Question

Calculate the work done by gravity as a 10 kg object is moved from point A = (0,0,0) to point B = (1,2,0). We are given s = (x sub f - x sub I)x(hat) + (y sub f - y sub I)y(hat) + (z sub f - z sub I)z(hat). Sorry if that doesn't make sense. I think I have to plug in the numbers into the equation but I don't know how to calculate the work done with the 10 kg object.

Answer 1

All that matters here is how far the object is lifted. (increase in U = m g h)
If z is the up direction, the work done is zero. If y is the up direction, U = 10*9.81*2

Answer 2

By the way usually the vector is written:

S = (X2-X1)i + (Y2-Y1)j + (Z2-Z1)k

Where I, j and k are unit vectors in the x, y and z directions.

If Z is up, the work done is zero going from z = 0 to z = 0

since the force vector is in the -k direction

dU = F dot dS

= [ 0 i + 0 j - m g k] dot [ dX i + dY j + dZ k]

= m g dZ (which is a scalar change in potential)