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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.

Level 3


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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