Physics 103: Lecture 10 Impulse and Momentum

Physics 103: Lecture 10Impulse and Momentum • Today’s lecture will cover the following new Concepts: • Impulse • Momentum • Impulse-Momentum Theorem • Momentum Conservation Physics 103, Spring 2003, U. Wisconsin

Impulse and Momentum (nothing new….. Newton’s second law) • Impulse =average force times time • I =Favet Assumption: mass m of the object is constant not necessary, but otherwise there are complications. Physics 103, Spring 2003, U. Wisconsin

Questions correct correct 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 Physics 103, Spring 2003, U. Wisconsin

Preflight Lecture 10 No.1 • The impulse delivered to a body by a force is • defined only for interactions of short duration. • equal to the change in momentum of the body. • equal to the area under an F versus x graph. • 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! Physics 103, Spring 2003, U. Wisconsin

Preflight Questions 2 & 3 correct 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/sImpulse = 1- (-1)=2 Case 2 mv(final)= 0 Impulse = 1 - 0 = 1 Physics 103, Spring 2003, U. Wisconsin

Preflight Question 4 & 5 correct time 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 Physics 103, Spring 2003, U. Wisconsin

Preflight Questions 6, 7 & 8 correct 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 Physics 103, Spring 2003, U. Wisconsin

Impulse and Momentum “External” is a VERY important qualifier • Momentum-Impulse Theorem • Favet I= pf- pi=p • For single object…. • F = 0  momentum conserved (p = 0) • For a collection of objects … • Fext = 0  total momentum conserved • Fext = mtotal a Physics 103, Spring 2003, U. Wisconsin

Some Terminology • Elastic Collisions: • collisions that conserve kinetic energy • Inelastic Collisions: • collisions that do not conserve kinetic energy • Completely Inelastic Collisons: • objects stick together Physics 103, Spring 2003, U. Wisconsin

Elastic Collision in 1-Dimension Physics 103, Spring 2003, U. Wisconsin

Elastic Collision Magnitude of relative velocity is conserved. Physics 103, Spring 2003, U. Wisconsin

Preflight Lecture 10 No.9 • In an elastic collision • kinetic energy is conserved. • momentum is conserved. • the magnitude of the relative velocity is conserved. • all of the above are correct. • True by definition of elastic • True by definition of collision • Total momentum is unchanged Physics 103, Spring 2003, U. Wisconsin

Preflight Lecture 10 No.10 • In an inelastic collision • both kinetic energy and momentum are conserved. • only kinetic energy is conserved. • only momentum is conserved. • neither kinetic energy nor momentum are conserved. • False by definition of inelastic collision • False by definition of inelastic collision • False by definition of collision Physics 103, Spring 2003, U. Wisconsin

Collisions “before” m2 m1 “after” m2 m1 “before” M “after” m2 m1 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 Physics 103, Spring 2003, U. Wisconsin

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

Totally Inelastic Head-on Collision v v m m Axis: postive to right “after” 2m vf Draw “before” and “after” “before” System = two blocks • Before:Ptotal,before =mv + (-mv) = 0 ! • After:Ptotal,after =(2m)vf • Ptotal,before = Ptotal,after • 0 = (2m)vf • vf = 0 ! • Therefore KEafter = 0 Physics 103, Spring 2003, U. Wisconsin

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

“before” v2 “after” v1 M m2 m1 Explosions • 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 kinetic energy conserved? • NO!! Physics 103, Spring 2003, U. Wisconsin

Example t2 tdown t1 • 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/s2.) 60.0 km 65.8 km 63.15 km Physics 103, Spring 2003, U. Wisconsin

Solution Physics 103, Spring 2003, U. Wisconsin

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

Physics 103: Lecture 10 Impulse and Momentum