Impulse Momentum From Newton 2 Previously WorkEnergy Fma

From Newton 2: • Previously: Work-Energy § F=ma multiply both sides by d §

From Newton 2: Two New Concepts Impulse & Momentum Impulse = Change in Momentum;

Preflight 1 A few weeks ago I did a lecture demonstration where I yanked

Preflight 2 & 3 Is it possible for a system of two objects to

Change in Momentum ACT If the bear and the ball have equal masses, which

Change in Momentum ACT 2 A 10 kg cart collides with a wall and

ACTs You drop an egg onto 1) the floor 2) a thick piece of

Pushing Off… Fred (75 kg) and Jane (50 kg) are at rest on skates

Momentum Change ACT A car w/ mass 1200 kg is driving north at 40

Impulse and Momentum Summary Fave t I = pf - pi = p •

• 4. • • IP Two air track carts move toward one another

• 9. • In a typical golf swing, the club is in contact

• 5. • • A 0. 150 -kg baseball is dropped from rest.

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Impulse & Momentum

From Newton 2: • Previously: Work-Energy § F=ma multiply both sides by d § F d= m a d (note a d = ½ v 2) § F d= ½ m v 2 § W = KE § Define Work and Kinetic Energy 08

From Newton 2: Two New Concepts Impulse & Momentum Impulse = Change in Momentum; Momentum is vector in direction of velocity. Impulse N-s Change In Momentum Kg m/s Impulse is vector in direction of force.

Preflight 1 A few weeks ago I did a lecture demonstration where I yanked a tablecloth out from under some dishes. Can you briefly explain why the dishes were not given much impulse by the tablecloth. Impulse is defined as force time the change in time. If the change in time is very small, the impulse is going to be small. The dishes just didn’t feel like moving… The cloth may have been made out of a slick material (i. e. silk) so the friction is negligible… 11

Preflight 2 & 3 Is it possible for a system of two objects to have zero total momentum while having a non-zero total kinetic energy? 67% 1. YES 33% 2. NO correct yes, when two objects have the same mass and velocities and they push off each other. . momentum is zero and kinetic energy is nonezero. 2 balls traveling at the same speed hit each other head-on.

Change in Momentum ACT If the bear and the ball have equal masses, which toy experiences the greater change in momentum? Change in momentum: p = pafter - pbefore Teddy Bear: p = 0 -(-mv) = mv Bouncing Ball: p = mv-(-mv) = 2 mv

Change in Momentum ACT 2 A 10 kg cart collides with a wall and changes its direction. What is its change in xmomentum px? y x a. -30 kg m/s b. -10 kg m/s c. 10 kg m/s d. 20 kg m/s e. 30 kg m/s

ACTs 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) Floor B) Foam C) the same I = P Same change in momentum same impulse In which case is the average force greater A) Floor p = F t B) Foam F = p/ t C) the same Smaller t = larger F

Pushing Off… Fred (75 kg) and Jane (50 kg) are at rest on skates facing each other. Jane then pushes Fred w/ a constant force F = 45 N for a time t=3 seconds. Who will be moving fastest at the end of the push? A) Fred B) Same Fred F = +45 N (positive direct. ) I = +45 (3) N-s = 135 N-s I = p = mvf – mvi I/m = vf - vi vf = 135 N-s / 75 kg = 1. 8 m/s C) Jane F = -45 N Newton’s 3 rd law I = -45 (3) N-s = -135 N-s I = p = mvf – mvi I/m = vf - vi vf = -135 N-s / 50 kg = -2. 7 m/s Note: Pfred + Pjane = (1. 8) 75 + (-2. 7) 50 = 0!

Momentum Change ACT A car w/ 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: Pfinal – Pinitial = (0 – 48000) = -48, 000 kg m/s 30 m/s East-West: Pfinal – Pinitial = (36000 - 0) = +36, 000 kg m/s Magnitude : Sqrt(P 2 North – P 2 East ) = 60, 000 kg m/s 40 m/s

Impulse and Momentum Summary Fave t 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

• 4. • • IP Two air track carts move toward one another on an air track. Cart 1 has a mass of 0. 45 kg and a speed of 1. 1 m/s. Cart 2 has a mass of 0. 65 kg. (a) What speed must cart 2 have if the total momentum of the system is to be zero? (b) Since the momentum of the system is zero, does it follow that the kinetic energy of the system is also zero? (c) Verify your answer to part (b) by calculating the system’s kinetic energy.

• 9. • In a typical golf swing, the club is in contact with the ball for about 0. 0010 s. If the 45 -g ball acquires a speed of 67 m/s, estimate the magnitude of the force exerted by the club on the ball. • •

• 5. • • A 0. 150 -kg baseball is dropped from rest. If the magnitude of the baseball’s momentum is just before it lands on the ground, from what height was it dropped?