Impulse on a Force-Time Graph (OCR A Level Physics) : Revision Note

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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

Impulse on a Force-TIme Graph, downloadable AS & A Level Physics revision notes

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

  • This is because

Impulse = FΔt

  • Where:

    • F = force (N)

    • Δt = change in time (s)

  • The impulse is therefore equal whether there is

    • A small force over a long period of time

    • 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

WE - Tennis ball contact time content part, downloadable AS & A Level Physics revision notes

Worked Example

A ball of mass 3.0 kg, initially at rest, is acted on by a force F which varies with t as shown by the graph.

Force-Time Graph Worked Example

Calculate the velocity of the ball after 16 s.

Answer:

Step 1: List the known quantities

  • Mass, m = 3.0 kg

  • Initial velocity, 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

Step 3 Impulse Worked Example

Area = Impulse = 32 × 103 N s

Step 3: Write the equation for impulse

Impulse, I = Δp = m(vu)

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

Examiner Tips and Tricks

Some maths tips for this section: Rate of Change

  • ‘Rate of change’ describes how one variable changes with respect to another

  • In maths, how fast something changes with time is represented as dividing by Δt (e.g. acceleration is the rate of change in velocity)

  • More specifically, Δt is used for finite and quantifiable changes such as the difference in time between two events

Areas

  • The area under a graph may be split up into different shapes, so make sure you’re comfortable with calculating the area of squares, rectangles, right-angled triangles and trapeziums!

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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