Impulse & Momentum

When you are hit by an object, the effect of the force on you depends on whether it bounces off you or you catch it
This is because the change in momentum of the ball is greater when it bounces off you
- A greater force is also produced, which is why it hurts a lot more than if you just catch it
The applied external impulse is also equal to the change in momentum of the system

$J = ∆ p = m v - m u$

Where:
- Δp = change in momentum (kg m s^–1)
- m = mass (kg)
- v = final velocity (m s^–1)
- u = initial velocity (m s^–1)
It can also be defined in terms of the average resultant force, F:

$J = F ∆ t$

Where:
- J = impulse (N s)
- F = average resultant force (N)
- Δt = time of contact (s)

This equation is only used when the force F is constant
- Since the impulse is proportional to the force, it is also a vector
- The impulse is in the same direction as the force
The impulse quantifies the effect of a force acting over a time interval
- This means a small force acting over a long time has the same effect as a large force acting over a short time

Impulse Examples

An example of impulse in everyday life is the effect of rain on an umbrella, compared to hail (frozen water droplets)
- When rain hits an umbrella, the water droplets tend to splatter and fall off it and there is only a very small change in momentum
- However, hailstones have a larger mass and tend to bounce back off the umbrella, creating a greater change in momentum
- Therefore, the impulse on an umbrella is greater in hail than in rain
- This means that more force is required to hold an umbrella upright in hail compared to rain

Rain & Hail Impulse, downloadable AS & A Level Physics revision notes

Since hailstones bounce back off an umbrella, compared to water droplets from rain, there is a greater impulse on an umbrella in hail than in rain

The concept of impulse is used to prevent injury
- Increasing the time in which the change in momentum occurs, reduces the force
For example, in cricket:
- A cricket ball travels at very high speeds and therefore has a high momentum
- When a fielder catches the ball, it exerts a force on their hands
- Stopping a ball with high momentum abruptly will cause a large force on their hands
- This is because a change in momentum (impulse) acts over a short period of time which creates a large force on the fielder's hands and could cause serious injury
- A fielder moves their hands back when they catch the ball, which increases the time for its change in momentum to occur
- This means there will be less force exerted on the fielder's hands and therefore less chance of injury

Impulse Cricket Ball

A cricket fielder moves their hands backwards when catching a cricket ball to reduce the force it will exert on their hands

Worked example

A 58 g tennis ball moving horizontally to the left at a speed of 30 m s^–1 is struck by a tennis racket which returns the ball to the right at 20 m s^–1.

(a)

Calculate the impulse delivered to the ball by the racket

(b)

State the direction of the impulse

Answer:

(a)

Step 1: List the known quantities

Taking the initial direction of the ball as positive (the left)
- Initial velocity, u = 30 m s^–1
- Final velocity, v = –20 m s^–1
- Mass, m = 58 g = 58 × 10^–3 kg

Step 2: Write down the impulse equation

$J = ∆ p = m v - m u = m (v - u)$

Step 3: Substitute in the known values

$J = (58 \times 10^{- 3}) \times (- 20 - 30) = - 2.9 N s$

(b)

Step 1: State the direction of the impulse

Since the impulse is negative, it must be in the opposite direction to which the tennis ball was initially travelling
Therefore, (since the left is taken as positive) the direction of the impulse is to the right

Exam Tip

Remember that if an object changes direction, then this must be reflected by the change in the sign of the velocity (and impulse). This is the most common mistake made by students. Velocity, impulse, force and momentum are all vectors!

For example, if the left is taken as positive and therefore the right as negative, an impulse of 20 N s to the right is equal to −20 N s

Impulse & Momentum (SL IB Physics)

Revision Note