Homework Help: Theoretical expression for relationship between height and force

1. Nov 30, 2013

thakshi

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

I did an experiment investigating what effect height has on force and now i need a theoretical value to compare it to

2. Relevant equations

f=ma but i dont think acceleration is constant here

3. The attempt at a solution

f=ma
f=0.104x9.8
f=1.01
i got 49 N with the force plate..help

2. Nov 30, 2013

Mandelbroth

3. Nov 30, 2013

Simon Bridge

The height of what?
On what force?

4. Dec 1, 2013

thakshi

what information do you need?

5. Dec 1, 2013

thakshi

basically the experiment was dropping a constant mass at different heights and seeing if the force exerted on the Force Plate increases or decreases as height increased. it increased and now i need an accepted value to compare my data to

6. Dec 1, 2013

Simon Bridge

The force on the plate will vary over the time of the collision - so I'm guessing the plate is recording either the maximum force or the time-average of the force or the specific impulse... which is it?

This is important because there is no such thing as the force of a collision.

The maximum force would be proportional to the change in momentum, which depends on the initial speed and the material properties of the plate and mass. So how does the speed that a mass hits the floor depend on the height it was dropped from?

What you should do it plot your height vs "force" and see what sort of curve it appears to be trying to be.
Compare with the speed vs height graph for the same values... you are comparing the shape not the exact values.

7. Dec 1, 2013

thakshi

it records max force

8. Dec 1, 2013

thakshi

well i did not record the time when it fell so i wont be able to do speed

and the graph i plotted-- as height increases, the force increases

i dropped a mass of 104 grams

9. Dec 1, 2013

Simon Bridge

You don't need to have timed the fall to get a theoretical value for the final speed - you know the height and you know the acceleration, and you know the kinematic equations.

Is this what you would have expected? i.e. do you normally expect objects to hit the ground harder when they fall from higher up?

In what way does it increase?
i.e. is it a line or a curve?
If a curve, what sort of curve?
If a line, what is it's slope?

What would air resistance do to a force vs height graph?

How does the mass matter?

10. Dec 1, 2013

thakshi

is it constant?

is there an equation relating height and force??????

11. Dec 1, 2013

Simon Bridge

Is what constant?

It's not an easy one.
It depends on the material properties of the object falling and the surface it lands on.
Basically it is Newton's second law - but using momentum.

12. Dec 1, 2013

thakshi

is acceleration constant?

13. Dec 1, 2013

Simon Bridge

Hah! You tell me ...

What determines acceleration?

(note: I've edited post #9 since you've replied)

14. Dec 1, 2013

thakshi

oh forget it

15. Dec 1, 2013

Simon Bridge

Giving up so easily?

Perhaps you are expect people to just give you the answers?

This was posted as "homework".
We do not spoon-feed people here - it's your homework, you have to do the work.
What I can do is point you in a useful direction.

Perhaps you do not know what determines acceleration?

Hint: Newton's second law. You seem to keep getting stuck on this - perhaps you should revise Newton's Laws?
The one you want is "the force on an object is equal to the rate of change of it's momentum".

Or you could just remember the famous Galileo experiment - dropping balls off the leaning tower of Piza?

16. Dec 2, 2013

thakshi

well i tried and i dont get it so i came here
thanks though

17. Dec 2, 2013

Simon Bridge

I'm sorry but I see no evidence of you trying at all.

Either that or you are doing physics that is way above your knowledge level ... you should be able to work out whether the acceleration of a falling object is a constant or not for instance. You should know Newton's Laws already. Stuff like that.

You need to get to grips with the basics before you can expect to be able to tackle experiments like the one you described.
Is this for school or is this something you rigged up for your own interest?
What's the context?

18. Dec 2, 2013

thakshi

What do you want me to answer?

19. Dec 2, 2013

Simon Bridge

From post #9:
From post #13:
From post #15:
From post #17:
The thing is - there is no "standard value" for the max-force of impact for you to compare your results with, but you do need to compare them with something in order to see if the theory is any good. The answers to the above questions will help me figure out something that you can use. You probably won't want to use the kind of thing I'd use...

At the very least you should be able to write a conclusion about the way the force increases with the height dropped from to show the marker that you've understood what you've done.

Note: drop tests using electronic sensors like you did are routine in engineering.

Last edited: Dec 3, 2013
20. Dec 3, 2013

thakshi

Is this what you would have expected? i.e. do you normally expect objects to hit the ground harder when they fall from higher up?- yes this is what i usually expect

In what way does it increase?- with my errors bars taken into account, the force is directly proportional to the height at which it dropped

How does the mass dropped matter?- as long as its constant, it shouldnt matter?

What determines acceleration?- mass, force? velocity over time?
Perhaps you do not know what determines acceleration?

Is this for school or is this something you rigged up for your own interest?- its for a lab due VERY soon, physics class
What's the context?

21. Dec 3, 2013

Simon Bridge

OK - do you know Newton's second law? F=ma => a=F/m
For your object: what are the forces on it as it falls? Do these forces change with the start-height at all?
If the forces are constant, the acceleration is constant.

It's tough that you are running out of time ... but you appear to have fundamental gaps in your physics.
Best practice is to read through the Lab notes a couple of days before you do the lab to make sure you understand the concepts involved ... just following instructions, as you are finding out, won't help.

Since you have your data you can do some analysis (find the equation of the best-fit line, pref. with errors) ... and you can write down a conclusion right away.

The exact wording depends on what the "aim" says ... but you want to say that the data is consistent with the max impact force being directly proportional to the drop height with relation [the equation of the best fit line].

Notice that you do not want to conclude that the force is directly proportional to the drop-height (it's not actually the case) ... just that your data is consistent with this.

To look extra good you want to comment on this result ... normally this is where you compare with some standard result. Unless you have information I don't, there won't be an easy way to get a standard result ... but you can comment on what the y-intercept of the graph means. Does the best-fit line go through the origin? Is this to be expected? (i.e. what would the theoretical force on the plate be for a zero drop-height?)

That should be good enough for a senior High School physics lab ... and it should scrape by good marks for entry-level college.

Technically the force should depend on the square-root of the height ... but your data does not show that so you'd have to derive it to use it.

22. Dec 3, 2013

thakshi

yeah i do know the second law
the best fit line does go through the origin cause when the height is zero, there won't be a force.
the comparing with the standard part is the part im having difficultly with...
"Technically the force should depend on the square-root of the height ... but your data does not show that so you'd have to derive it to use it." how would i derive it

23. Dec 3, 2013

Simon Bridge

... well you kept not answering any questions about it so I couldn't assume you did. We get people with all kinds of ability here so if you don't show off what you got we have to assume you ain't got it ;)

... so you are saying that an object just sitting on the force plate does not exert a force on it?

(a) you don't need it - just the observation about the y-intercept should count as a standard result. (Unless the instructions specifically tell you to compare something to a standard result?)
(b) you have to use you knowledge of Newton's Laws ... since you didn't answer the last round of questions I cannot be more specific.

- coefficient of restitution
- conservation of energy
- conservation of momentum
- specific impulse

I have the whole derivation sitting here but I cannot give it to you because you'll be tempted to just copy it - if you did that, it will be obvious that you have cheated and you'd be punished. I don't want to do that to you.

24. Dec 3, 2013

thakshi

thanks so much for your help
its due tomorrow and think i will not include the derivation then
yeah i have to compare it to a standard result!

25. Dec 3, 2013

Simon Bridge

Since you are told in the instructions that you need to compare it to a standard result - then you will have been provided with an appropriate result to do the comparison with. Most likely a result that can be derived from the data you collected.

Check the "aim" of the experiment and review the resources on hand.
Maybe you have been provided a theory already that you are supposed to use and you missed it? Check.