6 – 1 Momentum and Impulse 6 – 2 Conservation of Momentum Chapter 6 6 – 1 Momentum and Impulse 6 – 2 Conservation of Momentum

Momentum: the product of an object’s mass and velocity, a vector p = mv SI unit = kgm/s If the boulder and the boy have the same momentum will the boulder crush the boy? Hint: Which would have the larger speed?

To change an object’s momentum you must apply a force Example:  Wall exerts a force of 10,000 N. The contact time is 0.01 s. I = Impulse = F t            = 100 Ns

D(p) = Change in momentum = (mv)final - (mv)initial  = 0 - mv = - mv Ignoring negative sign: D(mv) = mv

Impulse-momentum theorem: Impulse = change in momentum FDt = Dp Only valid when force is constant

Impulse and Contact Time

Ex: A 0.11 kg softball moving at 12 m/s is hit by the batter; afterward the ball flies off at 15 m/s. If the time interval was 1.3 x10-3 s what force did the batter apply to the ball? Given: m = 0.11kg, vi = 12 m/s, vf = -15 m/s, Dt = 1.3 x10-3 s F = ? FDt = Dp F = Dp/ Dt F = (pf – pi )/ Dt F = m(vf – vi )/ Dt F = 0.11kg (-15 m/s – 12 m/s) / 1.3 x10-3 s F = -2.28 x103 N

Law of conservation of momentum: the total momentum of all objects interacting with each other is constant provided no external forces are involved pi = pf (in the absence of friction)

For example – firing a rifle Momentum Before = 0 ------------- Momentum After = 0 ------------- After firing, the opposite momenta cancel.

pi = pf 0 = M v + m V - M v = m V v = m V/ - M v = (0.010 kg)(300 m/s )/ - (4 kg)           v = -3 / 4 m/s = - 0.75 m / s