How High Can a Flea Jump Using Resilin Energy?

[PSEYE]

The resilin in the upper leg (coxa) of a flea has a force constant of about 26 N/m, and when the flea cocks its jumping legs, the resilin in each leg is stretched by approximately 0.10mm .

Given that the flea has a mass of 0.55mg , and that two legs are used in a jump, estimate the maximum height a flea can attain by using the energy stored in the resilin. (Assume the resilin to be an ideal spring.)


h=?


Thanks for the help!

 

[Varnick]

You need to make an attempt at a solution, it is not our job to do your homework for you. If you can show effort, than we can be of further assistance, if you are struggling.

 

[PSEYE]

So you don't know the answer? I have plenty of work on my paper, but it's all chicken scratch.

 

[Varnick]

I could work out the answer, but the stickies for this forum give a clear structure for posting, which includes an attempt at the solution. What have you tried so far? What is going wrong?

V

 

[PSEYE]

I'm trying to use hooke's law for the spring in the flea's legs.

which would be F=kx
F=(26N/m)(2x(for each leg)(0.0001m)
I got a force of 0.0052

I thought of using PE=mgh, the only equation I know of that would give me the height.
I'm sure it's a simple problem I just don't know which equation to plug the given values into.

U=mgh

1.16x10^-6 = 5.5x10^-6 (9.8)h
h=2.15cm, but it's wrong.

 

[Doc Al]

Hint: How much energy is stored in the flea's cocked legs?

 

[moemoney]

You're on the right track.

You have F = kx. Work is force over a distance right? So if you find the integral of F = kx over the interval [0,.10], you can find the enegry stored in the flea's coked legs as Doc Al stated above.

F = kx => W = 1/2kx^2

 

[PSEYE]

ahh...
1/2kx^2 = 1/2mv^2

then plug into 1/2mv^2=mgh

h= v^2/2g

 

[Doc Al]

ahh...
1/2kx^2 = 1/2mv^2

then plug into 1/2mv^2=mgh

h= v^2/2g

OK, but you can go directly from spring potential energy to gravitational potential energy. (No need to worry about kinetic energy.)