Question

A particle is acted upon by constant forces f1=2i-3j+4k and f2=-i+2j-3k, is displaced from the point a (2,1,0) to the point b (-3,-4,2). find the total work done by these forces.

Answer 1

Answer:

Here,

F

1

=4

i

^

+

j

^

−3

k

^

,

F

2

=3

i

^

+

j

^

−

k

^

r

1

=

i

^

+2

j

^

+3

k

^

,

r

2

=5

i

^

+4

j

^

+

k

^

Displacement,

r

=

r

2

−

r

1

=(5

i

^

+4

j

^

+

k

^

)−(

i

^

+2

j

^

+3

k

^

)=4

i

^

+2

j

^

−2

k

^

Work done by the forces,

W=[

F

1

+

F

2

]⋅

r

=[(4

i

^

+

j

^

−3

k

^

)+(3

i

^

+

j

^

−

k

^

)]⋅(4

i

^

+2

j

^

−2

k

^

)

=(7

i

^

+2

j

^

−4

k

^

)⋅(4

i

^

+2

j

^

−2

k

^

)=28+4+8=40 J.