Purdue University, Physics 220 Lecture 12 Momentum and Impulse Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Obama’s Momentum Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Impulse and Momentum Define Momentum Momentum is a VECTOR Define Impulse Change in momentum requires Force acting over a period of time or Impulse Dp = FDt or I = Dp Impulse: F t Vector Momentum transfer Work: Fr r Scalar Energy transfer Do some collisions to motivate idea Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Impulse and Momentum I  Ft = pf - pi = p impulse-momentum theorem For single object … F = 0  momentum conserved (p = 0) For collection of objects … ptotal = p Internal forces: forces between objects in system External forces: all other forces Fext = 0  total momentum conserved (ptot = 0) Lecture 11 Purdue University, Physics 220 1

Purdue University, Physics 220 1-D F vs t Plot Impulse is simply the area under the Fx(t) curve! Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 iClicker By what factor does an object’s kinetic energy change if its speed is doubled? By what factor does the magnitude of the momentum change? A) 0.5, 4 B) 2, 2 C) 4, 2 Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Pushing Off… Fred and Jane are on skates facing each other. Jane then pushes Fred with force F N2L Fred: FJF = mFred aFred DvFred = aFred Dt = (FJF/mFred) Dt mFred DvFred = FJF Dt N2L Jane: FFJ = mJane aJane DvJane = aJane Dt = (FFJ/mJane) Dt mJane DvJane = FFJ Dt N3L: For every action, there is an equal and opposite reaction. FFJ=-FJF mFred DvFred = -mJane DvJane a = v/t Do some collisions to motivate idea Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Pushing Off… Fred (75 kg) and Jane (50 kg) are on skates facing each other. Jane then pushes Fred with a constant force F = 45 N for a time Dt=3 seconds. Who will be moving fastest at the end of the push? A) Fred B) Same C) Jane Jane F = +45 [N] (positive direct.) I = +45  3 [N*s] = 135 [N*s] I = Dp = mvf – mvi I/m = vf - vi vf = 135 [N*s] / 50 [kg] = 2.7 [m/s] Fred F = -45 [N] Newton’s 3rd law I = -45  3 [N*s] = -135 [N*s] I = Dp = mvf – mvi I/m = vf - vi vf = -135 [N*s] / 75 [kg] = -1.8 [m/s] Note: pFred + pJane = (1.8) 75 + (-2.7) 50 = 0! Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Momentum is Conserved Define Momentum p = m v m1 Dv1 = -m2 Dv2 Dp1 = -Dp2 Dp1+p2) = Dp = 0 pinitial = pfinal Example: Jane pushes Fred so he is going 2.0 m/s. If Fred is twice as heavy as Jane, how fast does Jane end up moving. 0 = mFred vFred + mJane vJane vJane = -mFred vFred / mJane = -4 m/s Momentum is conserved p1f-p1i+p2f-p2i=0 p1f+p2f=p1i+p2i Do some collisions to motivate idea Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Momentum is a Vector A car with mass 1200 kg is driving north at 40 m/s, and turns east driving 30 m/s. What is the magnitude of the car’s change in momentum? A) 0 B) 12,000 C) 36,000 D) 48,000 E) 60,000 pinitial = m vinitial = (1200 kg) x 40 m/s = 48,000 kg m/s North pfinal = m vfinal = (1200 kg) x 30 m/s = 36,000 kg m/s East North-South: pNSfinal – pNSinitial = (0 – 48000) = -48,000 kg m/s East-West: pEWfinal – pEWinitial = (36000 - 0) = +36,000 kg m/s 40 m/s 30 m/s Magnitude: Sqrt(pNS2 + pEW2 ) = 60,000 kg m/s Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Soft vs Hard Impact 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) Floor B) Foam C) the same I = Dp Same change in momentum In which case is the average force greater A) Floor B) Foam C) the same Dp = F Dt F = Dp/Dt smaller Dt -> large F Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Bouncy vs Sticky Ball 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 p=mv = mat = Ft = I Bouncing Ball |I| = |Dp| = |mvfinal – m vinitial| = |m( vfinal - vinitial)| = 2 m v Sticky Ball |I| = |Dp| = |mvfinal – m vinitial| = |m(0 - vinitial)| = m v Might Add numbers here. Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Bouncy vs Sticky Ball 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 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 Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Question Two objects are known to have the same kinetic energy. Do these two objects necessarily have the same momentum? A) Yes B) No Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 iClicker At the instant a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. Which object has the greater kinetic energy? A) The same B) The gun C) The bullet Apply conservation of momentum: Pi=0 Pf=MgunVgun+mbulletvbullet Vgun=-(mbullet/Mgun)vbullet Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Outline We have learned: Work-Energy Theorem F = m a multiply both sides by Dx F Dx = m a Dx (note: aDx = ½ Dv2) F Dx = ½ m Dv2 W = DK Defines Work and Kinetic Energy We will learn: Impulse-Momentum Theorem F = m a multiply both sides by Dt F Dt= m a Dt (note: aDt = Dv) F Dt= m Dv I = Dp Defines Impulse and Momentum Lecture 11 Purdue University, Physics 220

Purdue University, Physics 220 Newton’s Second Law New formulation of Newton’s 2nd Law Lecture 11 Purdue University, Physics 220 1