A particle moves from position r = ( 2i +j - 4k ) m to position r' = ( 14i - Physics - Work Energy And Power

Question

A particle moves from position r = ( 2i +j - 4k ) m to position
r' = ( 14i + 13j - 9k ) m under the action of a force ( 4i +j +3k )
N Calculate the work done

Abhishek Gupta · Accepted Answer

Dear Student
Work done is given by scalar (or dot) product of force and
displacement vectors
Here, displacement will be given as d =
r' -r = [( 14i + 13j - 9k ) - (
2i +j - 4k )] = ( 12i + 12j - 5k) m
Force , F = (4i +j +3k) N
so, the work done, W = F d = (4i +j + 3k)
(12i + 12j - 5k) = 4 × 12 + 1 × 12 + 3 × (-5) =
45 J
Hence work done is equal to 45 joules
Hope it is clear!!
Cheers!!

A particle moves from position r = ( 2i +j - 4k ) m to position r' = ( 14i + 13j - 9k ) m under the action of a force ( 4i +j +3k ) N . Calculate the work done .