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Topic 3D: Momentum

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- Momentum considers speed and mass.
A bowling ball and a baseball can have the same momentum. How?

A small fast mass can have the same momentum as a large slow object.

Review: Can a bowling ball and baseball have the same inertia?

No, inertia means mass

Momentum = mass x velocity

In equation format:

p= m x v

Momentum is assigned the variable p in equations because this concept used to be referred to as “persistence”. It never changed because m is already taken for mass.

Units kg m/s

An object with a mass of 1 kg and a velocity of 5 m/s has the same momentum as an object with a mass of 5kg moving 1m/s or 2 kg at 2.5 m/s, etc…….

A force

How can we change an object’s momentum?

When a force acts on an object, it causes an acceleration .

Fnet =ma

Also can be stated: When a force acts on an object, it changes the velocity of the object.

The amount of time the force acts determines the change in velocity

What is the relationship between Force (F) and time (t)?

Inverse

Rearrange the above to:

Force acting for time is known as IMPULSE (J)

Mass times velocity is known as MOMENTUM (p)

Momentum: p=m x ∆v

Impulse: J = F x t = ∆p

An impulse (F x t) causes a corresponding change in momentum (m x ∆v).

* J = Ft = mΔv= m(vf-vi)=Δp *

Force is the time rate of change of momentum

* J = Ft = mΔv=m(vf-vi)=Δp*

Time and force have an inverse relationship.

F x t = ∆ p F x t= ∆ p

For any given momentum change a large time will equal less damage (Force)This is the idea behind air bags, bouncy castles and egg catching. Increase the time for the change in velocity in a way that considers the mass.

Which is the safest stop?

What does this equation show us?

Forces and car crashes

- If the change in velocity happens quickly the force experienced is large.
- If the change in velocity happens over a larger time the force experienced is smaller.

F x t = ∆ p F x t= ∆ p

The change in momentum is the same. The force and time are different. And the “pain” felt is different.

These equations are split up on the reference table.

Next topic

Here it is all connected

* J = Ft = mΔv =Δp *

- Momentum is a vector. Direction matters.
- Momentum has units
- Change in momentum is equal to IMPULSE (J)
- Impulse has the units (N s)

A Newton-second and a kilogram m/s are the same.

Newton-second is a kg (m/s2) x s = kg m/s

A Force of 12 N West acts on a 4.0 kg ball for 3.0 s. The ball is at rest.

- What is the magnitude of the impulse?
A) 12 N-s B) 36 N-s C) 48 N-s

- What is the change in momentum?
A) 12 N-s B) 36 N-s C) 48 N-s

- What is the change in velocity?A) 4 m/s East B) 4 m/s WestC) 9 m/s EastD) 9 m/s West

Who experiences a greater Impulse or change in momentum?

Don’t try this with your car!

Details about the car:

m = 1000 kg

vi = 20 m/s

vf = -10 m/s

∆pcar = ?

Details about the truck:

m = 3000 kg

vi = 0 m/s

vf = 10 m/s

∆ptruck = ?

Change in momentum of the car is equal and opposite to that of truck

Remember that this is another view of the 3rd law

Conservation of Momentum

Collisions and explosions are everywhere. What takes place in these situations is governed by:

The LAW of CONSERVATION OF MOMENTUM

The momentum before a collision or explosion is equal to the momentum after.

Newton's Cradle

MOMENTUM IS A CONSERVED QUANTITY.

While the objects might each experience a change in momentum as a result of the collision the total momentum remains the same.

This is a closed system, ie no extra force from a third object came into the situation.

CONSERVATION OF MOMENTUM IS A LAW

3 basic scenarios

Elastic collisions occurs when the two objects "bounce" apart from each other when they collide

Inelastic collisions occurs when two objects collide and do not bounce away from each other.

Perfectly elastic and inelastic examples

Explosions- objects originally at rest separate.

The cannon’s movement is called recoil.

These scenarios can be mixed and matched in real life.

In reality collisions occur across the spectrum of elastic to inelastic. More collision info

Lots of variations exist within these 3 scenarios

In order to solve problems we need to write an equation which summarizes what happens in the “collision” or “explosion”. Follow this general strategy.

- Picture the situation and list the objects and what you know about them. Remember that neg/pos are used to indicate direction. You must choose a positive v
- Apply the scenario to the equation pbefore=pafter by writing an equation that includes the masses and velocities. Label the knowns: pb, pa, m1b, m1a, m2b, m2a, v1b, v1a etc so that 1, 2, 3 represent the objects and “b” and “a” stand for before and after.

The only equation on the reference table is pbefore=pafter

For each of the following animations determine if it is elastic or inelastic and write a general equation in the format m1b etc.

1

2

3

4

6

5

1

pb=pa

elastic

m1v1b + m2v2b = -m1v1a + m2v2a

m1-car = 1000kg

m2 – truck = 3000kg

v1b= 20 m/s

v2b = 0

v1a= -10 m/s

v2a = 10 m/s

2

inelastic

pb=pa

m1v1b + m2v2b = (m1 + m2) va

When masses combine the only have one velocity. In this case, va

3

inelastic

pb=pa

m1v1b + m2v2b = (m1 + m2) va

V2b only relates to forward motion so the fact that it had vertical velocity does not matter

4

pb=pa

elastic

m1v1b + m2v2b = m1v1a + m2v2a

5

pb=pa

elastic

m1v1b + -m2v2b = -m1v1a + m2v2a

6

inelastic

pb=pa

m1v1b + (-m2v2b) = -(m1 + m2) va

If mass gets bigger velocity gets smaller

mbvb=(m1+m2)ava

Try these interactive momentum “applets”

Air Track "ScienceJoyWagon"

Cart JumpS

AstronautSpace

Rocket in space

air table

To combine momentums that are not on the same axes you follow vector rules

Use Pythagorean theorem and tan-1 to find momentum of each car after collision.

PRACTICE PROBLEMS

Case 1: Explosion

A cannon with clown are initially at rest. The clown with a mass of 100kg leaves the cannon with a velocity of 15m/s. What is the recoil velocity of the cannon?

Bullet is (0.04Kg) with realistic velocity (300m/s). What is the velocity of the person (60kg) once hit with the bullet.