# Proving that force and acceleration are proportional

1. Sep 16, 2012

### adam199

1. The problem statement, all variables and given/known data

I need to prove that force is proportional to acceleration given the results of my experiment. We used a frictionless air glide track at a fixed angle and took data on the velocity of a gliding flag moving down the track. In the experiment, I put more weight on the flag for each successive trial, yet the measured final velocity for each trial was the same, at around 0.4 m/s. So for each trial at a fixed angle, I got the exact same velocity for all runs, despite the change in weight put on the flag. Given this data, I'm supposed to prove that force is proportional to acceleration

2. Relevant equations

F=ma

a=F/m

a=[v(final)^2-v(initial)^2]/(2x) <-----x is the distance travelled, and v(initial) is 0

3. The attempt at a solution

The best I could come up with was that acceleration was fixed because force and mass were in the same ratio for each trial, but force must've increased for each trial along with the increase in mass to keep acceleration fixed. I'm not sure how a fixed acceleration with an increasing force can show how force and acceleration are proportional.

If you all need more information just let me know, and I may be able to provide it since I have more information from the experiment.

I would appreciate the help!

2. Sep 16, 2012

### Simon Bridge

Force was due to gravity - the gravitational force is proportional to the mass.

You'd have been able to vary the acceleration by changing the angle of the track.
You could have added a pulley and an extra mass and pulled the air-cart along the track with different falling weights. All kinds of stuff (that also have their own pitfalls).

So your force was $F=mg\sin(\theta)$, for different forces you measured the acceleration... then you can plot acceleration against force ... and you get a constant acceleration for a range of forces and you conclude that the experiment failed to show that the force was proportional to the acceleration.
In fact, what you have demonstrated is that all falling objects have the same acceleration ... Galileo did a similar experiment to demonstrate the same thing.

3. Sep 19, 2012

### adam199

I know this is late, but I wanted to thank you for helping me clear things up.

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