Momentum & Impulse (Edexcel IAL Maths)

Momentum

Spec point — 4.3

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 ( $m$kg) and its velocity ($vms^{-1}$)

  • Momentum =mv

• The SI unit for momentum is $\mathrm{kg}ms^{-1}$

• 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 $6ms^{-1}$_.

Find the momentum of the dog.

Answer:

Impulse

Spec point — 4.3

What is impulse?

• Impulse measures the effect of a force acting on a particle over time

• If a constant force ($FN$ ) acts on a particle for $t$ seconds then the impulse ($I$) of the force is defined to be the product of the force and time

  • $I=Ft$

• The SI unit for impulse is N s(newton seconds) which is equivalent to $\mathrm{kg}ms^{-1}$

  • 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

  • $I=mv-\mu$
  • 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

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.

Answers:

(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.

Exam Hint

• 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?