A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by 𝐹= - i ^ \hat{i} i ^ + 2 j ^ \hat{j} j ^ + 3 k ^ \hat{k} k ^ 𝑁 where i ^ , j ^ , k ^ \hat{i},\hat{j},\hat{k} i ^ , j ^ , k ^ are unit vectors along the x, y and z-axis of the system respectively. What is the work done (in J) by this force in moving the body a distance of 4 m along the z-axis ?
Physics · Work , Power and Energy · question based on work
JEE Mains

Question

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by 𝐹= - i ^ \hat{i} i ^ + 2 j ^ \hat{j} j ^ + 3 k ^ \hat{k} k ^ 𝑁 where i ^ , j ^ , k ^ \hat{i},\hat{j},\hat{k} i ^ , j ^ , k ^ are unit vectors along the x, y and z-axis of the system respectively. What is the work done (in J) by this force in moving the body a distance of 4 m along the z-axis ?

Physics · Work , Power and Energy · question based on work

G1 Physics · Accepted Answer

Only the z-component of force does work for a displacement 4k̂ m. Therefore W=F(z) Δz=3×4=12 J.