4.5.4 Impulse on a Force-Time Graph

• In real life, forces are often not constant and will vary over time
• If the force is plotted against time, the impulse is equal to the area under the force-time graph

When the force is not constant, the impulse is the area under a force–time graph

• This is because

Impulse = Force × Change in time

• The impulse is therefore equal whether there is a small force over a long period of time or a large force over a small period of time
• The force-time graph may be a curve or a straight line
  • If the graph is a curve, the area can be found by counting the squares underneath
  • If the graph is made up of straight lines, split the graph into sections. The total area is the sum of the areas of each section

Step 1: List the known quantities

    m = 3.0 kg

    u = 0 m s^-1 (since it is initially at rest)

Step 2: Calculate the impulse

    The impulse is the area under the graph. The graph can be split up into two right-angled triangles with a base of 8 s and a height of 4 kN

     Area = impulse = 32 × 10³ Ns

Step 3: Write the equation for impulse

Impulse, I = Δp = m(v – u)

Step 4: Substitute in the values

I = mv

32 × 10³ = 3.0 × v

v = (32 × 10³) ÷ 3.0

v = 10666 m s^–1 = 11 km s^-1

• Impact forces are reduced by increasing the contact time
• This fact is used in everyday life to lower the risk of injury
• Some example of where reducing impact force is important:
  • In sport
  • In packaging

In Sports

• For example, in cricket:
  • When a cricket fielder relaxes their hands and pulls them back when catching a ball
  • A cricket ball travels at very high speeds and therefore has a high momentum
  • When a fielder catches the ball, it exerts a force onto their hands
  • Stopping a ball with high momentum at once will cause a large force onto their hands
  • This is because a change in momentum (impulse) acts over a short period of time which creates a large force on the fielder's hands and could cause serious injury
  • A fielder moves their hands back when they catch the ball, which increases the time for its change in momentum to reduce
  • This means there will be less force exerted on the fielder's hands and therefore less chance of injury

A cricket fielder moves their hands backwards when catching a cricket ball to reduce the force it will exert on their hands

• In football:
  • Increasing the contact time is sometimes used to advantage, as the longer the contact time, the larger change in momentum
  • When kicking a football, after a strong kick the motion is followed through
  • The momentum from the foot is transferred to the ball
  • This creates a large impulse and the ball then has a higher velocity

The follow through action of a football kick increases the change in momentum of the ball

In Packaging

• Packaging, especially for fragile items, uses bubble wrap or polyester packaging to reduce the impact forces that items experience in transit
• These help cushion the items by increasing the time over which they experience a force, which reduces the risk of damage