Physics 101: Chapter 7Impulse and Momentum • Today’s lecture will cover Textbook Sections 7.1 - 7.5
correct Chapter 7, Preflight Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the impulse given to the ball by the floor the biggest? [See conceptual example 3] 1. Case 1 2. Case 2 3. The same The impulse-momentum theory says that the impulse that acts on an object is given by the change in the momentum of the object, and this change is proportional change in velocity. The ball that sticks has a velocity of downward to zero, but the velocity of the ball that bounces goes downward then upward. This change in momentum is greater and therefore has a greater impulse on it.
correct time Chapter 7, Preflight In both cases of the above question, the direction of the impulse given to the ball by the floor is the same. What is this direction? 1. Upward 2. Downward
You drop an egg onto 1) the floor 2) a thick piece of foam rubber In both cases, the egg does not bounce. In which case is the impulse greater? A) case 1 B) case 2 C) the same correct In which case is the average force greater A) case 1 B) case 2 C) the same correct Define momentum conservation
Impulse and Momentum Summary Favet I = pf - pi = p • For single object…. • F = 0 momentum conserved (p = 0) • For collection of objects … • Fext = 0 total momentum conserved (Ptot = 0) • Fext = mtotal a
correct Chapter 7, Preflight Is it possible for a system of two objects to have zero total momentum while having a non-zero total kinetic energy? 1. YES 2. NO the example of the ice skaters starting from rest and pushing off of each other...the total momentum is zero because they travel in opposite directions but the kinetic energy is not zero (they start with none and gain a bunch) if the objects have the same mass and velocities that cancel each other out, the total momentum is zero. but they still have kinetic energy, because they are moving, and the velocities are squared there so direction doesn't matter.
correct pgun = -pbullet Chapter 7, Preflight Movies often show someone firing a gun loaded with blanks. In a blank cartridge the lead bullet is removed and the end of the shell casing is crimped shut to prevent the gunpowder from spilling out. When a gun fires a blank, is the recoil greater than, the same as, or less than when the gun fires a standard bullet? 1. greater than 2. same as 3. less than If there is no bullet then pbullet = 0 so pgun = 0 As if ice skater had no one to push…
“before” m2 m1 “after” m2 m1 “before” M “after” m2 m1 Collisions Procedure • Draw “before”, “after” • Define system so that Fext = 0 • Set up axes • Compute Ptotal “before” • Compute Ptotal “after” • Set them equal to each other Explosions
CORRECT Chapter 7, Preflight A railroad car is coasting along a horizontal track with speed V when it runs into and connects with a second identical railroad car, initially at rest. Assuming there is no friction between the cars and the rails, what is the speed of the two coupled cars after the collision? 1. V 2. V/2 3. V/4 4. 0
CORRECT Chapter 7, Preflight What physical quantities are conserved in the above collision? 1. Only momentum is conserved 2. Only total mechanical energy is conserved 3. Both are conserved 4. Neither are conserved Momentum is conserved because the sum of external forces equal to zero. Total mechanical energy is not conserved because some of the energy is lost when the car runs into the other car.
CORRECT Chapter 7, Preflight Is it possible for a system of two objects to have zero total momentum and zero total kinetic energy after colliding, if both objects were moving before the collision? 1. YES 2. NO if both objects are moving in oposite directions with the same mass and velocity they would have a resulting velocity of zero. i really just dont think it is possible. but if i am wrong, i am sure you will have a great demo to make me feel dumb for answering the wrong question.
Some Terminology • Elastic Collisions: collisions that conserve energy • Inelastic Collisions: collisions that do not conserve energy • Completely Inelastic Collisons: objects stick together Demo: perfectly inelastic collision
Chapter 7, Ballistic Pendulum L L V=0 L L m H v M + m V M A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m+M rise to a height of H. Given H, what is the initial speed v of the projectile? See example 9 in textbook
“before” M “after” m2 m1 Explosions v2 v1 • Example: m1 = M/3 m2 = 2M/3 • Which block has larger momentum? • Each has same momentum • Which block has larger velocity? • mv same for each smaller mass has larger velocity • Which block has larger kinetic energy? • KE = mv2/2 = m2v2/2m = p2/2m • smaller mass has larger KE • Is energy conserved? • NO!!
y x before after Collisions or Explosions in Two Dimensions • Ptotal,x and Ptotal,y independently conserved • Ptotal,x,before = Ptotal,x,after • Ptotal,y,before = Ptotal,y,after
M Explosions “before” B A Which of these is possible? A B both
Shooting Pool... • Assuming • Collision is elastic (KE is conserved) • Balls have the same mass • One ball starts out at rest • Then the angle between the balls after the collision is 90o pf pi vcm Pf F before after
Shooting Pool... • Tip: If you shoot a ball spotted on the “dot”, you have a good chance of scratching !
Center of Mass = Balance point L m m L m 5m Center of Mass Example 1: xCM = (0 + mL)/2m = L/2 Example 2: xCM = (0 + 5mL)/6m = 5L/6 X=0 X=L
Center of Mass (Preflight 6) Shown is a yummy doughnut. Where would you expect the center of mass of this breakfast of champions to be located? Homer: "mmmm.....donut...(slobbering)...center of mass in tummy...." Flanders: "why no diddly-o there Homer. The center of mass would be in the center of the hole." Homer: "Doe!" Normally it's the geometric center, but since the geometric center isn't there....i'd have to guess that it'd be located evenly around the donut. The mass is, in other words, evenly distributed around the donut.
Center of Mass Ptot = MtotVcm FextDt = DPtot = MtotDVcm So is Fext= 0 then Vcm is constant Also: Fext = Mtotacm Center of Mass of a system behaves in aSIMPLEway- moves like a point particle!- velocity of CM is unaffected by collision if Fext = 0