Impulse (OCR AS Physics)

• 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

• 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

Examples of Impulse

• 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