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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.

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.

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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