# Experiment with forces - Formula question

1. Mar 8, 2012

### -Physician

1. The problem statement, all variables and given/known data
I took a ball of mass= 530g and someone held it in a high for me, i wanted to find that high and what i did is :
1. act a force of 7N on it
2. the time of ball going down was 3s
i wanted to find the high and what i did is:
$high=force acted * time / mass$
when i calculated that, the units were wrong and i squared the time. What i won was this:
$h=\frac{Ft^2}{m}$ and i got
$m=\frac{\frac{kgm}{s^2} * s^2}{kg}$
(kg simplified with kilogram, the s^2 with s^2 , and i won m)
I did the same thing again and the high was exactly as calculated ( 120.7547169811321m)(121m)
But I think there's still something wrong in formula because there's no gravity in formula , but then my friend said $a=F/m$ but in this case we have a high so gravity would be F/m, and we would still win $h=gt^2$ . Is all this right? thanks for reading !

2. Mar 8, 2012

### Camille

You mean the ball was in a free fall from this height?

The simplest equation you can get is $h = \frac{gt^2}{2}$. Your equation $h = \frac{Ft^2}{m}$ is exactly this (after simplification), and the acceleration of gravity is hidden in the force:

$h = \frac{Ft^2}{m} = \frac{mgt^2}{m} = gt^2$,

though $2$ in the denominator is missing.

You can also try the conservation of energy: $\frac{mv^2}{2} = mgh \rightarrow h = \frac{v^2}{2g}$ but then you would have to know the final velocity (before hitting the ground).

Last edited: Mar 8, 2012
3. Mar 9, 2012

### -Physician

So my formula is wrong?

4. Mar 9, 2012

### Staff: Mentor

This was a vertically-directed force? What arrangement did you use to cause 7N to continuously act on the ball while it was falling? How did you neutralize gravity for your experiment?
So you invented your own equation And you're surprised that it seems to give the right answer?
I'm surprised, too, but can't explain it.

The equation you need is: s = ut + ½·at2

5. Mar 11, 2012

### -Physician

As I see, you didn't read all the post bro, the high=force acted *time/mass was wrong, next time read all the post.....
s=ut+at^2/2, it's v_0t not ut , or vt - at^2/2