in m/s

Calculating Momentum Momentum is a vector quantity. Momentum = mass x velocity p = m x v An object can have a large momentum if it has either a large mass and/or a high speed.

Determining momentum A small sports car and a large delivery truck are traveling at the same speed. Which has more momentum? If the car is to have the same momentum as the truck, what about the car must be changed? If the truck is at rest, what is its momentum?

Sample Problems Determine the momentum of a... 1)A 60-kg halfback moving eastward at 9 m/s. Answer: 540 kg m/s east 2) A 1000-kg car moving northward at 20 m/s. Answer: kg m/s north 3) A 40-kg freshman moving southward at 2 m/s. Answer: 80 kg m/s south

Changing momentum In order to change the momentum of an object, the velocity must be changed (if the mass remains the same). Any change in velocity is called acceleration. Newton’s second law states that any acceleration requires a force.

Changing momentum (continued) F = m x a (Newton’s 2 nd law) a = v t F = m v t F t = m v

What is impulse? F t is called an impulse. Impulse is a change in momentum. Impulse is a force applied over a time interval. Impulse is measured in N. s.

What is the relationship between momentum and impulse? If two objects have the same momentum, the same impulse is required to change that momentum. A large force can be applied over a small time interval or A small force can be applied over a large time interval.

Applications of Impulse If you were to attempt to catch a baseball with your bare hand, you would probably move your hand backward as you catch the ball. Why? How do airbags or padded dashboards assist in protecting drivers in a crash?

Discussion Questions 1.Would you try to stop a 150 lb (68 kg) cannonball fired towards you at 30 mph (48 km/hr)? Why not? How does this compare with trying to brace yourself in a car collision? 2.Show mathematically why a 36,000 kg truck traveling 0.89 m/s has the same momentum as a 1800 kg SUV traveling at 18 m/s.

Discussion Questions 3.During the egg throwing demonstration, which egg experienced the greater impulse? Which egg experienced the greater force of impact? Which egg experienced the greater time of impact? 4.Describe three other examples where momentum is reduced by applying a smaller collision force over a longer impact time.

Practice Problem #1 A 0.50 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver catches the ball and brings it to rest in s. What is the force exerted on the receiver?

Practice Problem #2 A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?

Law of Conservation of Momentum The Law of Conservation of Momentum states that if no net force acts on a system, the momentum of the system cannot change. This means that the momentum before a collision is equal to the momentum after a collision.

Law of Conservation of Momentum (continued) The equation for the law of conservation of momentum: p A1 + p B1 = p A2 + p B2 p A1 + p B1 = p A2 + p B2 The momentum gained by object B is equal to the momentum lost by object A

Momentum is conserved if: The system is closed (no gain or loss in mass) Only internal forces are involved (forces outside the system are external forces- although there will always be some interaction with outside forces they are usually small and can be ignored ) There must be collisions (the objects can come apart or remain stuck together)

Sample Problem A 2275 kg car going 28 m/s rear ends a 875 kg car going 16 m/s on ice in the same direction. The two cars stick together. How fast does the wreckage move immediately after the collision?

Calculating the Answer p A1 + p B1 = p A2 + p B2 mv A1 + mv B1 = (m A + m B )v 2 (2275)(28) + (875)(16) = ( )x X = 25 m/s

Sample Problem #2 John has a mass of kg and is riding in a 100kg bumper car at 10.0 m/s. If he collides with Melinda who has a mass of 25 kg and is at rest, what is Melinda’s velocity after the collision if John continues ahead at a speed of 4.12 m/s after the collision? 10.0 m/s. If he collides with Melinda who has a mass of 25 kg and is at rest, what is Melinda’s velocity after the collision if John continues ahead at a speed of 4.12 m/s after the collision?

Calculating the Answer p A1 + p B1 = p A2 + p B2 (300.0)(10.0) + (125)(0) = (300.0)(4.12) + (125)x X = 14.1 m/s

Recoil Problem An astronaut at rest in space fires a thruster pistol that expels 35 g of 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?

Calculating the Answer p A1 + p B1 = p A2 + p B2 (m A + m B )v 1 = mv A + mv B (84)(0) = (.035)(875) + (84)x X = -.36 m/s (the direction is opposite to that of the gas leaving the pistol)

Homework Complete problems 7-12 on p. 210 and on p. 214