Impulse

Extended tier only

When an external resultant force acts on an object for a very short time and changes the object's motion, we call this impulse
- For example:
  - Kicking a ball
  - Catching a ball
  - A collision between two objects

The impulse equation

Impulse is the product of the force applied and the time for which it acts

$impulse = F ∆ t$

Where:
- $F$ = resultant force, measured in newtons (N)
- $∆ t$ = change in time, measured in seconds (s)
Therefore, the units of impulse are newton seconds (Ns)

The impulse of the resultant force is equal to the change in momentum of the object

$impulse = F ∆ t = ∆ p$

Change in momentum can also be described as:

$∆ p = ∆ (m v)$

$∆ p = m v - m u$

Where:
- $∆ p$ = change in momentum, measured in kilogram metres per second (kg m/s)
- $m$ = mass, measured in kilograms (kg)
- $v$ = final velocity, measured in metres per second (m/s)
- $u$ = initial velocity, measured in metres per second (m/s)

Therefore:

$impulse = F ∆ t = ∆ p = m v - m u$

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Examples of impulse

When rain and hail (frozen water droplets) hit an umbrella, they feel very different due to the impulse of the force

- Water droplets tend to splatter and roll off the umbrella because there is only a very small change in momentum
- Hailstones have a larger mass and tend to bounce back off the umbrella, because there is a greater change in momentum
- Therefore, the impulse that the umbrella applies on the hail stones is greater than the impulse the umbrella applies on the raindrops
- 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

The impulse exerted by the umbrella on the hail stones is greater than the impulse exerted on the raindrops.

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 back to the right at 20 m s^–1.

(i) Calculate the impulse of the force exerted by the racket on the ball
(ii) State which direction the impulse is in

Answer:

Part (i)

Step 1: Write the known quantities

Taking the initial direction of the ball as positive (the left)
Initial velocity, $u = 30 m / s$
Final velocity, $v = - 20 m / s$
Mass, $m = 58 g = 58 \times 10^{- 3} kg$

Step 2: Write down the impulse equation

$impulse = F ∆ t = ∆ p = m v - m u$

Step 3: Substitute in the values

$impulse = m (v - u)$

$impulse = 58 \times 10^{- 3} (- 20 - 30)$

$impulse = - 2.9 N s$

Part (ii)

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, 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 sign of the velocity. 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

Force & momentum

Extended tier only

Newton's second law is defined by the equation:

$F = m a$

Momentum is given by the equation:

$p = m v$

Combining these equations gives Newton's second law in terms of momentum:

$F = \frac{∆ p}{∆ t}$

Therefore, force can also be defined as the rate of change of momentum on a body
- Or the change in momentum per unit time

Worked example

A tennis ball hits a racket twice, with a change in momentum of 0.5 kg m/s both times.

During the first hit, the contact time is 2 s and during the second hit, the contact time is 0.1 s

Determine which tennis racket experiences the greatest force from the tennis ball.

2-4-we-different-contact-times

Answer:

Step 1: Calculate the force during the first hit

$F = \frac{∆ p}{∆ t}$

$F = \frac{0.5}{2}$

$F = 0.25 N$

Step 2: Calculate the force during the second hit

$F = \frac{∆ p}{∆ t}$

$F = \frac{0.5}{0.1}$

$F = 5.0 N$

Step 3: State your answer

The tennis racket experiences the greatest force from the ball during the second hit

Impulse (CIE IGCSE Physics)

Revision Note

Impulse

The impulse equation

Examples of impulse

Worked example

Exam Tip

Force & momentum

Worked example

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Author: Leander