How Can Gravitational Acceleration 'g' Be Expressed Using Ball Passage Times?

[dante714]

Homework Statement

In a physics laboratory the value of g , the gravitational acceleration in the vicinity of Earth, has been measured accurately by projecting a ball up an evacuated tube and electronically timing the passage of the ball in its upward and downward flight through two light beams, an accurately known distance 's' apart. [/B]

If the successive times of passage through the beams are: t0 ,t1 ,t2 ,and t3, express 'g' in terms of 's' and the times of the passage of the ball.

Homework Equations

[/B]
Fnet = ma

The Attempt at a Solution

I believe that Newton's 2nd law: Fnet = ma is imperative to solving this problem but I am not exactly sure how. Can anyone answer this problem?[/B]

 

[Orodruin]

You will need to provide a little more of an attempted solution than that. Ask yourself how the times should relate to the motion of the ball if the ball is moving only under the influence of gravity in a gravitational field $g$.

 

[dante714]

You will need to provide a little more of an attempted solution than that. Ask yourself how the times should relate to the motion of the ball if the ball is moving only under the influence of gravity in a gravitational field $g$.

Hello Orodruin,

This is what I have done so far

Setting u0 as an unknown at t0, s0
u1 at t1, s
u2 at t2, smax-s
u3 at t3, smax

As the tube is evacuated it should be expected that u3 = -u0 and u2 = -u1 - a quick check of t3-t2 and t1-t0 should confirm whether this is a good assumption (it will be closer than a similar experiment in air).

-u0 = u0 + g (t3-t0) :- u0 = 0.5 g (t0-t3)
{-u1 = u1 + g (t2-t1), and u1 = u0 + g (t1-t0) :- u0 + g (t1-t0) = 0.5 g (t2-t1) * not used in this solution}

s = u0 (t1-t0) + 0.5 g (t1-t0)^2
s = [0.5 g (t0-t3)](t1-t0)+0.5 g (t1-t0)^2
g [(t0-t3)+(t1-t0 )] = 2 s / (t1-t0)
g * (t1-t3) = 2s / (t1-t0)

g = 2 s /[(t1-t0)*(t1-t3)]

Please PM me to confirm if this is the correct answer