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International A LevelMaths: Mechanics 1EdexcelRevision Notes3. Forces & Newton’s Laws3.4 Momentum, Impulse & Collisions3.4.1 Momentum & Impulse

Momentum & Impulse (Edexcel International A Level Maths: Mechanics 1)

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Dan

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Dan

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Momentum

What is momentum?

  • Any object that has mass and is moving has momentum
  • Momentum measures the quantity of motion that an object has
  • The momentum of a particle is defined as the product of its mass ( begin mathsize 16px style bold italic m end stylekg) and its velocity (begin mathsize 16px style bold italic v bold space bold m bold space bold s to the power of bold minus bold 1 end exponent end style)
    • Momentum =mv
  • The SI unit for momentum is begin mathsize 16px style bold kg bold space bold m bold space bold s to the power of bold minus bold 1 end exponent end style
  • Momentum is a vector quantity - so it has a magnitude and direction
    • The direction of the momentum of a particle is the same as the direction of motion of the particle
    • The momentum is negative if the velocity is negative

Worked example

A dog of mass  15 kg is running with speed 6 space straight m space straight s to the power of negative 1 end exponent.

Find the momentum of the dog.

3-4-1-momentum--impulse-example-solution-1

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Impulse

What is impulse?

  • Impulse measures the effect of a force acting on a particle over time
  • If a constant force (begin mathsize 16px style bold italic F bold space bold N end style ) acts on a particle for t seconds then the impulse (begin mathsize 16px style bold italic I end style) of the force is defined to be the product of the force and time
    • begin mathsize 16px style bold italic I bold space bold equals bold space bold italic F bold italic t end style
  • The SI unit for impulse is N s(newton seconds) which is equivalent to begin mathsize 16px style bold kg bold space bold m bold space bold s to the power of bold minus bold 1 end exponent end style
    • This is the same as the units for momentum
  • Impulse is a vector quantity – so it has magnitude and direction
    • The direction of the impulse of a force is the same as the direction of the force
  • The Impulse-Momentum Principle states that impulse is equal to the change in momentum
    • begin mathsize 16px style bold italic I bold space bold equals bold space bold italic m bold italic v bold minus bold space bold italic m bold italic u end style 
    • where m is the mass, u is the initial velocity and  v is the final velocity

What happens when two objects are in contact?

  • If two objects are in contact with each other then by Newton’s Third Law there will be equal and opposite reaction forces
  • This means there will be equal and opposite impulses
  • For example, consider hitting a tennis ball with a racket, there will be
    • an impulse exerted by the racket on the ball which propels the ball forward
    • an impulse exerted by the ball on the racket which reduces the velocity of the racket
    • The magnitudes of these impulses are equal but they are in opposite directions

3-4-1-impulse

Worked example

A car with mass 1200 kg is driving to the right along a smooth horizontal road with speed 16 m s-1 . The driver applied a constant braking force of magnitude 1800 N for 5 seconds.

(a)
Find the magnitude of the impulse of the braking force.

(b)     State the direction of the impulse.

(c)      Find the speed of the car 5 seconds after the braking force was applied.

(a)
Find the magnitude of the impulse of the braking force.

3-4-1-momentum-_-impulse-example-solution-2_a

(b)
State the direction of the impulse.

 3-4-1-momentum-_-impulse-example-solution-2_b

(c)
Find the speed of the car 5 seconds after the braking force was applied.

3-4-1-momentum---impulse-example-solution-2-c-fixed

Examiner Tip

  • Always define a positive direction and be careful with negatives. Use common sense to see if your answer makes sense - would you expect the velocity to have increased or decreased?

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    Dan

    Author: Dan

    Expertise: Maths

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.