Momentum

Momentum The “Quantity of Motion” Unit: Vector p = momentum m = mass v = velocity Unit: Vector Direction of momentum is determined by the direction of the velocity

Momentum Newton’s 2nd Law of Motion in terms of momentum Net External Force = time rate of change of momentum External to the system

Momentum

Impulse I = Impulse F= force ∆t = change in time

Force vs Time Graphs F t Area = Impulse = Δp

Impulse Actual force experienced during a collision F t Area = Favg

Impulse - Problems Force on a 1 kg object F (N) If v = 0 at t = 0, find vf at t = 4 s 10 2 4 t (s)

Impulse - Problems Find the change in momentum 2 kg 3 m/s 2 kg - + If ∆t = 0.020 s, find the average force the wall exerts on the ball

Impulse - Problems If mass = 2 kg and v = 0 at t = 0, find vf at t = 12 s F (N) 20 t (s) 4 8 12

Momentum Find ΔP 10 m/s 40° 10 m/s m = 2 kg

Momentum Find ΔP 15 m/s 30° 15 m/s m = 3 kg 12

Momentum Example 2 cont’d m = 2 kg 10 m/s 6 m/s 60° 40° 13

Conservation of Momentum If no external unbalanced forces, so Conservation of momentum for a system w/ no external imbalance in forces Total initial momentum of a system = Total final momentum of a system

1-D Explosion Before 5 kg 10 kg After 10 kg 5 kg

2-D Explosions 6 kg 3 kg θ=? 6 kg 50 m/s 4 kg 3 kg 4 kg 30 m/s

Collisions and Explosions Before 10 m/s 2 kg 3 kg After θ=? 2 kg 3 kg 40◦ 2 m/s

Examples 3 kg 7 kg Before 3 kg 7 kg After 18

Examples 5 kg 7 kg Before 5 kg 7 kg After 19

Explosions and Collisions vf = ?  = ? ma= 950 kg vai= 16 m/s vbi= 21 m/s mb= 1300 kg

Types of Collisions Elastic Collisions – Kinetic energy is conserved KEi = KEf Inelastic collision – Some kinetic energy is lost Typically lost to friction, sound, deformation, etc. Most collisions in “real life” 21