6 Linear Momentum Collisions Motion and its conservation

6 Linear Momentum & Collisions • Motion and its conservation • Impulse-Momentum Theorem • Homework: • 6, 9, 13, 21, 40, 63, 72, 87. 1

Conserved Quantities • • • Energy – has _________ Motion – has only ________ How does Nature conserve motion? Speed? Velocity? Mass x Velocity? 2

Motion and Its Conservation Not Conserved Not Conserved stops smooth and level rough 3

Momentum • • • Momentum = mv Symbol: p , P. SI Unit: kg·m/s Ex. 1000 kg car moves at 8 m/s. mv = (1000 kg)(8 m/s) = _______ kg·m/s 4

Impulse • impulse = Ft • • force x time = change in momentum SI Unit: N·s = kg·m/s Ex. A 4000 N force acts for 0. 010 s. impulse = Ft = _______= 40 N·s 5

Impulse and Momentum • Impulse = Ft = ___________ • consequence of Newton’s 2 nd law that Ft = change in momentum • F = ma • Ft = mat • Ft = (m)(at) • Ft = (m)(Dv) • ___________ 6

Impulse Example • A braking force of 4000 N acts for 0. 75 s on a 1000 kg car moving at 5. 0 m/s. • impulse = Ft = (-4000 N)(0. 75 s) = -3000 N·s • m. Dv = Ft = -3000 kg·m/s • Dv = (-3000 kg·m/s)/1000 kg = -3 m/s • vf = vi + Dv • = ____________ 7

Collisions • • “Brief” interaction between objects Objects share the collision force (N 3 L) One object gets +Ft, the other gets –Ft. As a whole, they receive no impulse, thus no change in total momentum of this system (due to the collision) 8

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Conservation of Momentum (i. e. Motion): Initial Momentum (Motion): Final Momentum (Motion): (Since ) 10

Collisions • elastic: total KE _________ • inelastic: total KE ________ • complete inelastic: objects move at ___________ after collision, total KE decreases 11

Conservation of Linear Momentum 12

2 objects • • (m 1 v 1)initial + (m 2 v 2)initial = (m 1 v 1)final + (m 2 v 2)final Each car has mass 1000 kg (1000)(10) + (1000)(0) = (1000)v + (1000)v 10, 000 = 2000 v v = 5 m/s 13

When does Conservation of Momentum occur? • Answer: When Fnet = 0 (e. g. level frictionless surface) • or ________________ 14

Conservation of Momentum may occur when KE is lost • Ex: Mass m, Speed v, hits & sticks to another mass m, speed = 0. Final speed of each object is v/2. • K-initial = ½(m)(v)2 + 0 = ½mv 2. • K-final = ______________ • ______ the original KE converted to heat, sound, etc. 15

2 dimensional p conservation 16

Example: m 1 = 0. 010 kg, m 2 = 1. 0 kg, v 1 i = 200 m/s. • Calculate vf (mom. cons. ), Then calculate h (using energy). 17

Summary • momentum = mass x velocity • Ft = change-in-momentum • Momentum is conserved when net external forces are negligible • Momentum conservation may occur for elastic & inelastic collisions 18