Unit 5 Momentum and Impulse 1 Momentum What

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. • 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 = 350 m/s 6

Varying Forces • Forces are not always constant. Many forces change as they are applied over a period of time. Average Force (F) t 0 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. • Units: Newton * seconds (Ns) • Impulse is a vector that points in the same direction as the average force. 8

Impulse-Momentum Theorem • Remember Newton’s 2 nd Law: • And acceleration is defined as • Substitute: • Rearrange: Impulse-Momentum Theorem 9

Impulse-Momentum Theorem • Another way to write theorem is: • 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? v 0 = +4. 0 m/s vf = -21 m/s m = 0. 35 kg 11

Impulse Why doesn’t the egg break? ? http: //www. youtube. com/watch? v=7 RSUjxi. Zn. ME 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. 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 1 AFTER Collision 2 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. 5 m/s to the right. Find the recoil velocity of Skater 1. BEFORE Explosion 1 2 AFTER Explosion 1 2 18

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 1 AFTER Collision 2 ? 1 2 ? This is the hardest type of problem since there are two pieces on both sides! 20

Elastic Collisions Example • 21

Elastic Collisions BEFORE Collision 1 AFTER Collision 2 ? 1 2 ? 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