Impulse

Linear Momentum Momentum is the measure of inertia in motion. Momentum equals mass times velocity Momentum is symbolized by p Like velocity, momentum is a vector. Momentum is parallel to velocity p m v

Applying Force Newton’s law uses mass and acceleration. Acceleration is the time rate of change of velocity. If the mass is constant the force depends on momentum.

Change in Momentum A force acting during a time changes momentum. The change in momentum is called the impulse (J).

Storm Force At 60 mph the momentum of the air is due to the mass (m) and velocity (v). At 120 mph the speed is double. Half as much time to get the same amount of mass p = mv p = m(2v)

Nonzero Force When momentum changes in a system, an external force has acted. Constant force like gravity Position-dependent force like the elastic force Time-dependent force during brief contact pi pf F(t) before after

Force of Collision Collisions seem instantaneous. They actually take place during a short time span. The force (an elastic force) greatly increases during the contact, then decreases.

Impulsive Force A karate strike to a board can break it. Mass of the hand: 0.70 kg Weight of the hand: 6.9 N Velocity of the hand: 5.0 m/s Thickness: 1.6 cm pi = -(0.7 kg)(5.0 m/s) = -3.5 kg m/s pf = 0 J = pf - pi = 3.5 kg m/s directed upwards on the hand

Average Force The average force is the constant force that gives the same impulse in the same time. Impulse = area under force vs. time curve

Brief Time Breaking an object benefits from a short time interval. The average force is about a hundred times larger than the weight. Dt = Dy / vav = Dy / (v/2) = (0.016 m) / (2.5 m/s) = 6.4 ms Fav = J / Dt = (3.5 kg m/s)/(0.0064 s) = 550 N