Momentum, Impulse, and Collisions

Momentum (P)

A quantity that expresses the motion of a body and its resistance to slowing down.

P = mv P = momentum (kg.m/s or N.s) m = mass (kg) v = velocity (m/s)

Try it…

A toy car has a mass of 5kg. If it is moving at a velocity of 5m/s, what is its momentum?

25kg·m/s What is the momentum of a 25kg boy

moving at a speed of 1m/s?

25kg·m/s

Worksheet Answers

Project Time

Impulse

measures a change in momentum; arrived at by multiplying the average force acting on a body by the length of time it acts.

Impulse = F(t)

F = force (N or Newtons) t = time (s)

Another one…

An 8N force acts upon an object for 5 seconds. What impulse is given this object?

40N·s

Impulse-momentum Theorem

Force is reduced when the time interval of an impact is increased.

Examples Nets or giant air

mattresses used to catch people

Putting it all together… F=ma (Newton’s 2nd Law) a=Δv/t Insert “Δv/t” for “a” in “F=ma” This gives us “F=mΔv/t” Multiply by “t” to get-

F(t) = m(vf-vi) Notice impulse, on the left side, is equal to

the change in change in momentummomentum of an object.

Try it…

A ball changes velocity from 20m/s to 30m/s. If it has a mass of 5kg, what impulse was necessary to cause this change?

50N·s How long would it take a 5N force to

change the velocity of the ball?

(Hint: use Impulse=F(t))

10s

Law of Conservation of Momentum The Law of Conservation of Momentum:

The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

m1v1,i + m2v2,i = m1v1,f + m2v2,f

total initial momentum = total final momentum

Conservation of Momentum So far we only

have considered the momentum of only one object at a time.

Now we will look at two or more objects interacting with each other.

PICTURE THIS… You are playing pool.

You strike the cue ball it hits the 8 ball. The 8 ball had no momentum no momentum before they collided.

During the collision the cue ball loses loses momentum momentum and the 8 ball gains momentumgains momentum.

The momentum the cue ball loses is the same loses is the same amount that the 8 ball amount that the 8 ball gained.gained.

Momentum is Conserved Newton’s third law leads

to conservation of momentum

During the collision, the force exerted on each bumper car causes a change in momentum for each car.

The total momentum is the same before and after the collision.

Elastic Collisions A collision in which the total momentum and the

total kinetic energy are conserved is called an elastic collision.

Elastic means that after a collision the objects remain separated.

Two objects collide and return to their original shapes with no loss of total kinetic energy. After the collision the two objects move separately.

Both the total momentum and total kinetic energy are conserved.

Inelastic Collisions

Perfectly inelastic collisionA collision in which two objects stick

together after colliding and move together as one mass is called a perfectly inelastic collision.

Example: The collision between two football players during a tackle.

Video time

http://youtu.be/Dz5q0KKSlf4

http://www.youtube.com/watch?v=FSAR86MMJ2w&safety_mode=true&persist_safety_mode=1&safe=active

Kinetic Energy in Inelastic Collisions In an inelastic collision the total kinetic energy does not

remain constant when the objects collide and stick together.

Some energy is converted into sound energy and internal energy as the objects deform during the collision.

Elastic in physics refers to a material that when work is done to deform the material during a collision the same amount of work is done to return the material to its original shape.

Inelastic material does not return to its original shape and therefore some energy is converted to sound or heat.

Real Collisions

Most collisions are not perfectly inelastic (they don’t stick together and move as one)

Most collisions are not elastic. Even nearly elastic collisions result in some

decrease of kinetic energy.A football deforms when kickedA sound is produced (sound signifies a

decrease in kinetic energy)

For all intensive purposes…

We will consider all collisions in which objects do not stick together to be elastic collisions.

Therefore, total momentum and total kinetic energy will stay the same before and after the collision.

There are 2 types of collisions Elastic

m1iv1i + m2iv2i = m1fv1f + m2fv2fWhere 1 implies object 1, 2 implies object 2Where i implies initial & f implies final

Inelastic

m1iv1i + m2iv2i = mTvTWhere T implies total

Use + and – velocities to show direction.

Try these… A 2kg ball strikes another ball head on at an

initial velocity of +2m/s. If the second ball had a mass of 3kg and was initially moving at -1m/s, what is the final velocity of the 2kg ball if the vf of the 3kg ball is now +1.33m/s?

Set it up-

m1iv1i + m2iv2i = m1fv1f + m2fv2f

2kg(2m/s)+3kg(-1m/s) = 2kg(v1f)+3kg(1.33m/s)

v1f = -1.5m/s

Last one…

A 500kg car is driving at a velocity of 10m/s. Another car (700kg) hits it from behind at a velocity of 25m/s and the two cars interlock bumpers. What is the resulting velocity of the two cars?

Set it up-

m1iv1i + m2iv2i = mTvT

500kg(10m/s)+700kg(25m/s) = 1,200kg(vT)

vT = 18.75 m/s