• 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:

Defining Impulse

• The force and momentum equation can be rearranged to find the?impulse of a force
• 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)
  • Δp?= change in 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