MOMENTUM the product of mass and velocity Units are kgm/s, or any mass velocity combo Example: Which has more momentum, a 8000-kg hippo trotting at 1.5.

MOMENTUM

• the product of mass and velocity

vmp •Units are kg•m/s, or any mass velocity combo

•Example: Which has more momentum, a 8000-kg hippo trotting at 1.5 m/s or a 150-g bullet whizzing by at 1500 m/s?

hippo:1.2 x 104 kg•m/s

bullet: 225 kg•m/s

The second Law of Motion says any unbalanced force acting on an object will change its motion:

Change in momentum

IMPULSE

vmpimpulse

vmtF

tt

vmtF

amF

So….. tFimpulse

•Units of impulse are Ns or kgm/s

•Momentum, impulse and velocity are vectors: magnitude and direction must be considered

•A small force for a long period of time can cause the same change in momentum as a large force acting for a very short period of time

•The area under a force-time graph is the impulse acting on the object

F

t

impulse

Two Types of Collisions:1) Elastic collisions: kinetic energy is conserved.

2) Inelastic collisions: kinetic energy is not conserved.

•The bulls are moving slower after the collision, so kinetic energy is not conserved (inelastic)

• Momentum is conserved. (approx 0 kg•m/s before and after)

2) Inelastic collisions: kinetic energy is not conserved.

•The bulls are moving slower after the collision, so kinetic energy is not conserved (inelastic)

• Momentum is conserved. (approx 0 kg•m/s before and after)

Examples1.Determine the magnitude of the impulse required to stop a 1000 kg car moving at 21.0 m/s.

1. A 0.120 kg ball moving at 11.0 m/s strikes a solid massive steel wall. The ball bounces straight back at 8.9 m/s.

a.If the ball was in contact with the wall for 0.17 s, what is the magnitude of the force acting on the ball?

b. An identical ball with the same initial speed strikes a glass window. The window cracks and the ball stops in 0.17 s. Using principles of physics, explain which ball experiences the greater force.

The force multiplied by the change in time = change in momentum. Since both collisions occur in the same amount time, the ball that has the larger force acting on it is the ball in part “a” because it had the greatest change in momentum since it changed direction.

3. An object experiences a varying force as shown below. Which graph shows the largest change in momentum?

CONSERVATION OF MOMENTUM

Collisions:momentum is always conserved in collisionsmomentum before = momentum after

afterbefore pp

Example1. A 900 kg car is moving at 20.0 m/s when it collides with a 50.0 kg bale of hay at rest on the road. If the two objects remain together, determine their speed after the collision.

smv

vkgsmkg

ppp

pp

haycarhaycar

afterbefore

/9.18'

')950(0)/0.20)(900(

'

2. A 5.30 kg wagon is moving at 2.00 m/s to the right. A 0.180 kg blob of putty moving at 32.0 m/s also to the right strikes the wagon and sticks to it. With what speed will the wagon and the putty move after the collision?

Explosions:• Remember: if the momentum before the explosion is zero, then the momentum after the explosion is zero.

• When a gun fires, the bullet goes one way, the gun goes in the opposite way (recoil). The momentum adds up to zero.

gunbullet

bulletgun

afterbefore

pp

pp

pp

0

0

Example1.A 600 kg cannon fires a 35.0 kg person horizontally at 250 m/s, left. Determine the recoil velocity of the cannon.

smv

kg

smkgv

m

vmv

vmvm

pp

pp

pp

gun

gun

gun

bulletbulletgun

bulletbulletgungun

bulletgun

bulletgun

afterbefore

/6.14

600

/2500.35

0

0

vv