# Momentum, impulse, impact

1. May 13, 2004

### thingsfallapart

Hi- I have a quiz tomorrow on Newton's 1st and 2nd Laws. I'm kind of iffy with the second law, especially when it comes to impulse and impact. What is impact, and how can you measure impulse? For example, what if an object is dropped onto a soft couch, etc, etc.. basic theories... i haven't yet studied conservation of momentum so leave that out.. someone please explain the 2nd law and all that momentum/impact/impulse PLEASE!!

2. May 13, 2004

### arildno

Now, I assume you have learnt about integration:
Newton's 2.law for a single object (I'll use a point particle with constant mass as my object) states:
F=ma,
where F is the sum of all forces acting on the object, m is the mass of the object, and a the acceleration of the object.
Let's integrate Newton's law from time t=0 to a time t=T.
Then we have:
$$\int_{0}^{T}Fdt=mv(T)-mv(0)$$
where v(T) is the velocity of the object at time t=T and v(0) is the velocity of the object at time t=0.
Hence, the right-hand side of the equation is simply the change in the object's momentum between times 0 and T.

What is the left-hand side?
That is the impulse I acting upon the object in the time interval 0 to T, or:
$$I=\int_{0}^{T}Fdt$$

The integrated version of Newton's 2.law states therefore:
The impulse acting upon an object during a time interval is equal to the object's momentum change during the same interval.

Is it okay so far?