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Work, Power and Energy

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Question : 11 of 30
Marks: +1, -0
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
F=−i^+2j^+3k^ NF = -\hat{i} + 2\hat{j} + 3\hat{k} \, \mathrm{N}
where i^,j^,k^\hat{i}, \hat{j}, \hat{k} are unit vectors along the x, y and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?
Solution:  
Given that F⃗=(−i^+2j^+3k^) N\vec{F} = (-\hat{i} + 2\hat{j} + 3\hat{k}) \, \mathrm{N}, d⃗=4k^\vec{d} = 4 \hat{k}
W=F⃗⋅d⃗W = \vec{F} \cdot \vec{d} =(−i^+2j^+3k^)⋅(4k^)= (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (4 \hat{k})
=12k^⋅k^=12 J= 12 \hat{k} \cdot \hat{k} = 12 \, \mathrm{J}
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