##### 2.4.1 Define Linear Momentum and impulse

If you get hit by something with a small mass but high velocity (a bullet) it hurts. If you get hit by something with a large mass but low velocity (slowly rolling car) it still hurts. Newton called momentum (velocity times mass) the quantity of motion, momentum is a fundamental quantity.

Newton originally wrote his second law as:

(1)The more common format of $F_{net}=ma$is a special case of Newton’s second law.

Let's define a few terms:

**Linear Momentum** – mass times linear velocity: $\vec p=m\vec {v }$

**Impulse** – equal to the change in momentum $\Delta \vec p = \vec F \Delta t$. Graphically the impulse is the area under the curve of a force vs. time graph.

##### 2.4.2 State the law of conservation of momentum

##### 2.4.3 Derive the law of conservation of momentum for an isolated system consisting of two interacting particles.

Consider two balls, with *initial* momentum *p _{1,i}* and

*p*approaching each other, after the collision they have

_{2,i}*final*momentum,

*p*and

_{1,f}*p*.

_{2,f}Therefore we can define the change of momentum for each ball as:

(2)When they collide they each apply force to the other ball, F_{1} and F_{2}, according to Newton’s 3rd law the forces must be equal and opposite.

Since the time the forces are applied (the time the balls are in contact) is the same we can simplify:

(6)**or**

Grouping the initial and final momentums together:

(8)Where the left hand side is the total initial momentum and the right hand side is the final momentum.

This is the law of conservation of momentum, i.e. the amount momentum you start with is the amount you end with (direction matter too!). **Momentum is ALWAYS conserved.**

thanks again. Very useful and helpful for tests/exams

ReplyOptionsnot useful

ReplyOptionsMaybe add something on Elastic and Inelastic collisions?

Elastic collisions: (When objects A and B collide and separate)No mechanical energy is lost. Only on the molecular level because, in reality, colliding objects will always lose some energy.

Totally inelastic collision: (When objects A and B collide and stick together) Lots of lost mechanical energy and converted into heat and sound but the momentum is still conserved.

Inelastic collision: (Objects A and B collide, separate but both objects are travelling in the same direction) Some lost energy, not as much as the "totally inelastic collision". As always, momentum is conserved.

ReplyOptionsThanks helped a lot!

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