If a force F = 4i + 8j + 16k moves a block wieghing 12 kg from (0,3,1) to (3, 8, 2) what is the work done?
The work done by a force is given by the dot product of the force and the resulting displacement.
Here, the block moves from the point (0,3,1) to (3, 8, 2) due to the force acting on it. The displacement of the block is D = i( 3 - 0) + j(8 - 3) + k(2 - 1) = 3i + 5j + k
The force F = 4i + 8j + 16k
The dot product of the vectors representing displacement and force is given by:
D`.`F = (3i + 5j + k)`.`(4i + 8j + 16k)
=> 3*4 + 5*8 + 1*16
=> 12 + 40 + 16
The mass of the block does not need to be considered as work is merely the product of force and displacement. It is also not possible to give the unit a unit for the work done as the unit for force is not given.
The work done by the force F = 4i + 8j + 16k in moving the block from the point (0, 3, 1) to the point (3, 8, 2) is 68.