A force is given by the vector F = {2,3} and moves an object from the point {1,3} to {5,9}. The force and displacement are in the same direction. Find the work done in foot - pounds.

Answer 1

To find the work done by a force along a displacement, we use the formula:

Work = force dot displacement

Where the dot product of two vectors is given by:

A dot B = |A|*|B|*cos(theta)

In this case, the force vector F = {2,3} and the displacement vector d = {5-1,9-3} = {4,6}.

First, we need to calculate the magnitudes of the vectors:

|F| = sqrt(2^2 + 3^2) = sqrt(4 + 9) = sqrt(13)

|d| = sqrt(4^2 + 6^2) = sqrt(16 + 36) = sqrt(52)

Now, we calculate the dot product:

F dot d = |F|*|d|*cos(theta) = sqrt(13)*sqrt(52)*cos(0)

Since the force and displacement are in the same direction, theta is 0 degrees and cos(0) = 1.

Therefore, the work done is:

Work = sqrt(13)*sqrt(52)*1 = sqrt(676) = 26 foot-pounds

So, the work done by the force in moving the object from {1,3} to {5,9} in the same direction given by the vector F = {2,3} is 26 foot-pounds.