Finding the acceleration of a held object suddenly released

[SelfTeaching]

Hello, I was trying to think of how one would find the acceleration of an object which was suddenly released from being held in place, the object would be trying to move beforehand but unable to.

For example, a boat is tethered to a dock, the cranks the gas up, when suddenly the tether snaps, how would you find how quickly the boat ends up accelerating until it reaches its final velocity?

 

[berkeman]

If you are holding an object and drop it, the acceleration due to gravity is constant, g=9.8m/s^2.

If you have an object that wants to move horizontally, and you are holding it back, then the force you are holding it back with is basically equivalent to the force that will accelerate it when you let go. That force will produce an initial acceleration per the classic equation:

F=ma

Are you familiar with that equation yet?

 

[SelfTeaching]

yes, but my problem stems more from what if you have neither acceleration nor the force, do you just find out with experiments?

 

[berkeman]

yes, but my problem stems more from what if you have neither acceleration nor the force, do you just find out with experiments?

Sure, you can do experiments, especially if the force will vary over time (like with a car acceleration).

You can still figure out the initial acceleration by just putting a force meter (like a spring-based fish scale) in the rope or whatever is holding the thing from moving.

 

[SelfTeaching]

Could you find the acceleration theoretically though? I knew before that I could do an experiment if I really needed to, but I don't have the money for what I have in mind, sorry I should have been more specific in the original post.

 

[berkeman]

Could you find the acceleration theoretically though? I knew before that I could do an experiment if I really needed to, but I don't have the money for what I have in mind, sorry I should have been more specific in the original post.

Yes, generally you can figure it out by calculation. If you can be more specific, we should be able to point you in the right direction.

 

[SelfTeaching]

okay, well, say you have some aircraft, but in order to make it require no run way, you simply hold it in place and have some source of thrust attached to the aircraft blow air at very high speeds over the wings until it begins to create enough lift to lift itself. the problem would be i know what the max acceleration should be so the person doesn't fall unconscious (about 1G i think is common, so i decided two thirds would be an acceptable max acceleration) but i don't have the force stopping the aircraft from moving would be, all i know is that the air would be flowing at say 30 m/s, so assuming that creates enough lift to make the aircraft break free and take off right away, how fast would the aircraft accelerate if it had a final speed of 30m/s, from rest. (I know that air resistance will be a factor, and most likely a little bit of wing deflection, but for simplicitys sake id rather not think about it yet)

Anyways, thanks for your help so far.
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Thanks for the reference material, ill look it up a bit more maybe it will give me ideas, my plan was to make this whole thing on a much smaller scale, which is why this can't be used just as is, it needs to be self sufficient, although i still don't know how to find out the acceleration. Thank you.

 

[berkeman]

okay, well, say you have some aircraft, but in order to make it require no run way, you simply hold it in place and have some source of thrust attached to the aircraft blow air at very high speeds over the wings until it begins to create enough lift to lift itself. the problem would be i know what the max acceleration should be so the person doesn't fall unconscious (about 1G i think is common, so i decided two thirds would be an acceptable max acceleration) but i don't have the force stopping the aircraft from moving would be, all i know is that the air would be flowing at say 30 m/s, so assuming that creates enough lift to make the aircraft break free and take off right away, how fast would the aircraft accelerate if it had a final speed of 30m/s, from rest. (I know that air resistance will be a factor, and most likely a little bit of wing deflection, but for simplicitys sake id rather not think about it yet)

Anyways, thanks for your help so far.

The problem, though, is that you will need to keep adding the moving air over the wings until the plane gets up to its minimum flight speed. That's why aircraft carrier catapult launchers exist:

http://science.howstuffworks.com/aircraft-carrier3.htm

The "holdback bar" is doing exactly what you are describing -- the plane is up at full throttle, and the holdback bar is holding the nosewheel so that the plane does not move until the catapult fires. The plane thrust plus the catapult shuttle pulling force breaks the holdback bar connection, and away she goes...