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IGCSEPhysicsEdexcelRevision Notes1. Forces & MotionMomentumForces & Momentum

Forces & Momentum (Edexcel IGCSE Physics)

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Katie M

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Katie M

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Forces & momentum

  • When a force acts on an object that is moving, or able to move, the object will accelerate (or decelerate)

    • This causes a change in momentum

Rate of change in momentum

  • The resultant force acting on an object is defined by the equation:

F space equals space m a

  • Momentum is calculated using the equation:

space p space equals space m v

  • Change in momentum is given as:

increment p space equals space m v space minus space m u

  • Combining these equations gives:

force space equals space fraction numerator change space in space momentum over denominator time end fraction

F space equals space fraction numerator open parentheses m v space minus space m u close parentheses over denominator t end fraction

  • Where:

    • F = resultant force, measured in newtons (N)

    • a = acceleration, measured in metres per second squared (m/s2)

    • m = mass, measured in kilograms (kg)

    • ∆p = change in momentum, measured in kilogram metres per second (kg m/s)

    • v = final velocity, measured in metres per second (m/s)

    • u = initial velocity, measured in metres per second (m/s)

    • t = time, measured in seconds (s)

  • Remember to consider the direction of object's motion

    • If you take the initial direction as positive then the reverse direction is negative

  • Force can also be described as the rate of change of momentum on a body

    • The rate of change describes how a variable changes with respect to time

  • The shorter the time over which momentum changes, the bigger the force 

  • So, force and time are inversely proportional to each other

Examiner Tips and Tricks

When two quantities are inversely proportional, it means that as one increases, the other decreases by a proportional amount

  • If one is doubled, the other is halved

  • If one is decreased by a factor of 4, the other is increased by a factor of 4

Worked Example

A tennis ball hits a racket twice, with a change in momentum of 0.5 kg m/s both times.

During the first hit, the contact time is 2 s and during the second hit, the contact time is 0.1 s

Determine which strike of the tennis racket experiences the greatest force from the tennis ball.

2-4-we-different-contact-times

Answer:

Step 1: List the known quantities

  • Change in momentum each time, straight capital delta p = 0.5 kg m/s

  • Contact time of first hit, t subscript 1 = 0.1 s

  • Contact time of section hit, t subscript 2

Step 1: Calculate the force during the first hit

F subscript 1 space equals space fraction numerator increment p over denominator t subscript 1 end fraction

F subscript 1 space equals space fraction numerator 0.5 over denominator 2 end fraction

F subscript 1 space equals space 0.25 space straight N

Step 2: Calculate the force during the second hit

F subscript 2 space equals space fraction numerator increment p over denominator t subscript 2 end fraction

F subscript 2 space equals space fraction numerator 0.5 over denominator 0.1 end fraction

F subscript 2 space equals space 5.0 space straight N

Step 3: State your answer

  • The tennis racket experiences the greatest force from the ball during the second hit

Worked Example

A car of mass 1500 kg hits a wall at an initial velocity of 15 m/s and rebounds with a velocity of 5 m/s. The car is in contact with the wall for 3 seconds.

Calculate the average force experienced by the car and state the direction of the force.

Answer:

Step 1: List the known quantities and assign direction

  • Mass of car, m = 1500 kg

  • Initial velocity before collision, u = 15 m/s

  • Final velocity after collision, v = −5 m/s

  • Time of impact, t = 3 s

Step 2: Draw a diagram of the collision

  • The diagram should include:

    • The velocity before and after the collision

    • The direction of motion before and after the collision

2-4-we-solution-diagram

  • In momentum questions , a positive direction is always chosen

    • Here, right is chosen as the positive direction

    • This means final velocity, which is in the left direction, must be negative

Step 3: Write out the force and momentum equation

  • Recall that force is change in momentum over time

F space equals space fraction numerator straight capital delta p over denominator t end fraction space equals space fraction numerator p subscript f space minus space p subscript i over denominator t end fraction

  • Momentum is mass × velocity

    • Initial momentum is mass × initial velocity, u

    • Final momentum is mass × final velocity, v

p subscript f space equals space m v and p subscript i space equals space m u

F space equals space fraction numerator m v space minus space m u over denominator t end fraction

Step 4: Substitute in the known values to calculate force

F space equals space fraction numerator open parentheses 1500 space cross times space minus 5 close parentheses space minus space open parentheses 1500 space cross times space 15 close parentheses over denominator 3 end fraction

F space equals space fraction numerator negative 7500 space minus space 22 space 500 over denominator 3 end fraction

F space equals space fraction numerator negative 30 space 000 over denominator 3 end fraction

F space equals space minus 10 space 000 space straight N

  • The minus sign means the direction of the force is to the left (or in the opposite direction to the car's initial motion)

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    Katie M

    Author: Katie M

    Expertise: Physics

    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.