Momentum & Impulse | Edexcel International A Level Maths: Mechanics 1 Revision Notes 2020

Momentum

What is momentum?

Any object that has mass and is moving has momentum
Momentum measures the quantity of motion that an object has
The momentum of a particle is defined as the product of its mass ( $m$ kg) and its velocity ( $v m s^{- 1}$ )
- Momentum =mv
The SI unit for momentum is $kg m s^{- 1}$
Momentum is a vector quantity - so it has a magnitude and direction
- The direction of the momentum of a particle is the same as the direction of motion of the particle
- The momentum is negative if the velocity is negative

Worked example

A dog of mass 15 kg is running with speed $6 m s^{- 1}$ _.

Find the momentum of the dog.

3-4-1-momentum--impulse-example-solution-1

Impulse

What is impulse?

Impulse measures the effect of a force acting on a particle over time
If a constant force ( $F N$ ) acts on a particle for $t$ seconds then the impulse ( $I$ ) of the force is defined to be the product of the force and time
- $I = F t$
The SI unit for impulse is N s(newton seconds) which is equivalent to $kg m s^{- 1}$
- This is the same as the units for momentum
Impulse is a vector quantity – so it has magnitude and direction
- The direction of the impulse of a force is the same as the direction of the force
The Impulse-Momentum Principle states that impulse is equal to the change in momentum
- $I = m v - m u$
- where m is the mass, u is the initial velocity and v is the final velocity

What happens when two objects are in contact?

If two objects are in contact with each other then by Newton’s Third Law there will be equal and opposite reaction forces
This means there will be equal and opposite impulses
For example, consider hitting a tennis ball with a racket, there will be
- an impulse exerted by the racket on the ball which propels the ball forward
- an impulse exerted by the ball on the racket which reduces the velocity of the racket
- The magnitudes of these impulses are equal but they are in opposite directions

3-4-1-impulse

Worked example

A car with mass 1200 kg is driving to the right along a smooth horizontal road with speed 16 m s^-1 . The driver applied a constant braking force of magnitude 1800 N for 5 seconds.

(a)

Find the magnitude of the impulse of the braking force.

(b) State the direction of the impulse.

(a)

Find the magnitude of the impulse of the braking force.

3-4-1-momentum-_-impulse-example-solution-2_a

(b)

State the direction of the impulse.

3-4-1-momentum-_-impulse-example-solution-2_b

(c)

Find the speed of the car 5 seconds after the braking force was applied.

3-4-1-momentum---impulse-example-solution-2-c-fixed

Examiner Tip

Always define a positive direction and be careful with negatives. Use common sense to see if your answer makes sense - would you expect the velocity to have increased or decreased?

Momentum & Impulse (Edexcel International A Level Maths: Mechanics 1)

Revision Note

Momentum

What is momentum?

Worked example

Impulse

What is impulse?

What happens when two objects are in contact?

Worked example

Examiner Tip

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Author: Dan