Chapter 7. Impulse and Momentum

Transcription

1 Chapter 7 Ipulse and Moentu

2 7. The Ipulse-Moentu Theore There are any situations when the force on an object is not constant.

3 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE The ipulse of a force is the product of the aerage force and the tie interal during which the force acts: J Ft Ipulse is a ector quantity and has the sae direction as the aerage force. newton seconds (Ns)

4 7. The Ipulse-Moentu Theore J Ft

5 7. The Ipulse-Moentu Theore DEFINITION OF LINEAR MOMENTUM The linear oentu of an object is the product of the object s ass ties its elocity: p Linear oentu is a ector quantity and has the sae direction as the elocity. kilogra eter/second (kg /s)

6 7. The Ipulse-Moentu Theore t o f a a F t f o F o f F t

7 7. The Ipulse-Moentu Theore IMPULSE-MOMENTUM THEOREM When a net force acts on an object, the ipulse of this force is equal to the change in the oentu of the object ipulse F t f o final oentu initial oentu

8 7. The Ipulse-Moentu Theore Exaple A Rain Stor Rain coes down with a elocity of -5 /s and hits the roof of a car. The ass of rain per second that strikes the roof of the car is kg/s. Assuing that rain coes to rest upon striking the car, find the aerage force exerted by the rain on the roof. F t f o

9 7. The Ipulse-Moentu Theore Neglecting the weight of the raindrops, the net force on a raindrop is siply the force on the raindrop due to the roof. Ft f o F t o F kg s 5 s 0.90 N

10 7. The Ipulse-Moentu Theore Conceptual Exaple 3 Hailstones Versus Raindrops Instead of rain, suppose hail is falling. Unlike rain, hail usually bounces off the roof of the car. If hail fell instead of rain, would the force be saller than, equal to, or greater than that calculated in Exaple?

11 7. The Principle of Conseration of Linear Moentu WORK-ENERGY THEOREM CONSERVATION OF ENERGY IMPULSE-MOMENTUM THEOREM??? Apply the ipulse-oentu theore to the idair collision between two objects..

12 7. The Principle of Conseration of Linear Moentu Internal forces Forces that objects within the syste exert on each other. External forces Forces exerted on objects by agents external to the syste.

13 7. The Principle of Conseration of Linear Moentu Ft f o OBJECT W F t f o OBJECT W F t f o

14 7. The Principle of Conseration of Linear Moentu o f F W t o f F W t + o o f f F F W W t F F f P o P

15 7. The Principle of Conseration of Linear Moentu The internal forces cancel out. W W t P f Po suof aerage external forces t Pf Po

16 7. The Principle of Conseration of Linear Moentu suof aerage external forces t Pf Po If the su of the external forces is zero, then P f P o 0 P f Po PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM The total linear oentu of an isolated syste is constant (consered). An isolated syste is one for which the su of the aerage external forces acting on the syste is zero.

17 7. The Principle of Conseration of Linear Moentu Conceptual Exaple 4 Is the Total Moentu Consered? Iagine two balls colliding on a billiard table that is friction-free. Use the oentu conseration principle in answering the following questions. (a) Is the total oentu of the two-ball syste the sae before and after the collision? (b) Answer part (a) for a syste that contains only one of the two colliding balls.

18 7. The Principle of Conseration of Linear Moentu PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM The total linear oentu of an isolated syste is constant (consered). An isolated syste is one for which the su of the aerage external forces acting on the syste is zero. In the top picture the net external force on the syste is zero. In the botto picture the net external force on the syste is not zero.

19 7. The Principle of Conseration of Linear Moentu Exaple 6 Ice Skaters Starting fro rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woan and one is a 88-kg an. The woan oes away with a speed of +.5 /s. Find the recoil elocity of the an.

20 7. The Principle of Conseration of Linear Moentu P f P o f f 0 f f 54 kg.5 s f 88 kg.5 s

21 7. The Principle of Conseration of Linear Moentu Applying the Principle of Conseration of Linear Moentu. Decide which objects are included in the syste.. Relatie to the syste, identify the internal and external forces. 3. Verify that the syste is isolated. 4. Set the final oentu of the syste equal to its initial oentu. Reeber that oentu is a ector.

22 7.3 Collisions in One Diension The total linear oentu is consered when two objects collide, proided they constitute an isolated syste. Elastic collision -- One in which the total kinetic energy of the syste after the collision is equal to the total kinetic energy before the collision. Inelastic collision -- One in which the total kinetic energy of the syste after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be copletely inelastic.

23 7.3 Collisions in One Diension Exaple 8 A Ballistic Penduli The ass of the block of wood is.50-kg and the ass of the bullet is kg. The block swings to a axiu height of aboe the initial position. Find the initial speed of the bullet.

24 7.3 Collisions in One Diension o o f f Apply conseration of oentu to the collision: o f f o

25 7.3 Collisions in One Diension Applying conseration of energy to the swinging otion: gh gh f f gh f f f gh f s

26 7.3 Collisions in One Diension f s o f o kg.50 kg 9.80 s kg s

27 7.4 Collisions in Two Diensions A Collision in Two Diensions

28 7.4 Collisions in Two Diensions x o x o x f x f y o y o y f y f

29 7.5 Center of Mass The center of ass is a point that represents the aerage location for the total ass of a syste. x c x x

30 7.5 Center of Mass x c x x c

31 7.5 Center of Mass c In an isolated syste, the total linear oentu does not change, therefore the elocity of the center of ass does not change.

32 7.5 Center of Mass BEFORE c 0 AFTER c 88 kg.5 s 54 kg.5 s 88 kg 54 kg