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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.

# Work: Level 3 Challenges

A well fed laborer can sustain a mechanical power output of roughly 75 Watts. How many person-hours are required to generate the total amount of work needed to raise the pyramid blocks off the ground into the shape of the great pyramid?

###### Image credit: Wikipedia Mike Knell

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 $$\frac{P_1}{P_0}$$?

Two forces $$\left(6\hat{i} + 2\hat{j} - 3\hat{k}\right) \si{\newton}$$ and $$\left(5\hat{i} - 3\hat{j} + 7\hat{k}\right) \si{\newton}$$ act on an object that moves on a frictionless surface and, in doing so, displace it from $$\left(2\hat{i} + 3\hat{j} - 5\hat{k}\right) \si{\metre}$$ to $$\left(-3\hat{i} - 3\hat{j} + 4\hat{k}\right) \si{\metre}$$.

Find the magnitude of the work done on the object, $$W$$ in joules.

Suppose you are standing still and upright, and you decide you want to jump into the air. Why do you have to bend your legs first?

A $$1.2\text{ kg}$$ mass is projected down a rough semi-circular vertical track of radius $$2.0 \text{ m}$$, as shown in the diagram below. The speed of the mass at point $$A$$ is $$3.2\text{ m/s}$$, and that at point $$B$$ is $$6.0 \text{ m/s}$$.

How much work is done on the mass between $$A$$ and $$B$$ by the force of friction?

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