1 50 points The work W done by a constant force F in moving

1. (50 points) The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as W-F AB . Use this definition to find the work done in moving an object along a vector u-3i + 2j -5k if the applied force is FH2i-i-k. Use meters for distance and newtons for force.

Solution

Ans: Moving an object along the vector means moving from initial point of the vector to final point.

Here the vector is u = 3i + 2j - 5k & force F = 2i -j -k

Work done W = dot product of F & u. So by definition of dot product

W = (2i -j -k). (3i +2j -5k). In dot product we multiply the coefficients of same unit vector and then add them.

Here, W = (2*3) + (-1*2) + (-1*-5) = 6 - 2 + 5 = 9 Newton metre = 9 Joule.