Question

a workman carries some lumber up a staircase. the workman moves 9.6 m vertically and 22 m horizontally. if the lumber weighs 45 n. how much work was done by the workman?
a 562 nm
b 402 nm
c 432 nm
d 316 nm

Explanation:

Step1: Recall the work formula

Work \(W = F\times d\times\cos\theta\). When moving horizontally, the force (weight of lumber, \(F = 45\ N\)) and the horizontal displacement (\(d_{x}=22\ m\)) are perpendicular (\(\theta = 90^{\circ}\), \(\cos90^{\circ}=0\)), so work done horizontally \(W_{x}=F\times d_{x}\times\cos90^{\circ}=0\). When moving vertically, \(\theta = 0^{\circ}\), \(\cos0^{\circ} = 1\), and \(d_{y}=9.6\ m\).

Step2: Calculate work done vertically

Using \(W = F\times d\times\cos\theta\), with \(F = 45\ N\), \(d = 9.6\ m\) and \(\cos\theta=1\) (since force and displacement are in the same direction vertically), we have \(W=45\times9.6\times1\).

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Answer:

C. \(432\ Nm\)