A body constrained to move along Z-axis of a coordinate system is subjected to a constant force F given by F ⁡ = - i ⁡ ^ + 2 j ⁡ ^ + 3 k ^ N ⁡ where i ^ , j ^ and k ^ are the unit vector along the X,

Question

A body constrained to move along Z-axis of a coordinate system is subjected to a constant force F given by F ⁡ = - i ⁡ ^ + 2 j ⁡ ^ + 3 k ^ N ⁡ where i ^ , j ^ and k ^ are the unit vector 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?

TestHub · Accepted Answer

Force, F ⁡ = - i ^ + 2 j ^ + 3 k ^ N Displacement, s ⁡ = 4 k ^ m = 0 i ^ + 0 j ^ + 4 k ^ m ⁡ Work done by the force is given by W = F . s = - i ^ + 2 j ^ + 3 k ^ · 0 i ^ + 0 j ^ + 4 k ^ = ( – 1 × 0 ) + ( 2 × 0 ) + ( 3 × 4 ) = 0 + 12 ∵ i ^ · j ^ = j ^ · j ^ = k ^ · k ^ = 1 and i ^ · j ^ = j ^ · k ^ = k ^ · i ^ = 0 = 12 J

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