İmpulse from the string

1. Feb 2, 2017

Arman777

1. The problem statement, all variables and given/known data
A ball of mass 1.00Kg is attached to a loose string fixed to a ceiling.The ball is released from the rest and falls 2.00m,where the string suddenly stops it.Find the impulse on it from the string.

2. Relevant equations.
Kinematic equations
$\vec J=\vec FΔt=Δ\vec P$

3. The attempt at a solution
+z direction is upward.
$ΔH=v_0t+\frac 1 2at^2$ so this becames

$-2m=0-\frac 1 2gt^2$
$t=0.638 s$

and

$-2m=v_0t-\frac 1 2gt^2$
we know $t$ so
$-2-1.99=v_0(0.638s)$
$v_0=-6.25\frac m s$

then
$\vec J=\vec FΔt=Δ\vec P$
so
$P_f=m(-6.25)$
$P_i=m0$
$ΔP=-m6.25=-6.25Ns=J$

answer says $6.25Ns$ so theres no minus sign...
I didnt understand why...The question says "Find the impulse on it from the string" so the thing I found is some other impulse which created by something else..?

2. Feb 2, 2017

jbriggs444

The final momentum $P_f$ is what again? Did the problem statement not say that the string stops it?

3. Feb 2, 2017

Arman777

Is it wrong ?.I just wrote the velocity of the ball...Sure,spring stops it.I see I guess.

4. Feb 3, 2017

jbriggs444

What is the "initial" condition just before the string stops the ball?
What is the "final" condition just after the string stops the ball?

5. Feb 3, 2017

Arman777

Ohh $P_i$ is not $0$ its $-mv$ so $0-(-m v)=mv$ I solved

6. Feb 3, 2017

Thank you