Physics 101: Lecture 11 Momentum and Impulse

Key Ideas Last Time: Work-Energy This Time: Impulse-Momentum S F = m a multiply both sides by d S F d= m a d (note a d = ½ Dv2) S F d= ½ m Dv2 S W = DKE Define Work and Kinetic Energy This Time: Impulse-Momentum S F = m a multiply both sides by Dt S F Dt= m a Dt (note a Dt = Dv) S F Dt= m Dv S I = Dp Define Impulse and Momentum 08

Demo/Example Two identical balls are dropped from the same height onto the floor. In each case they have velocity v downward just before hitting 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 magnitude of the impulse given to the ball by the floor the biggest? A. Case 1 B. Case 2 C. The same Bouncing Ball Sticky Ball Might Add numbers here. 16

Question 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? A. Upward B. Downward time 19

Demo I = DP Same change in momentum Dp = F Dt F = Dp/Dt You throw an egg into 1) A sheet 2) A wall In both cases, the egg stops. In which case is the impulse greater? A) Sheet B) Wall C) the same I = DP Same change in momentum In which case is the average force greater A) Sheet B) Wall C) the same Dp = F Dt F = Dp/Dt Smaller Dt = large F 24

Example: stopping car m = 1500 kg Vo=40 m/s How long does it take the car to stop? µs = 0.6

Momentum is Conserved This is a BIG deal! Momentum is “Conserved” meaning it can not be created nor destroyed Can be transferred Total Momentum does not change with time. This is a BIG deal! Maybe do example of conservation (like cookies) and counter example. Force is NOT conserved. 30

Example: collision “before” “after” M2=3kg M2=3kg M1=2kg M1=2kg Vo = 0m/s Vo = 5m/s M2=3kg M2=3kg M1=2kg M1=2kg Two blocks collide and stick together, what is their final velocity?

Example: collision “before” “after” M2=3kg M2=3kg M1=2kg M1=2kg Vo = 2m/s Vo = 5m/s M2=3kg M2=3kg M1=2kg M1=2kg Two blocks collide and stick together, what is their final velocity?

Example: cannon (explosion) mc = 200kg What is the velocity of the cannon? mb = 5 kg v = 300 m/s

Explosions A=1, B=2, C=same Example: m1 = M/3 m2 = 2M/3 “before” “after” M m1 m2 A=1, B=2, C=same v1 v2 Example: m1 = M/3 m2 = 2M/3 Which block has larger |momentum|? Each has same |momentum| Which block has larger speed? 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 mechanical (kinetic) energy conserved? NO!! 0 = p1+p2 p1= -p2 35

Impulse and Momentum Summary Collisions and Explosions Draw “before”, “after” Define system so that Fext = 0 Set up axes Compute Ptotal “before” Compute Ptotal “after” Set them equal to each other 33 1

Summary Impulse I = FDt Momentum p = mv Momentum is VECTOR Gives change in momentum I = Dp Momentum p = mv Momentum is VECTOR Momentum is conserved (when SF = 0) S mvinitial = S mvfinal 50