Phy 201
You define impulse as the product of F*'dt. In the first few problems you say that impulse is equal to the change in momentum, by the Impulse-Momentum Theorem. What is the Impulse-Momentum Theorum, and will impulse always equal momentum?
The Generalized Solution of the first problem tells you something very much like the following, except that when I wrote that I didn't have the sense to use F_net instead of F and to specify that F_net is constant:
If a constant net force F_net acts on object of constant mass m for `dt seconds, the object will experience acceleration a = F / m for `dt seconds, resulting in velocity change
* `dv = a `dt = (F_net / m) `dt = (F_net `dt) / m.
When the relationship `dv = (F_net `dt) / m is rearranged into the form
* m `dv = F_net `dt
we have the Impulse-Momentum Theorem for object of constant mass.
We can use the Impulse-Momentum Theorem to find any of the quantities `dv, F, m or `dt given the values of three of these quantities.
The quantity m v is called the momentum of a mass m at velocity v. We use the letter p to denote momentum.
If m remains constant, then the change in momentum is
`dp = m vf - m v0 = m ( vf - v0 ) = m `dv.
So the impulse-momentum theorem says that m `dv = F_net `dt, which in words says that
change in momentum is equal to the impulse of the net force.