Chapter 07 impulse and momentum

1. Impulse and Momentum

2. ASTRONAUT Edward H. White II is in the zero gravity of space. By firing the gas-powered gun, he gains momentum and maneuverability. Credit: NASA

3. Momentum Defined Momentum is defined as the product of mass and velocity . (vector quantity) Units : kg m/s; g cm/s; slug ft/s Momentum m = 1000.0 kg      

4. IMPULSE D t Impulse: Impulse is a force acting for a small time interval D t.  

5. Example 1: The face of a golf club exerts an average force of 4000 N for 0.002 s . What is the impulse imparted to the ball? D t Impulse: The unit for impulse is the n ewton -second ( N-s ) Other units are dyne-second and pound-second ( lb-s )

6. Impulse from a Varying Force Normally, a force acting for a short interval is not constant. It may be large initially and then play off to zero as shown in the graph. F time, t In the absence of calculus, we use the average force F avg .

7. Example 2: Two flexible balls collide. The ball B exerts an average force of 1200 N on ball A . How long were the balls in contact if the impulse is 5 N s ? D t = 0.00417 s The impulse is negative ; the force on ball A is to the left. B A

8. In a ½ sheet of pad paper, discuss briefly the movie clip Spiderman 2 in the application of impulse and momentum (their relationship): Notice: Train and its motion How spiderman wants to stop the train using his legs, single shot of spiderweb by each hand; and multiple shots of spiderwebs ; “stopper” in the railroad.

9. Impulse Changes Velocity and Momentum Consider a mallet hitting a ball: Impulse = Change in “ mv ”

10. Impulse and Momentum Impulse = Change in momentum D t F mv A force F acting on a ball for a time D t increases its momentum mv . Conversion: 1.00 N.s = 1.00 kg m/s Newton’s Second Law of Motion

11. Example 3: A 50-g golf ball leaves the face of the club at 20 m/s . If the club is in contact for 0.002 s , what average force acted on the ball? D t F mv Given: m = 0.05 kg; v o = 0; D t = 0.002 s; v = 20 m/s + Choose right as positive. Average Force:

12. Vector Nature of Momentum Consider the change in momentum of a ball that is dropped onto a rigid plate: v o v A 2-kg ball strikes the plate with a speed of 20 m/s and rebounds with a speed of 15 m/s . What is the change in momentum? + D p = mv - mv o D p = 70 kg m/s D p = (2 kg)(15 m/s) - (2 kg)(-20 m/s)

13. Impulse = Change in momentum Momentum Impulse    

14. More Sample Problems: A 0.10-kg ball is thrown straight up into the air with an initial sped of 15 m/s. Find (a) the ball’s initial momentum; (b) its momentum at its maximum height; and (c) impulse of the weight on the ball from initial to maximum height. The force shown in the force vs. time diagram acts on a 1.5 kg object. Find (a) the impulse of the force, (b) the final velocity of the object if it is initially at rest . F x (N) t (s )    

15. Momentum is conserved in this rocket launch. The velocity of the rocket and its payload is determined by the mass and velocity of the expelled gases. Photo: NASA Conservation of Linear Momentum

16. Conservation of Momentum The total momentum of an isolated system of bodies remains constant. system = set of objects that interact with each other. An isolated system is one in which the only force present are those between the objects of the system; that is there is no net external force. therefore  

17.               Since   Initial momenta = final momenta Conservation of Momentum

18.       Sample Illustrations: Initially, the system is at rest: Rocket: Gas:     Conservation of Momentum Revisited: Into Details

19. 1 2     1 2   ’   1 2       APPLICATION: COLLISIONS and Conservation of Momentum

20. Simple Collisions (Head-on Collisions) Example 01 A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics book horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore? A car with a mass of 9.00 x 10 2 kg is traveling at +15.0 m/s while an SUV with a mass of 1.80 x 10 3 kg is traveling at -15.0 m/s. (a) If the cars collide head-on, becoming entangled, find the velocity of the entangled cars after the collision. (b) If the SUV stops after collision and not entangled, what is the velocity of the car after collision?