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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 3

         

A locomotive of mass \(m\) starts moving so that its velocity varies according to the law \(v=k \sqrt{s}\), where \(k\) is a constant and \(s\) is the distance covered. Find the total work performed by all the forces which are acting on the locomotive during the first \(t\) seconds, after the beginning of motion.

  • If \( W=\large\frac { m{ k }^{ \alpha }{ t }^{ \beta } }{ \mu } \), find \(\alpha +\beta +\mu \).

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.

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 \(\frac{P_1}{P_0}\)?

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

A \(1\text{ kg}\) object is lifted from point A to point B through two different pathways as shown in the figure above. What are the respective amounts of work done in the left and right figures?

The gravitational acceleration is \(g=9.8\text{ m/s}^2.\)

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