• 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