How much energy does a fly exert if it does a single push-up in cgs (centimeters, grams, seconds) units. This should be about equal to the standard cgs unit of energy. Assume a fly is approximated by a cube 0.25 cm on a side, and is made of water (density of 1 g cm\(^2\)).
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| \(s = 0.25\) cm \(\rho = 1\) g cm\(^{-3}\) |
First, we must find the mass of the fly. To do this, we can estimate the size of the fly to find its volume, and then multiply by its density. We are already given that a fly can be considered as a cube with a side-length of 0.25 cm and with the density of water. Solving for the volume, we get:
\(V=s^3=0.25^3\approx 0.015cm^3\)
And multiply by density to find the mass:
\(m=V\rho=(0.015cm^3)(1g\cdot cm^{-3})=0.015g\)
Then to find the energy exerted by the fly, we must solve for the work done by the fly. Let's assume that a push-up is the upward lift of the fly's body and that the fly must lift its body 0.25cm.
\(W=mgh=(0.015g)(1000cm\cdot s^{-2})(0.25cm)\approx 3.8ergs\)
We found that the energy exerted by the fly is around 3.8 ergs. This is likely an overestimate since we were told in the question that 1 erg is a reasonable answer. The error in our answer could have resulted from a large approximation of the density of the fly and/or its volume. Perhaps treating the fly as a sphere with a diameter of 0.25cm might have been a better estimate since this would decrease the volume by a factor of two.
I would like to thank Charles Law for his assistance in solving this problem and in proofreading this blog post.
Image of fly: http://images.wisegeek.com/common-fly.jpg
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