Question

Two constant forces F, = 2i - 3j + 3k (N)
and F, = i + j - 2 K (N) act on a body and
displace it from the position r = i +2j-2 k
(m) to the position r2 = 7ỉ + 10j + 5k (m).
What is the work done ?​

Answer 1

Answer:

W = 9 Nm

Explanation:

Data:

First force = F1 = 2i - 3j + 3k  (N)

Second force = F2 = i + j - 2K (N)

First position vector = r1 = i + 2j - 2k (m)

Second position vector = r2 = 7ỉ + 10j + 5k (m)

Required:

Work = W = ?

Calculation:

We know that

Resultant of forces = R = F1 + F2

Putting values we get

R = 2i - 3j + 3k + i + j - 2K = 3i - 2j + k

R = 3i - 2j + k

And we know that

Displacement = d= r2 - r1

Putting values we get

d =  7ỉ + 10j + 5k - ( i + 2j - 2k ) = 6i + 8j + 7k

And

We know that

W = F · d            (Here F = R )

Putting values we get

W = ( 3i - 2j + k ) · (6i + 8j + 7k) = 18 - 16 +7

W = 2 + 7 = 9 Nm

So

W = 9 Nm