MOMENTUM AND IMPULSE

Momentum-The quantity that describes the mass and velocity of an object. Vector quantity.

momentum = mass x velocity

ρ = mv

m= mass(kg) v= velocity (m/s) ρ= momentum (kgm/s)

Ex 1- A 0.06kg tennis ball travels at 23m/s after being hit. What is its momentum?

ρ = mvρ= 0.06kg (23m/s)ρ= 1.4 kgm/s

What caused the momentum of the tennis ball?

Impulse- The properties that change the momentum of an object

Impulse = Force x contact time

J = Fnet t

F= force (N) t- time(sec) J= impulse (Ns)

EX 2: If the tennis racquet applies 5.6N of force for 0.25 seconds, what is the impulse acting on the ball?

J = Fnet t

J = 5.6N(0.25sec)

J = 1.4 Ns

Impulse-momentum theory- the momentum gained by an object is equal to the impulse that caused the motion.

F= m a or F = mΔv t

SO

Ft=mΔv or J = Δρ

Following through when swinging a bat will increase the contact time for the applied force. This will increase the gain in momentum of the baseball.

More mass increases the net force. This will create more momentum for a football player that’s tackling another player.

Ex3: A 19620.0 N car is accelerated from rest by a net force of 1000N. How long does it take the car to reach a velocity of 25m/s?

Fg= mg

19620.0N = m 9.81 m/s2

m= 2000kg Fnett = mΔv

1000N( t) = 2000kg (25m/s) t = 50 seconds

CONSERVATION OF MOMENTUM

Conservation of momentum- total momentum before the collision is equal to the total momentum after the collision.

COLLISIONS

A) Elastic collision- No energy is lost. Occur in ideal situations and between atomic and nuclear particles.

B) Inelastic collision- Energy is lost and velocities change. In a complete inelastic collision the bodies stick together and have the same velocity.

Ex 1: A 25.0g ball traveling at 5.0m/s collides with a 50.0g ball traveling in the opposite direction. After colliding, they come to a complete stop. What is the velocity of the second ball?

m1 =.025kg ρbefore = ρ after

m2= .05kg m1v1 + m2v2 = 0

V1 = 5.0m/s .025kg(5m/s) + .05kg(v2)= 0

V2= ? .05kg(v2)= -.125kgm/s

ρ=0 after collision v2 = -2.5m/s

(-) indicates opposite direction

Ex 2: A 2275kg car moving at 28m/s hits the backend of a 1875kg car traveling at 16m/s in the same direction. If the cars move off together what is their new velocity?

Before After m 1 =2275kg m1 =2275kg

v 1= 28m/s v1 = v2

m2 =1875kg m2 =1875kg

v 2 =16m/s

Set up formula and substitute ρ before = ρafter

ρ1 + ρ2 = ρ1 + ρ2

m1v1+ m2v2 = m1v1 + m2v1

2275kg(28m/s) + 1875kg(16m/s) = 2275kg(v1) + 1875(v1)

63700kgm/s + 30000kgm/s = 4150 v1

93700kgm/s = 4150 v1

v1= 22.58m/s = v2