Transcript File
Unit 5: Momentum and Impulse 1 Momentum What does it mean to have momentum? 2 Sports Example • Coach: “We have all the momentum. Now we need to use that momentum and bury them in the third quarter.” • What does the coach mean? • His team is on the move and will take some effort to stop. 3 Momentum • All objects in motion have momentum! • What factors determine how much momentum an object has? 4 Linear Momentum • Linear momentum (p) – product of an object’s mass and velocity. p mv • Momentum is a vector that points in the same direction as the velocity. • Units: kg *m/s 5 • Example #1: A freight train moves due north with a speed of 1.4 m/s. The mass of the train is 4.5 x 105 kg. How fast would an 1800 kg automobile have to be moving due north to have the same momentum? ptrain = mtrainvtrain =(4.5 x 105 kg)(1.4 m/s) = 630,000 kg*m/s pauto = mautovauto pauto vauto mauto kg m 630,000 s = 350 m/s 1800 kg 6 Varying Forces • Forces are not always constant. Many forces change as they are applied over a period of time. Average Force (F) t0 tf When a baseball hits a bat, the ball is in contact with the bat for a short time interval. The force reaches its maximum value towards the middle of the time interval. 7 Impulse • For a baseball to be hit well, both the size of the force and the time of contact (Follow through!) are important. • Impulse (J) – product of the average force F and the time interval Δt over which the force acts. J F t • Units: Newton * seconds (Ns) • Impulse is a vector that points in the same direction as the average force. 8 Impulse-Momentum Theorem nd • Remember Newton’s 2 Law: F m a v • And acceleration is defined as a t v • Substitute: F m t • Rearrange: Impulse-Momentum Theorem F Δt m Δv 9 Impulse-Momentum Theorem • Another way to write the theorem is: J p • In words: Impulse = Change in Momentum 10 • Example #2: A volleyball is spiked so that its incoming velocity of +4.0 m/s is changed to an outgoing velocity of -21 m/s. The mass of the volleyball is 0.35 kg. What impulse does the player apply to the ball? v0 = +4.0 m/s vf = -21 m/s m = 0.35 kg J p mv f mv0 (0.35kg)( 21m / s) (0.35kg)( 4.0m / s) 8.75 Ns 11 Impulse Why doesn’t the egg break?? http://www.youtube.com/watch?v=7RSUjxiZnME 12 Impulse An object with 100 units of momentum must experience 100 units of impulse to be brought to a stop . This can come from any combination of Force x time. As time Force 13 Conservation of Momentum • closed system – system where nothing is lost and no net external forces act. • Law of Conservation of Momentum – the total momentum of any closed system does not change; the momentum before an interaction equals the momentum after the interaction. p0 p f 14 Collisions in 1-Dimension Inelastic • Inelastic collision- a collision in which the objects stick together and move with one common velocity after colliding. • 2 objects 1 object 15 Inelastic Collisions Example 3: Two cars collide and become entangled. If car #1 has a mass of 2000 kg and a velocity of 20 m/s to the right, and car #2 has a mass of 1500 kg and a velocity of 25 m/s to the left, find the velocity of the system after the collision. BEFORE Collision AFTER Collision p0 p f m1v1 m2 v2 mtotalv f m1v1 m2 v2 vf mtotal (2000kg)( 20m / s) (1500kg)( 25m / s) (3500kg) 0.71 m/s to the right 16 Explosions • Explosion- process of one object splitting into 2 (or more) objects • Recoil- kickback; momentum opposite a projectile • 1 object 2 objects (or more) 17 Explosions Example 4: Starting from rest, two skaters push off each other on smooth level ice. Skater 1 has a mass of 88 kg and Skater 2 has a mass of 54 kg. Upon breaking apart, Skater 2 moves away with a velocity of 2.5m/s to the right. Find the recoil velocity of Skater 1. BEFORE Explosion AFTER Explosion p0 p f mtotalv0 m1v1 f m2 v2 f 0 m1v1 f m2 v2 f v1 f m2 v2 f m1 (54 kg)( 2.5 m/s ) 1.53 m/s (88 kg) 18 OR 1.53 m/s to the left Collisions in 1-Dimension Elastic • Elastic collision – a collision in which the colliding objects bounce off each other. • 2 objects stay 2 objects 19 Elastic Collisions BEFORE Collision AFTER Collision ? ? p0 p f m1v10 m2v20 m1v1 f m2v2 f This is the hardest type of problem since there are two pieces on both sides! 20 Elastic Collisions Example 21 Elastic Collisions BEFORE Collision AFTER Collision ? ? p0 p f m1v10 m2v20 m1v1 f m2v2 f If there are 2 unknowns we would need to use Conservation of Energy and solve a system of equations… We may do this type of problem, but NOT YET! 22 Is Kinetic Energy Conserved? •Elastic Collision: KE is conserved •Inelastic Collision: KE is NOT conserved 23 Practice Problem #1 24 Practice Problem #2 • An automobile accident investigator needs to determine the initial westerly velocity of a Jeep (m=1720 kg) that may have been speeding before colliding head-on with a Volkswagen (m=1510 kg) that was moving with a velocity of 21 m/s east. The speed limit on the road was 55 mi/hr. After the collision, the Jeep and Volkswagen stuck together and continued to travel with a velocity of 4.3 m/s west. a. Find the initial westerly velocity of the Jeep. b. Was the jeep speeding? 25 Practice Problem #2 26