Momentum & ImpulseTopic 2.2

When have you heard this term?

Some examples: The Maple Leafs have won 5 straight games

and they are building momentum towards the playoffs

The momentum to use technology has been huge in the past few years

Keeping your momentum is the key to reaching yearly resolutions

Momentum

Momentum What makes an object hard to stop?

Is it harder to stop a bullet, or a truck travelling along the highway?

What makes each object hard to stop?

Momentum The bullet is hard to stop because it is

travelling very fast, whereas the truck is hard to stop because it has a very large mass.

Momentum It makes sense to assume that a bullet

travelling twice as fast would be twice as hard to stop, and a truck twice the mass would also be twice as hard to stop.

Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as

Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)

p = mv

Momentum

An easy example A truck has a mass of 10 000 kg and a

velocity of 3 m.s-1. What is its momentum?

Momentum = Mass x velocity = 10 000 x 3 = 30 000 kg.m.s-1.

The momentum p of a body of constant mass m moving with velocity v is, by definition mv

p = mv It is a vector quantity

Its units are kg m s-1 or Ns It is the property of a moving body.

Linear Momentum

1. In a collision between two objects, momentum is conserved (total momentum stays the same)

2. In an isolated system (no outside forces), momentum remains constant

isolated system = translational equilibrium

We can use this to calculate what happens after a collision (and in fact during an “explosion”).

Conservation of momentum

Momentum is not energy!

To derive this law we apply Newton´s 2nd law to each body and Newton´s 3rd law to the system

i.e. Imagine 2 bodies A and B interacting mass of mA and mB A has a velocity change of uA to vA and

B has a velocity change of uB to vB during the time of the interaction t

Deriving This Law

Then the force on A given by Newton 2 is

FA = mAvA – mAuA

t And the force on B is

FB = mBvB – mBuB

t But Newton 3 says that these 2 forces are

equal in magnitude and opposite in direction

Therefore

mAvA – mAuA = - (mBvB – mBuB)

t tmAvA – mAuA = mBuB – mBvB

Rearranging gives:

mAuA + mBuB = mAvA + mBvB

Total Momentum before = Total Momentum after

A car of mass 1000 kg travelling at 5 m.s-1 hits a stationary truck of mass 2000 kg. After the collision they stick together. What is their joint velocity after the collision?

What does ‘joint velocity’ mean?

What ELSE does it mean?

A harder example!

A harder example!

5 m.s-1

1000kg

2000kgBefore

After

V m.s-1

Combined mass = 3000 kg

Momentum before = 1000x5 + 2000x0 = 5000 kg.m.s-1

Momentum after = 3000v

The law of conservation of momentum tells us that momentum before equals momentum after, so

p1total= p2total

5000 = 3000v

V = 5000/3000 = 1.67 m.s-1

A harder example

Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations

Momentum is a vector

An even harder example!

Snoopy (mass 10kg) running at 4.5 m.s-1 jumps onto a skateboard of mass 4 kg travelling in the opposite direction at7 m.s-1

What is the velocity of Snoopy and skateboard after Snoopy has jumped on? I love

physics

An even harder example!

10kg

4kg-4.5 m.s-1

7 m.s-1

Because they are in opposite directions, we make one velocity negative

14kg

v m.s-1

Momentum before = 10 x -4.5 + 4 x 7 = -45 + 28 = -17

Momentum after = 14v

Momentum before = Momentum after-17 = 14v

V = -17/14 = -1.21 m.s-1

An even harder example!

The negative sign tells us that the velocity is from left to right (we choose this as our “negative direction”)

F = ma F = m v - m u t t

F = mv – mu F =p t t

The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.

Newton´s Second Law - Revisited

Where have you heard this term?

Some Examples: I bought that from the internet on impulse

after seeing the commercial on TV I got into a fight on impulse after being

called a name

Impulse

F = p F = mv – mu t t

Ft = mv – mu = p

This quantity Ft is called the impulse of the force on the body

It is a vector quantity

Its units are kg m s-1or Ns

Impulse

Ft = mv – mu = p

The quantity Ft is called the impulse, and

mv – mu is the change in momentum

(v = final velocity and u = initial velocity)

Impulse = Change in momentum

Impulse

Units

Impulse is measured in N.s (Ft)

or [kg.m.s-2]x[s] = [kg.m.s-1]

(mv – mu)

Note: For a ball (mass m) bouncing off a wall, don’t forget the initial and final velocity are in different directions, so you will have to make one of them negative.

In this case mv – mu = 5m – (-3m) = 8m

Impulse

5 m/s

-3 m/s

Dylan punches Joseph in the face. If Joseph’s head (mass 10.0 kg) was initially at rest and moves away from Dylan’s fist at 3.0 m/s, and the fist was in contact with the face for 0.20 seconds, what was the force of the punch?

m = 10.0kg, t = 0.20s, u = 0, v = 3.0 m/s Ft = mv – mu 0.2F = 10x3 – 10x0 0.2F = 30 F = 30/0.2 = 150N

Example

A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?

Another example

A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?

Another example

3 m/s

-6 m/s

A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?

Impulse = mv – mu == 0.3x-6 – 0.3x3 = -2.7kg.m.s-1

Another example

3 m/s

-6 m/s