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

Conserved Quantities Energy – has __________________ Motion – has only _______________ How does Nature conserve motion? Speed? Velocity? Mass x Velocity?

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

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

Impulse impulse = Ft force x time = change in momentum SI Unit: N·s = kg·m/s Ex. A 4000N force acts for 0.010s. impulse = Ft = ______________= 40 N·s

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

Impulse Example A braking force of 4000N acts for 0.75s on a 1000kg car moving at 5.0m/s. impulse = Ft = (-4000N)(0.75s) = -3000 N·s mDv = Ft = -3000 kg·m/s Dv = (-3000 kg·m/s)/1000kg = -3m/s vf = vi + Dv = ____________

Collisions “Brief” interaction between objects Objects share the collision force (N3L) 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)

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

Collisions elastic: total KE _________________ inelastic: total KE ________________ complete inelastic: objects move at _____________________ after collision, total KE decreases

Conservation of Linear Momentum

2 objects (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final Each car has mass 1000kg (1000)(10) + (1000)(0) = (1000)v + (1000)v 10,000 = 2000v v = 5 m/s

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

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 = ½mv2. K-final = ___________________________ ______ the original KE converted to heat, sound, etc.

2 dimensional p conservation

Example: m1 = 0.010kg, m2 = 1.0kg, v1i = 200m/s. Calculate vf (mom. cons.), Then calculate h (using energy).

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