- #1

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^{2}and a and t were both functions of F

a(F) = F-g

t(F) = gT/F

and I wanted to know how much X changes with respect to F, how would I do that?

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- Thread starter Zula110100100
- Start date

- #1

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a(F) = F-g

t(F) = gT/F

and I wanted to know how much X changes with respect to F, how would I do that?

- #2

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Are g and T constant?

- #3

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yes, they are

- #4

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First step substitute (F - g) for a and gT/F for t to get x in terms of F and the constants.

- #5

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x(F)= g

x(F) = g

x'(F) = g

- #6

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^{2}T^{2}/2F - g^{3}T^{2}/2F^{2}

QUOTE]

It is better if one leaves the two terms seperate as above.

- #7

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x(F) = g

x'(F) = -g

That is correct?

- #8

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[itex]\frac{g^{2}T^{2}F^{-1}}{2}[/itex] - [itex]\frac{g^{3}T^{2}F^{-2}}{2}[/itex]

- #9

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Your differentiation is correct.

- #10

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I am not sure if I need to take the derivative now, so I guess let me lay it on ya

gT = Ft

gX = Fx

a = F-g

t = gT/F

x = 1/2at

x = g

If I am trying to find F for a given g, X, and T

I could just put x = gX/F in for x and get

gF

divide by gF

gives me

X=gT

multiply by F and rearrange a bit to get

gT

pull out F for F((gT

divide for

F = g

Any of that look right?

- #11

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Your final line x'(F) = -g2T2/2F2 + g3T2/F3

was ok. That is you were asked to find dX/dF and you found it because your differentiation was ok.

- #12

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If the non-differentiated version is correct, and i know the equation

gX = Fx

can I not solve for x = gX/F

substitute that back into the equation I had gotten for x(F), and then I have F in terms of only g, X, and T, getting rid of x and t?

The resultant equation should be correct to give me F for a given g, X and T, right?

- #13

- 993

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From where did you get gX = Fx?

- #14

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Right, so what I am looking at here is g = gravity, X is the total displacement, F is a force that is greater than and opposite to gravity, and x is a distance less than X, at s=0 the velocity is 0 and s=X the velocity is 0, so the potential energy given by gX must equal the energy put into the system Fx

Or to keep this as he math sub-forum, it is a given from post#10

Or to keep this as he math sub-forum, it is a given from post#10

Last edited:

- #15

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- #16

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Which they both indeed are

- #17

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- #18

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It is getting rather late over here...Sorry.

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