02/24/2003 Physics 103, Spring 2003, U. Wisconsin1 Physics 103: Lecture 10 Impulse and Momentum l Today’s lecture will cover the following new Concepts: çImpulse çMomentum çImpulse-Momentum Theorem çMomentum Conservation

02/24/2003 Physics 103, Spring 2003, U. Wisconsin2 Impulse and Momentum l Impulse = average force times time çI = F ave  t (nothing new….. Newton’s second law) Assumption: mass m of the object is constant not necessary, but otherwise there are complications.

02/24/2003 Physics 103, Spring 2003, U. Wisconsin3 You drop an egg onto a) the floor b) 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 In which case is the average force greater A) case 1 B) case 2 C) the same correct Questions

02/24/2003 Physics 103, Spring 2003, U. Wisconsin4 Preflight Lecture 10 No.1 The impulse delivered to a body by a force is 1. defined only for interactions of short duration. 2. equal to the change in momentum of the body. 3. equal to the area under an F versus x graph. 4. defined only for elastic collisions. Often useful in this situation, but not ONLY equal to the area under an F versus t graph! it is defined for all collisions elastic and inelastic!

02/24/2003 Physics 103, Spring 2003, U. Wisconsin5 Preflight Questions 2 & 3 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? 1. Case 1 2. Case 2 3. The same the impulse is greater for case one because... the change in momentum of the object... is proportional to the change in velocity which is greater in case one because it has a greater final velocity (down then up) than case 2 (which is only from down to zero). Impulse must be greater for case 1. Example: suppose m=1 kg, v(initial)=-1 m/s mv(initial)= -1 kg-m/s Case 1 mv(final)= +1 kg-m/s Impulse = 1- (-1)=2 Case 2 mv(final)= 0 Impulse = = 1 correct

02/24/2003 Physics 103, Spring 2003, U. Wisconsin6 Preflight Question 4 & 5 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 time correct

02/24/2003 Physics 103, Spring 2003, U. Wisconsin7 Preflight Questions 6, 7 & 8 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 in an isolated system, two ice skaters starting at rest and pushing on one another will move in opposite directions thus the momenta of the two are equal and opposite and total momentum is zero. but they are moving apart after the push and therefore the KE is non-zero. two hockey pucks moving towards each other with the same speed on a collision course have zero total momentum, but a non zero total kinetic energy correct

02/24/2003 Physics 103, Spring 2003, U. Wisconsin8 Impulse and Momentum l Momentum-Impulse Theorem çF ave  t  I = p f - p i =  p l For single object…. çF = 0  momentum conserved (  p = 0) For a collection of objects … o F ext = 0  total momentum conserved “External” is a VERY important qualifier oF ext = m total a

02/24/2003 Physics 103, Spring 2003, U. Wisconsin9 Some Terminology Elastic Collisions : collisions that conserve kinetic energy Inelastic Collisions: collisions that do not conserve kinetic energy * Completely Inelastic Collisons: objects stick together

02/24/2003 Physics 103, Spring 2003, U. Wisconsin10 Elastic Collision in 1-Dimension

02/24/2003 Physics 103, Spring 2003, U. Wisconsin11 Elastic Collision Magnitude of relative velocity is conserved.

02/24/2003 Physics 103, Spring 2003, U. Wisconsin12 Preflight Lecture 10 No.9 In an elastic collision 1. kinetic energy is conserved. 2. momentum is conserved. 3. the magnitude of the relative velocity is conserved. 4. all of the above are correct. True by definition of elastic True by definition of collision Total momentum is unchanged

02/24/2003 Physics 103, Spring 2003, U. Wisconsin13 Preflight Lecture 10 No.10 In an inelastic collision 1. both kinetic energy and momentum are conserved. 2. only kinetic energy is conserved. 3. only momentum is conserved. 4. neither kinetic energy nor momentum are conserved. False by definition of inelastic collision False by definition of collision

02/24/2003 Physics 103, Spring 2003, U. Wisconsin14 Collisions “before” m1m1 m2m2 “after” m1m1 m2m2 Explosions “before” M “after” m1m1 m2m2 Draw “before”, “after” Define system so that F ext = 0 Set up axes Compute P total “before” Compute P total “after” Set them equal to each other Procedure

02/24/2003 Physics 103, Spring 2003, U. Wisconsin15 Conceptual Example Consider two blocks (mass m and M) sliding toward one another (with velocities v m and v M ) on a frictionless plane. m M vmvm vMvM What happens after the collision? What does your result depend on? How would the answer change if there was friction between the blocks and the plane? P m + P M = P m + P M Is the collision elastic or? Energy would be lost during the motion. We would need initial distances to calculate!

02/24/2003 Physics 103, Spring 2003, U. Wisconsin16 Draw “before” and “after” “before” “after” 2m vfvf System = two blocks Axis: postive to right Before: P total,before = mv + (-mv) = 0 ! After: P total,after = (2m)v f P total,before = P total,after 0 = (2m)v f v f = 0 ! Therefore KE after = 0 m m v v Totally Inelastic Head-on Collision

02/24/2003 Physics 103, Spring 2003, U. Wisconsin17 Preflight Question 11 & 12 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 correct Impulse is the same in the two cases

02/24/2003 Physics 103, Spring 2003, U. Wisconsin18 Explosions “before” M Example: m 1 = M/3 m 2 = 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 = mv 2 /2 = m 2 v 2 /2m = p 2 /2m  smaller mass has larger KE Is kinetic energy conserved? *NO!! “after” m1m1 m2m2 v1v1 v2v2

02/24/2003 Physics 103, Spring 2003, U. Wisconsin19Example l A rocket of mass 200 kg is fired at with the vertical component of the initial velocity 1000 m/s and the horizontal component of 300 m/s. When it reaches the highest point on the trajectory an explosion occurs. The rocket is split in half and part A develops a vertical component to its velocity of 100 m/s. How far from the launching point does part A hit the ground? (Assume the ground is flat and use g = 10 m/s 2.) a)60.0 km b)65.8 km c)63.15 km t down t1t1 t2t2

02/24/2003 Physics 103, Spring 2003, U. Wisconsin20Solution

02/24/2003 Physics 103, Spring 2003, U. Wisconsin21Reprise 3) Kinetic energy may be conserved (elastic) or may not (inelastic) 2)Conservation of Momentum is useful. Depends (as always) on the situation. 1a) Impulse is average force times time of action 1b) Momentum is mass times velocity.