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Unit 6: Momentum and Impulse (Chapter 7). Momentum. What does it mean to have momentum?. 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?
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Momentum What does it mean to have momentum?
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.
Momentum • All objects in motion have momentum! • What factors determine how much momentum an object has?
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
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
Varying Forces • Forces are not always constant. Many forces change as they are applied over a period of time. 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. Average Force (F) t0 tf
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.
Impulse-Momentum Theorem • Remember Newton’s 2nd Law: • And acceleration is defined as • Substitute: • Rearrange: Impulse-Momentum Theorem
Impulse-Momentum Theorem • Another way to write the theorem is: • In words: Impulse = Change in Momentum
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
Impulse Why doesn’t the egg break?? http://www.youtube.com/watch?v=7RSUjxiZnME
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
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.
Collisions in 1-DimensionInelastic • Inelastic collision- a collision in which the objects stick together and move with one common velocity after colliding. • 2 objects 1 object
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 1 2 1 2
Explosions • Explosion- process of one object splitting into 2 (or more) objects • Recoil- kickback; momentum opposite a projectile • 1 object 2 objects (or more)
Explosions • Explosion- process of one object splitting into 2 (or more) objects • Recoil- kickback; momentum opposite a projectile • 1 object 2 objects (or more)
Explosions • Explosion- process of one object splitting into 2 (or more) objects • Recoil- kickback; momentum opposite a projectile • 1 object 2 objects (or more)
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 1 2 1 2
Collisions in 1-DimensionElastic • Elastic collision – a collision in which the colliding objects bounce off each other. • 2 objects stay 2 objects
Elastic Collisions BEFORE Collision AFTER Collision ? ? 1 2 1 2 This is the hardest type of problem since there are two pieces on both sides!
Elastic Collisions BEFORE Collision AFTER Collision ? ? 1 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!
Is Kinetic Energy Conserved? • Elastic Collision: KE is conserved • Inelastic Collision: KE is NOT conserved
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. • Find the initial westerly velocity of the Jeep. • Was the jeep speeding?