A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F = −ˆi + 2 ˆj + 3 kˆ N where ˆi, ˆj, kˆ 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 ?
Given: The constant force applied on a body is F → = ( − i ^ + 2 j ^ + 3 k ^ ) N .
The body is being moved along the z- axis and is at a distance 4 m from the origin.So, the displacement vectorof the body at this instant will be S → = ( 0 i ^ + 0 j ^ + 4 k ^ ) m .
Thework done by the force in moving the body is given as,
W = F → ⋅ S →
By substituting the given valuesin the above equation, we get
W = ( − i ^ + 2 j ^ + 3 k ^ ) ⋅ ( 0 i ^ + 0 j ^ + 4 k ^ ) = ( 3 k ^ ) ⋅ ( 4 k ^ ) = 12 J
Thus, the work done by the force in moving the body a distance of 4 m along the z –axisis 12 J.
Given: The constant force applied on a body is
The body is being moved along the z- axis and is at a distance 4 m from the origin.So, the displacement vectorof the body at this instant will be
Thework done by the force in moving the body is given as,
By substituting the given valuesin the above equation, we get
Thus, the work done by the force in moving the body a distance of 4 m along the z –axisis 12 J.
