Question

1.
A force F = (4i - 4j – 2k) N displaces a particle by
d = (3ỉ +2j – 2k)m, calculate work done.
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Answer 1

Explanation:

Given F= (4i-4j-2k)N

S=(3i+2j-2k)m

work=F.s

=(4)(3)+(-4)(2)+(-2)(-2)

=12-6+4

=10 jouls

Answer 2

Given info : A force F = (4i - 4j - 2k) N displaces a particle by d = (3i + 2j - 2k) m.

To find : the work done is ..

solution : work done is the dot product of force applied on a body and the displacement of that body due to applied force.

i.e., W = $\vec F.\vec s$

here,

       $\vec F=4\hat{i}-4\hat{j}-2\hat{k}\\\vec{s}=3\hat{i}+2\hat j-2\hat k$

now   $W=(4\hat{i}-4\hat{j}-2\hat{k}).(3\hat{i}+2\hat j-2\hat k)$

= (4)(3) + (-4)(2) + (-2)(-2)

= 12 - 8 + 4

= 8

therefore the work done by the particle due to force is 8 Joules.