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Work

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.

Level 2

         

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

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?

Bicyclists and other things that go fast must overcome air resistance, or drag, even to maintain a constant speed. A simple empirical model for the drag force on an object when the air flows smoothly around the object is \(\vec{F}_{Drag}=-c\vec{v}\), where \(\vec{v}\) is the velocity of the object and \(c\) is a constant that depends on the size and shape of the object. Consider a bicyclist putting out some power \(P_0\) (in watts) to overcome drag and maintain some constant speed \(v_0\). She then increases her speed to \(1.2 v_0\), which requires her to put out a power \(P_1\) to maintain. What is the ratio \(\frac{P_1}{P_0}\)?

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

There is a chain of uniform density on a table with negligible friction. The length of the entire chain is \(\si{1\ \meter}\). Initially, one-third of the chain is hanging over the edge of the table. How long will it take the chain (in seconds) to slide off the table?

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