Momentum and Impulse

Transcription

1 Momentum and Impulse

2 Momentum All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum which an object has is dependent upon two variables: how much matter is moving? how fast the matter is moving?

3 Momentum Inertia in motion Vector quantity Momentum = mass x velocity p = mv p is momentum m is mass v is velocity Units will be Kg m/s Momentum is a measure of moving inertia. An object at rest has inertia but no momentum.

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6 Let s Compare A moving truck has more momentum than a car moving at the same speed because the truck has more mass. A fast car can have more momentum than a slow truck. A truck at rest has no momentum at all. A truck rolling down a hill has more momentum than a roller skate with the same speed. But if the truck is at rest and the roller skate moves, then the skate has more momentum.

7 Think about Which has more momentum 1200 kg steamroller moving at 1 m/s or 1 kg bullet moving at 1200 m/s

8 Think About What is the momentum of a 40 kg jogger running southward at 2 m/s? What is the momentum of a 60 kg halfback moving east at 9 m/s?

9 Think About What is the momentum of a 40 kg jogger running southward at 2 m/s? 80 kg m/s south What is the momentum of a 60 kg halfback moving east at 9 m/s? 540 kg m/s east

10 If the boulder and the boy have the same momentum, will the boulder crush the boy? No. The boy has less mass, thus he will need to have a much higher velocity in order to have the same momentum as the boulder with a much greater mass. p = mv

11 Impulse/ DMomentum Theorem As the force acts upon the object for a given amount of time, the object's velocity is changed. Remember Newton s 2nd law equation: F = ma & a = Dv/ Dt F Dt = D(mv) = mv f mv i = m(v f v i ) Impulse = change in momentum

12 IMPULSE A force applied for a period of time which results in a change of momentum. Impulse = change in momentum F t = p = (mv) F t = mv f - mv i F t = m (v f v i )

13 To change the momentum of a body, a force must be applied to the mass. The longer this force is applied to the mass, the greater effect it will have on changing the momentum.

14 Impulse Change in momentum Impulse = (mv) Impulse = F t Ft = (mv) F is Force t is time Force is applied m is mass v is velocity Impulse will have the same units as momentum (Kg m/s) but it is NOT momentum It is a CHANGE in momentum

15 Think About A hockey player applies an average force of 80 N to a.25 kg puck for a time of 0.1 seconds. Determine the impulse experienced by the hockey puck.

16 Think About A hockey player applies an average force of 80 N to a.25 kg puck for a time of 0.1 seconds. Determine the impulse experienced by the hockey puck. imp = F t = (80N)(.10s) = 8 N s or kg m/s

17 Increasing Momentum To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swing. Think of rifle vs. hand gun barrel

18 Decreasing Momentum Think about riding in an out of control car would you prefer hitting a haystack or brick wall? When hitting either the wall or the haystack and coming to a stop, the momentum is decreased by the same impulse. The same impulse does not mean the same amount of force or the same amount of time. It means the same product of force and time. To keep the force small, we extend the time.

19 Decreasing Momentum If the change in momentum occurs over a long time, the force of impact is small. If the change in momentum occurs over a short time, the force of impact is large.

20 Decreasing Momentum Examples A padded dashboard in a car is safer than a rigid metal one. Airbags save lives. To catch a fast-moving ball, extend your hand forward and move it backward after making contact with the ball. Egg toss game. Jump off roof or fence bend your knees. Drop glass on tile/concrete vs. carpet. Circus acrobats and net Boxer rides a punch Others?

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22 Conservation of Momentum Remember Newtons 2 nd Law To accelerate an object exert a force on it. To change momentum of an object, exert an impulse on it. Need unbalanced or net impulse Law of Conservation of Momentum- states that, in the absence of an external force, the momentum of a system remains unchanged The force or impulse that changes momentum must be exerted on the object by something outside the object. Molecular forces within a basketball have no effect on the momentum of the basketball. A push against the dashboard from inside does not affect the momentum of a car. These are internal forces. They come in balanced pairs that cancel within the object.

23 Conservation of Momentum The momentum before firing is zero. After firing, the net momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball. Momentum of cannon and momentum of cannon ball

24 Collisions Objects collide in absence of external forces net momentum before = net momentum after Very short impact so ignore changes from outside forces (ex. Car crash do not consider rubber on concrete etc.) Types of Collisions Elastic Inelastic Break Apart

25 Collisions Elastic Objects bounce off each other Neither deformed permanently No heat or sound given off (Ex. Bumper cars, baseball and bat, basket ball and floor, golf club and ball, billiard balls.)

26 Collisions Inelastic Objects become tangled or coupled They stick! Distortion happens Heat and sound given off (Ex. Sticking car crash, linebacker and running back)

27 Collisions Break Apart or Explosion Objects start as one Objects move in opposite directions (Ex. Shooting a gun or astronaut throwing something)

28 Collision Equations Elastic Collision m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 Inelastic Collision m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v f Break Apart or Explosion (m 1 + m 2 )v i = m 1 v 1 + m 2 v 2

29 Think About A 4o kg football player leaps through the air to collide with and tackle a 60 kg player heading toward him (also in the air). If the 40 kg player is heading to the right at 7 m/s and the 60 kg player is heading toward the left at 3 m/s, what is the speed and direction of the tangled players?

30 Think About 1 m/s. Positive so to the right.