Find the work done by the force in moving the body from A to B.?

Question

A force F acting at a point A displaces a body to a point B.

The coordinates of A are (-3,17,-15)
The coordinates of B are (16,4,15)
The force is given by F=22i +22j 2+2k

Answer 1

I would think that the equation W = F*d where d is distance would work. In that case I would use the vector magnitudes.
d = sqrt((16+3)^2+(4-17)^2+(15+15)^2) = 37.815
F = sqrt(22^2+22^2+22^2) = 38.105
Assuming that the 22j2+2k is supposed to be 22j+22k the W would be 1440.94.

Answer 2

This is done using the equation
work = force * distance

force (F) = (22,22,22)

distance (D) = B - A = (19, -13, 30)

then take the scalar product of force and distance

work done = (22*19) + (22*(-13)) + (22* 30)
work done = 418 - 286 + 660
work done = 792

if the force is in newtons and the distance is in metres then the units would be joules

Answer 3

vector AB = b - a = (19, -13, 30) = 19i - 13j + 30k
Force = 22i + 22j + 22k
Work done = (22i + 22j + 22k ) . (19i - 13j + 30k)
joules
= 22 (i + j + k) . (19i - 13j + 30k) joules
=22(19 -13 + 30) joules = 22 x 36 joules= 792 joules

Answer 4

Look up the definition of (Mechanical) Work in Wiki (see below).

When you understand the definition you will be able to calculate the answer yourself.

To calculate distance from co-ordinates, look up in Wiki for 'distance' (the formula you need is 2nd para in Geometry)

Answer 5

W=a*m* IdI