# 4.5.3 Impulse

### Force & Momentum

• Force is defined as the rate of change of momentum on a body
• The change in momentum is defined as the final momentum minus the initial momentum
• These can be expressed as follows: #### Direction of Forces

• Force and momentum are vectors so they can take either positive or negative values
• The force that is equal to the rate of change of momentum is still the resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity
• This means that the force is produced by the object it has collided with The wall produces a force of -300N on the car and (due to Newton’s Third Law) the car also produces a force of 300 N back onto the wall

#### Worked Example

A car of mass 1500 kg hits a wall at an initial velocity of 15 m s-1.
It then rebounds off the wall at 5 m s-1 and comes to rest after 3.0 s.

Calculate the average force experienced by the car.

#### Exam Tip

In an exam question, carefully consider what produces the force(s) acting. Look out for words such as ‘from’ or ‘acting on’ to determine this and don’t be afraid to draw a force diagram to figure out what is going on.

### Impulse

• The force and momentum equation can be rearranged to find the impulse
• Impulse, I, is equal to the change in momentum:

#### I = FΔt = Δp = mv – mu

• Where:
• I = impulse (N s)
• F = force (N)
• t = time (s)
• p = momentum (kg m s–1)
• m = mass (kg)
• v = final velocity (m s–1)
• u = initial velocity (m s–1)

• This equation is only used when the force 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 unit of impulse is N s
• 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
• An example in everyday life of impulse is when standing under an umbrella when it is raining, 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 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

#### 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 delivered to the ball by the racket

(ii) State which direction the impulse is in

(i) Step 1Write 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

Impulse I = Δp = m(vu)

Step 3: Substitute in the values

I = (58 × 10–3) × (–20 – 30) = –2.9 N s

(ii) Direction of the impulse

• Since the impulse is negative, it must be in the opposite direction to which the tennis ball was initial travelling (since the left is taken as positive)
• 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. As long as the magnitude is correct, the final sign for the impulse doesn’t matter as long as it is consistent with which way you have considered positive (and negative)

For example, if the left is taken as positive, an impulse of 20 N s is equal to an impulse of –20 N s where the right is taken as positive ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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