Chapter 6Momentum and Collisions

…What Would You Rather Be Hit With!!!!

Today’s Choices Are……Mr. Friel’s Dry Erase Marker!!!…Mr. Friel’s Whiffle Ball !!!…Mr. Friel’s 10.00 kg shot put!!!

Now Choose!!!!!

Let’s Play…

Why did you make your decision?

Now…the Bonus Round!!!

Who would you rather have throw the object?…Mr. Frielor…Aroldis Chapman, 105 mph flamethrower for the Cincinnati Reds

What factors were involved in your decision?- mass- velocity

Remember, Fnet = ma = m (Δv/Δt)

- it takes force to alter the motion of an object

Ex.Randy Johnson Pitch

Momentum (p) – possessed by any object in motion (must have mass and velocity)

p = mv

- SI Units are kg m / s

- Vector quantity, the direction of the momentum is the same as the velocity

The amount of momentum is also directly proportional to the inertia when an object is moving.

As long as no external force (friction) acts on an object in motion, momentum is conserved (Δp = 0)

Any change in momentum due to an outside force is known as impulse.

Conservation of Momentum and Impulse

F = maF = m (Δv/Δt), multiply both sides by Δt Impulse = FΔt = mΔv = Δp

Vector quantity, the direction is the same as the direction of the force.

Impulse

The theorem states that the impulse acting on the object is equal to the change in momentum of the object.

◦ ◦ If the force is not constant, use the average force

applied

Impulse-Momentum Theorem

fit m mI F p v v

Think about how an airbag works in a car- increases Δt- decreases ΔF

What if you hit the steering wheel?- ouch…

What are some other objects that take advantage of impulse?

Why can we belly flop onto our beds, but not onto the kitchen floor, and other pertinent questions of our time…

Let’s do another quick example, everyone climb up onto your chair……now jump off……how did you land?

…what happed to your knees?

Conservation of Momentum, Example

The momentum of each object will change

The total momentum of the system remains constant

When objects collide, total momentum change (impulse) = 0

Initial momentum (pB + pA) is equal to final momentum (pB’ + pA’)

Notice how Δp for object A and Δp for object B are exact opposites.

ΔpA = - ΔpB

Law of conservation of momentum – the momentum of any closed, isolated system does not change

- no net external forces

Mathematically:

◦ Momentum is always conserved for the system of objects

◦ p1init + p2init = p1final + p2final

Conservation of Momentum

1 1 2 2 1 1 2 2i i ffm m m m v v v v

Momentum is conserved in any type of collision

Collisions are one of the following:

◦ Perfectly elastic

◦ Perfectly inelastic

◦ Somewhat elastic

Types of Collisions

Only happens in a closed system (no friction in collision, no thermal energy loss).

Both momentum and kinetic energy conserved in a perfectly elastic collision.

Perfectly Elastic Collisions

Inelastic collisions◦ Kinetic energy is not conserved◦ Perfectly inelastic collisions occur when the

objects stick together Not all of the KE is necessarily lost In a perfectly inelastic collision, the final velocity is

the same for both objects

Example of Perfectly Inelastic Collision - Office Linebacker

Perfectly Inelastic Collisions

More About Perfectly Inelastic Collisions

When two objects stick together after the collision, they have undergone a perfectly inelastic collision

Conservation of momentum becomes

◦ Because the masses have stuck together after colliding and are moving at the same velocity

f21i22i11 v)mm(vmvm

Perfectly elastic collision◦ Both momentum and kinetic energy are

conserved

Actual collisions◦ Most collisions fall between perfectly elastic and

perfectly inelastic collisions◦ In this case, kinetic energy is not conserved

either.

More Types of Collisions

Both momentum and kinetic energy are conserved

Typically solved using systems of equations – two equations, two unknowns

More About Elastic Collisions

2f22

2f11

2i22

2i11

f22f11i22i11

vm2

1vm

2

1vm

2

1vm

2

1

vmvmvmvm

For a collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved

Glancing Collisions

fy22fy11iy22iy11

fx22fx11ix22ix11

vmvmvmvm

andvmvmvmvm

Glancing Collisions

The “after” velocities have x and y components Momentum is conserved in the x direction and in the y

direction Apply conservation of momentum separately to each

direction