Motion

Transcription

1 Momentum The momentum of an object depends on its mass and its velocity. Consider a force F acting on mass m for a time t so that it accelerates from velocity u to velocity v. Since F ma and Momentum = mass x velocity Momentum = mv Units of momentum are kg m / s a ( v u) t m( v u) mv mu, then F. t t Rate of change of momentum: Impulse = 1

2 Example Jerome plays middle linebacker for South's varsity football team. In a game against cross-town rival North, he delivered a hit to North's 82-kg running back, changing his eastward velocity of 5.6 m/s into a westward velocity of 2.5 m/s. a. Determine the initial momentum of the running back. b. Determine the final momentum of the running back. c. Determine the momentum change of the running back. d. Determine the impulse delivered to the running back. 2

3 Safety in Cars Consider first a boy kicking a stone of mass 1kg and accelerating it from rest to 10m/s. Because the stone is rigid, the force of his foot acts for only 0.01seconds. Now consider the same boy kicking a football of the same mass to give it the same speed and therefore the same momentum. Because the ball is soft and he follows through with his foot, this force is applied for 0.1 seconds. The longer the time of a collision, the smaller the force. This idea is used to design the safety in cars. Safety features in vehicles are the following: - Crumple zones: The front and back of a car is designed to crumple, in order to spread out the time of a collision, and so reduce the force on you. - Seat Belts: A seat-belt is designed to stretch slightly, to spread out the time of the crash even further, and so reduce the force on the passenger to a safe level. - Helmets: A motor-cyclist s safety helmet is padded inside so as to extend the time of any collision. Oppositely, the hammer is used for hard metal. This is so that the time of the collision is as small as possible, and so the force of the hammer on the nail is as large as possible. 3

4 Collisions Consider two balls rolling towards each other so that they collide. When they collide they exert a force F on each other for a time t. Thus, the momentum of each ball undergoes a change. Since the forces are equal and opposite (Newton s third law), the changes in momentum are equal and opposite. In other words, the momentum gained by one ball is equal to the momentum lost by the other ball. The principle of Conservation of momentum states that when two or more bodies act on each other, their total momentum remains constant, providing there is no external force acting. Total momentum before collision = Total momentum after collision Collisions can be of two types: Elastic or Inelastic Inelastic : The colliding bodies stay together after collision (e.g. plasticene and floor) Elastic : The colliding bodies separate after collision (e.g. bouncing ball) 4

5 Explosions In an explosion, momentum is also conserved. The total momentum before the explosion is always zero since velocity of an object before the explosion is 0. Therefore, the total momentum after the explosion is also 0. Examples 1. A bullet of mass 100g is fired into a stationart target of mass 4kg. The target is mounted on low friction wheels and moves off at a velocity of 5 m/s when the bullet enters it. Calculate the velocity of the bullet before it strikes the taget. 5

6 2. A candy-filled piñata is hung from a tree for Matthew's birthday. During an unsuccessful attempt to break the 4.4-kg piñata, Hayden cracks it with a 0.54-kg stick moving at 4.8 m/s. The stick stops and the piñata undergoes a gentle swinging motion. Determine the swing speed of the piñata immediately after being cracked by the stick. 3. A 70.9-kg boy and a 43.2-kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 4.64 m/s. Neglecting friction, determine the subsequent velocity of the boy. 6