Momentum
- If a body of mass m has a velocity v, then its momentum ρ is
- Ρ=mv
- The units of momentum are kg ms¯¹ or Newton Seconds (Ns)
- Momentum is a vector quantity so it has a direction ⬆️.
Law of conservation of momentum
Momentum is conserved in all collisions, explosions and interactions. There are no exceptions.
- When it comes to AS/ A-level physics exam, the total momentum of a system before any interaction is exactly equal to the total momentum after it provided no external forces act.
- Then two objects collide, the changes in their momenta will be equal in size but opposite in direction. The momentum gained by one body equals the momentum lost by the other.
Tackling problems:
- Choose which direction is positive ➕
- Draw before and after sketches of the objects ✏️
- Calculate every momentum you can 🖩
- Apply the law of conservation of momentum for collisions involving 2 bodies. 💥
Recoil and explosions
Guns and cannons recoil when fired because of the law of conservation of momentum. The positive momentum gained by the bullet or cannon ball is equal to the negative recoil momentum of the gun or cannon, and so the total momentum before and after the explosion is zero.
Elastic and inelastic collisions
- Kinetic energy is conserved in elastic collisions.
- Kinetic energy is not conserved in inelastic collisions.
- Momentum is conserved in all collisions
- Total energy is conserved in all collisions
In inelastic collisions some kinetic energy is converted to other forms of energy ( mainly heat) ☀️. Large scale collisions are inelastic: collisions between hard steel spheres are nearly elastic: some particle collisions are elastic.
Impulse and Newton’s second law of motion
Most bodies have constant mass, so we normally note that un-balanced forced cause acceleration. At a more fundamental level we can state that unbalanced forced cause a change in momentum. The change in momentum depends on the size and direction of the force and the period of time over which it is applied. I.e. it depends in its impulse.
- Impulse is the product of force and time
- Impulse = change in momentum
- Ft = mv – mu (mu is initial and mv is final momentum)
- Force = rate of change of momentum = (mv-mu)t. This is another version of Newton’s second law of motion.
Impulse is measured in either newton seconds of kgms¯¹. Basically the same units as momentum.
References:
- https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.entrepreneur.com%2Farticle%2F330477&psig=AOvVaw2ioJpJoIwFDWdSwde33r_W&ust=1624765183660000&source=images&cd=vfe&ved=0CAcQjRxqFwoTCMjJjZWwtPECFQAAAAAdAAAAABAD
- https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.wired.com%2F2008%2F03%2Fmystery-anti-re%2F&psig=AOvVaw1jf8oZ7c6HaXSeAbcuCVoQ&ust=1624765571517000&source=images&cd=vfe&ved=0CAcQjRxqFwoTCLDv28ixtPECFQAAAAAdAAAAABA_
- https://www.google.com/url?sa=i&url=https%3A%2F%2Fquizlet.com%2F293258606%2Fmomentum-and-impulse-practice-problems-diagram%2F&psig=AOvVaw0wdCsxULInOwL4bgo45iQf&ust=1624765842841000&source=images&cd=vfe&ved=0CAcQjRxqFwoTCMiOtM6ytPECFQAAAAAdAAAAABAD
And we're all done for today!
Drafted by Kin (Physics)