Throwing a pen and measuring gravity

[Hawksteinman]

Homework Statement

We were given this question on a worksheet last lecture. The question is this:

‘Throw a tennis ball/your pen/some non-dangerous object into the air, straight up (and catch it again), observe its motion. Use your observation to measure the gravitational acceleration due to Earth [6 marks]

Homework Equations

v = u + at
s = ut + 1/2at²
v² = u² + 2as
a = (v - u)t/2

The Attempt at a Solution

’

So me and three of other people in this lecture just started discussing it. We started off by saying that it makes no sense, and trying to figure what it means.

In the end we said you would need a ruler to measure how high the object went and a stopwatch to measure time. You would then use s=ut + 1/2at² where u = 0 and t is half the time measured between throwing and catching.

So that is how we would measure it. But the question says to observe the motion not to measure it?

 

[Orodruin]

She did not say it had to be an accurate measurement. Regardless of the measurement you do it will come with associated errors.

 

[Hawksteinman]

He did not say it had to be an accurate measurement. Regardless of the measurement you do it will cone with associated errors.

Thx, so our method was correct?

*She

 

[Hawksteinman]

She said it was correct

 

[Orodruin]

A better way of controlling the distance parameter would be to simply drop the object instead of throwing it. Dropping it from about your own height should at least give you an error of at most 10 cm, which should be enough for the error to be dominated by the error achievable for the time without more precise instruments. (Even a stopwatch would give large errors on such small times.)

 

[mfb]

I would expect the largest uncertainty to come from the release process (time and initial speed). Timing the impact with the ground will be quite accurate. To improve that, you can throw the object up to nearly hit the ceiling, that gives an additional constraint. Or let it hit the ceiling and measure the time to fall down only.

 

[Orodruin]

I would expect the largest uncertainty to come from the release process (time and initial speed).

If you have the time and position relative to the top of the motion, you do not need the initial speed. If your release is quick enough, its contribution to the uncertainty in time should be negligible compared to the uncertainty coming to actually estimating time without a stopwatch.

Or let it hit the ceiling and measure the time to fall down only.

I would actually advice against that. If you hit the ceiling, you will not know that the velocity at that point is zero unless you can somehow make sure that the bounce is inelastic. A better way to measure time falling down only would be what I proposed in #5, which will give you a quite good handle on the distance.

 

[Hawksteinman]

Yes, she said make it almost hit the ceiling :)

 

[Hawksteinman]

 

[Orodruin]

Now here comes the tougher (but fun) extra exercise: Estimate your experimental error.

 

[mfb]

If you have the time and position relative to the top of the motion, you do not need the initial speed. If your release is quick enough, its contribution to the uncertainty in time should be negligible compared to the uncertainty coming to actually estimating time without a stopwatch.

Time and initial speed are linked depending on what exactly you account how. Fingers are not a very precise release mechanism, the object will accelerate slower than g for a while until it is fully released, and finding the time of that is difficult.

I would actually advice against that. If you hit the ceiling, you will not know that the velocity at that point is zero unless you can somehow make sure that the bounce is inelastic. A better way to measure time falling down only would be what I proposed in #5, which will give you a quite good handle on the distance.

Use something that doesn't bounce. The point here is the more precise timing estimate. There might be some initial speed, but as you discussed before, that alone doesn't lead to a large error.