Question

Consider a particle on which several forces act, one of which is known to be constant in time: Fi = 3.00 i +4.00 ) N. As a result, the particle moves along a straight path from a Cartesian coordinate of 0.00 m, 0.00 m) to (5.00 m, 6.00 m). What is the work done by Fi?

Answer 1

Given that.

F=3•i+4•j

And it from point (0,0)m to (5,6)m

dx=final position - initial position

dx=(5,6)-(0,0)

dx=(5,6)m

dx=5•i +6•j

Work done by the force is give by

W = F•dx

W=F•dx

Note that i•i=j•j=1 and i•j=j•i=0

Then,

W=(3i+4j)•(5i+6j)

Therefore,

W=3i•(5i+6j)+4j•(5i+6j)

W=15i•i+18i•j+20j•i+24j•j

W=15+0+0+24

W=39J

Then the work done by the force is 39 Joules