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Work transfers energy to a system through the forceful manipulation of its state. Do some work on yourself to master this fundamental mode of energy transfer.

Water in a river speeds up as it goes over the top of a waterfall. What is the primary reason this happens?

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Consider a village of area 0.16 square kilometers on the equator. The total energy intensity of sunlight at the surface of the earth when the sun is directly overhead is \(1370\text{ W/m}^2\). How much solar energy in Joules hits the village per second at noon?

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Suppose that to hike a distance \(L\) while carrying nothing, your body requires an amount \(L \gamma_0\) of food, and that when you carry an extra weight \(M\) in your backpack, your body is less efficient and requires the amount of food \[L \gamma_0 \left(1+\frac{M}{W_\text{body}}\right)\] where \(W_\text{body}\) is the weight of your body.

If you start out with the weight \(M\) of food in your ultralight (weightless) backpack, how far (in miles) can you hike in total?

**Assumptions**

- All your energy comes from eating the food in your backpack.
- You eat the food as needed for your energy needs.
- \(M\) = 50 lb
- \(W_\text{body}\) = 160 lb
- \(\gamma_0=12^{-1}\) lb food per mile

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