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What is momentum?
A quantity relating to a moving object that is calculated by multiplying its mass by its velocity. is the product of The amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). and The speed of an object in a particular direction.. Momentum is also a A physical quantity that has both magnitude (size) and direction. Eg force, velocity, displacement, acceleration. quantity – this means it has both a The size of a physical quantity. and an associated direction.
For example, an elephant has no momentum when it is standing still. When it begins to walk, it will have momentum in the same direction as it is travelling. The faster the elephant walks, the larger its momentum will be.
Podcast: Momentum
In this episode, James and Ellie introduce momentum and explain how to calculate it. They also explore the definition of conservation of momentum and share examples of how to understand it.
ELLIE: Hello, and welcome to the BBC Bitesize Physics podcast.
JAMES: The series designed to help you tackle your GCSE in physics and combined science. I'm James Stewart, I'm a climate science expert and TV presenter.
ELLIE: And I’m Ellie Hurer, a bioscience PhD researcher. This is the eighth and final episode of our series on forces.
JAMES: Let's kick off our final episode, I’m emotional, where we'll be talking about momentum.
ELLIE: Momentum is mass multiplied by velocity, which is written out as ‘p’ for momentum equals ‘m’ for mass and ‘v’ for velocity.
JAMES: Momentum is measured in kilogram metres per second, mass is measured in kilograms, and velocity is measured in metres per second.
ELLIE: So James, let me test your memory. Do you still remember what we talked about in episode one?
JAMES: Gosh, a long time ago. Yeah, scalar and vector quantities. And because we measure momentum by both magnitude and direction, it is a vector quantity.
ELLIE: So James, I think it's time for an example. Okay, let's get on the motorway, not literally, and measure the momentum of a lorry. So look at that lorry over there. Its mass is 40,000 kilograms and it's driving up north to Edinburgh at a velocity of 20 metres per second.
JAMES: Speedy lorry. So to calculate its momentum, we would multiply its mass, that's 40,000 kilograms, by its velocity. 20 metres per second north. To get the answer, 800,000 kilogram metres per second north.
So Ellie, do you remember how we talked about dodgems in episode 7?
ELLIE: Yeah, the dodgem cars at the theme park.
JAMES: Yeah, we're gonna use those as the example again to describe our next topic, conservation of momentum.
ELLIE: Imagine there were just two dodgem cars in a rink that's completely closed off to the rest of the world. No other cars can come in, and those two cars can't leave.
JAMES: That would be a closed system, because it cannot be affected or affect anything outside of it.
ELLIE: Right, so when two objects collide in a closed system, the total momentum before an event is equal to the total momentum after an event. This is called conservation of momentum.
JAMES: Let's zoom in to an example. Okay, so let's say you and I we’re in the dodgems. I'll take the green one.
ELLIE: Well, I'll take the blue one.
JAMES: Good. If I was driving straight towards you with a momentum of 60 kg/m per second north, and you were driving straight towards me with a momentum of 50 kg/m per second south, and then we collided, what would our combined momentum be?
I'll give you a second to use the equation to work it out. As a recap, remember the total momentum before an event is equal to the total momentum after an event.
Okay, so the answer is: our combined momentum before crashing will be 10 kg/m per second north.
ELLIE: And our combined momentum after crashing would still be 10 kg/m per second north. This is because energy can't move in or out of a closed system. Therefore, our momentum would be the same before and after we collide.
JAMES: So in this example, our cars would move together to the north. My car would push your car backwards.
ELLIE: Rude. However, we definitely wouldn't recommend driving straight into another car in a game of dodgems.
JAMES: Even for scientific research?
ELLIE: Not even for scientific research.
JAMES: We could also look at how this works when a total momentum of zero is conserved. Let's look at a party popper, for example. Didn't think I was going to say that, did you?
ELLIE: So, before you pull the string, the momentum is zero. So the total momentum after pulling it must be zero too.
JAMES: That means if you were to add up all the momentums of all the little bits of paper that came out the end of the party popper, they would all actually cancel each other out to make zero overall. A momentum of zero has been conserved. Zero fun was had at that party.
ELLIE: So let's summarise what we've learnt. Firstly, momentum equals mass multiplied by velocity.
Our second point is, in a closed system, the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.
And finally, momentum is a vector quantity, which means both its magnitude and its direction must be given.
And sadly, with that comes the end of our eight-part series all about forces.
JAMES: We hope you found it helpful, and if you didn't get the chance to listen to all the episodes, please do go back. Make sure you can listen again and really get stuck into them. Thank you for listening to Bitesize Physics. If you're preparing for your GCSEs, firstly, good luck, and secondly, why not also check out our Bitesize Biology podcast, or our range of Bitesize English literature series.
ELLIE: There’s also the Bitesize Study Support podcast, which is full of tips to help you stay focused during revision and get the best out of your exam day.
BOTH: Bye!
Calculating momentum
Momentum can be calculated using the equation:
momentum = mass × velocity
\(p = m\) \(v\)
This is when:
- momentum (\(p\)) is measured in kilogram metres per second (kg m/s or kg ms-1)
- mass (\(m\)) is measured in kilograms (kg)
- velocity (\(v\)) is measured in metres per second (m/s)
Example
A lorry has a mass of 7500 kg. It travels south at a speed of 25 m/s. Calculate the momentum of the lorry.
\(p = m\) \(v\)
\(p = 7500\) \(×\) \(25\)
\(p = 187,500\) \(kg\) \(m/s\) \((south)\)
Question
An ice skater has a mass of 60 kg and travels at a speed of 15 m/s. Calculate the momentum of the skater.
\(p = m\) \(v\)
\(p = 60\) \(×\) \(15\)
\(p = 900\) \(kg\) \(m/s\)
Impulse
Impulse is defined as the product of average A push or a pull. The unit of force is the newton (N). and time of contact for a collision.
\(\text{impulse} = F\times t\)
\(\text{impulse} = F\Delta t\)
There is no symbol for impulse but the units are Unit of force named after British scientist Isaac Newton (1642-1727), eg the frictional force on the boat is 20,000 N. seconds (N s)
The equations of motion can be used to show that impulse is equal to the change in momentum.
Use the equation for change in velocity \( \Delta v = v - u\)
Change in momentum equals:
\(mv - mu = m(v - u)= m\Delta v\)
Newton's Second Law:
\(F=ma=m\frac{{\Delta v}}{t}\)
Rearranging:
\(F\times t = m\Delta v\)
ie, \(\text{impulse}\) = \(\text{change}\) \(\text{in}\) \(\text{momentum}\)
This means that the units of impulse (N s) and the units of momentum (kg ms-1) must be equivalent.
Example
A squash ball of mass 25 g is moving from left to right at 3.2 ms-1. It is hit by a squash racquet which applies a force for 4 milliseconds, so that the ball leaves the racquet at 8.4 ms-1 moving from right to left. Impulse-momentum can be used to calculate the average force on the ball.
Initial momentum of ball:
\(=m\times u\)
\(= 0.025 \times 3.2\)
\(= 0.08kg\) \(m{s^{ - 1}}\) (to the right)
Final momentum of ball:
\(=m\times v\)
\(= 0.025\times -8.4\)
\(= 0.21kg\) \(m{s^{ - 1}}\) (moving to the left)
Change in momentum = final momentum – initial momentum
\(= -0.21 - 0.08\)
\(= 0.29kg\) \(m{s^{ - 1}}\) (moving to the left)
This change in momentum is equal to the impulse so:
\(F \times t = -0.29\)
\(F = \frac{{-0.29}}{{0.004}}\)
\(F = -72.5N\) (value is negative as moving to the left)
The negative sign in front of the \(-72.5N\) indicates that the movement is to the left, but you can also write this down in order to make it clear.
Conservation of momentum
In a closed system:
Total momentum before an event = total momentum after the event
A ‘closed system’ is something that is not affected by external forces. This is called the principle of The principle that the total momentum of a system remains the same. When bodies collide, whatever momentum is lost by one body, the other gains in equal amounts.. Momentum is conserved in When two objects meet and interact, eg two particles moving towards each other will collide. and When parts of a system separate and move apart. For example, a supernova is an exploding star - the outer layers are thrown out into space in all directions..
Conservation of momentum explains why a gun or cannon recoils backwards when it is fired. When a cannon is fired, the cannon ball gains forward momentum and the cannon gains backward momentum. Before the cannon is fired (the ‘event’), the total momentum is zero. This is because neither object is moving. The total momentum of the cannon and the cannon ball after being fired is also zero, with the cannon and cannon ball moving in opposite directions.
Change in momentum over time
Force is the change in momentum over time, as shown here:
\(F=\frac{{\Delta (mv)}}{\Delta t}\)
This can be rearranged to:
\(F=\frac{{\Delta p}}{\Delta t}\)
Where \(p\) is momentum.
So resultant force is the change in momentum per unit time.
Quiz
Test your knowledge with this quiz on momentum.
Teaching resources
Are you a physics teacher looking for more resources? Share this short film presented by scientist and rapper Jon Chase with your students. Jon explains Newton's third law with the help of some skateboarders.
More on Motion, forces and energy
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