Impulse (CIE IGCSE Physics)

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• When a resultant (unbalanced) force acts on a mass, the momentum of that mass will change
• The impulse of a force is equal to that force multiplied by the time for which it acts:

impulse  =  force × change in time

impulse = FΔt

• The change in momentum of a mass is equal to the impulse provided by the force:

impulse = change in momentum

impulse = FΔt  = Δp

• Change in momentum can also be described as:

Δp = Δ(mv)

Δp = mv − mu

• Where:
  • m = mass in kg
  • v = final velocity in m/s
  • u = initial velocity in m/s

• Therefore:

impulse = FΔt  = Δp = mv − mu

• 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

(i) Step 1: Write 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(v – u)

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

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• Force can also be 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: