A mover pulls a crate on a smooth warehouse floor with a constant force represented (in newtons) by F=5i+3j−2k. During the pull the crate is displaced (in metres) through d=2i−6j+4k.
a. (i) Find the magnitude of the force acting on the crate.
b. (ii) Calculate the work done by the force during the given displacement.
c. (iii) If the force acts through a second displacement 2d, determine the additional work done.
d. (iv) Comment on the sign of the work obtained in part (ii) and its physical implication for the motion of the crate.