GCSEScienceAQACombined Science: SynergyPhysical SciencesRevision NotesMovement & InteractionsForces & MotionMomentum (HT only)

Momentum (HT only) (AQA GCSE Combined Science: Synergy: Physical Sciences): Revision Note

Exam code: 8465

Ashika

Written by: Ashika

Updated on

AQA Combined Science: Synergy: Physical SciencesAQA Combined Science: Trilogy: PhysicsAQA Physics

Conservation of Momentum

  • The principle of conservation of momentum states that:

    In a closed system, the total momentum before an event is equal to the total momentum after the event

  • A closed system means the energy within the system is constant and the absence of external forces (e.g. friction)

  • In other words:

    The total momentum before a collision = The total momentum after a collision

  • A system is a certain number of objects under consideration

    • This can be just one object or multiple objects

  • Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out

    • Momentum is always conserved over time

  • The diagram below shows two masses m with velocity u and M at rest (ie. zero velocity)

Diagram showing conservation of momentum in a collision: before the collision, mass m moves to the right with velocity u while mass M is stationary; after the collision, mass m moves to the left with velocity v and mass M moves to the right with velocity V
The momentum of a system before and after a collision

  • Before the collision:

    • The momentum is only of mass m which is moving

    • If the right is taken as the positive direction, the total momentum of the system is m × u

  • After the collision:

    • Mass M also now has momentum

    • The velocity of m is now -v (since it is now travelling to the left) and the velocity of M is V

    • The total momentum is now the momentum of M + momentum of m

    • This is (M × V) + (m × -v) or (M × V) – (m × v)

Worked Example

The diagram shows a car and a van, just before and just after the car collided with the van, which is initially at rest.

Diagram showing a car (mass 990 kg, velocity 10 m/s) approaching a stationary van (mass 4200 kg) before a collision, and both vehicles moving in the same direction after the collision with the car at 2 m/s and the van at unknown velocity V

Use the idea of conservation of momentum to calculate the velocity of the van when it is pushed forward by the collision.

Answer:

Step 1: State the principle of conservation of momentum

  • In a closed system, the total momentum before an event is equal to the total momentum after the event

Step 2: Calculate total momentum before the collision

p = mv

  • Momentum of the car:

    p = 990 × 10 = 9900 kg m/s

  • Momentum of the van:

The van is at rest, therefore v = 0 m/s and p = 0 kg m/s

  • Total momentum before:

pbefore = 9900 + 0 = 9900 kg m/s

Step 3: Calculate the momentum after the collision

  • Momentum of the car:

p = 990 × 2 = 1980 kg m/s

  • Momentum of the van:

p = 4200 x v

  • Total momentum after:

pafter = 1980 + 4200v kg m/s

Step 4: Rearrange the conservation of momentum equation for the velocity of the van

pbefore = pafter

9900 = 1980 + 4200v

9900 - 1980 = 4200v

V = fraction numerator 9900 minus 1980 over denominator 4200 end fraction = 1.9 m/s

Examiner Tips and Tricks

If it is not given in the question already, drawing a diagram of before and after helps keep track of all the masses and velocities (and directions) in the conservation of momentum questions.

Calculating Momentum

  • A moving object has momentum which is defined by the equation:

p = mv

  • Where:

    • p = momentum in kilogram metre per second (kg m/s)

    • m = mass in kilograms (kg)

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

  • This means that an object at rest (i.e v = 0) has no momentum

  • Momentum keeps an object moving in the same direction, making it difficult to change the direction of an object with a large momentum

  • Since velocity is a vector this means that the momentum of an object also depends on its direction of travel

  • This means that momentum can be either positive or negative

    • If an object travelling to the right has positive momentum, an object travelling in the opposite direction (to the left) will have negative momentum

Diagram comparing the momentum of a tennis ball and a brick: the tennis ball has a small mass but high velocity, while the brick has a large mass but low velocity; both have equal momentum, also with an arrow showing the tennis ball's velocity reversing direction, giving it negative momentum
The tennis ball's momentum is negative when it moves in the opposite direction to which it initially was travelling in

  • Therefore, the momentum of an object will change if:

    • The object accelerates (speeds up) or decelerates (slows down)

    • Changes direction

    • Its mass changes

Worked Example

Which object has the most momentum?

Answer:

  • Both the tennis ball and the brick have the same momentum

  • Even though the brick is much heavier than the ball, the ball is travelling much faster than the brick

  • This means that on impact, they would both exert a similar force (depending on the time it takes for each to come to rest)

Examiner Tips and Tricks

Remember the units of momentum as kg m/s which is the product of the units of mass (kg) and velocity (m/s).Which direction is taken as positive is completely up to you in the exam. In general, the right and upwards are taken as positive, and down or to the left as negative.

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent

Our rating represented in Trustpilot stars
Read more reviews
Previous:Newton’s Third LawNext:Kinetic Energy
Ashika

Author: Ashika

Expertise: Physics Content Creator

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.