Question

A body of mass 10 kg is displaced from point A(2,
1, 3) to point B(3, 3, 4) under the effect of a force
of magnitude 20 N in the direction of 6î+8).
Calculate W.D. by the force :- 24+164
(1) 22 J (2) 2016 J (3) 44 J (4) Zero​

Answer 1

$\displaystyle\large\boxed {\sf {W=22\ J}}$

The force vector is,

• $\displaystyle\sf {\vec F=6\hat i+8\hat j}$

And the displacement vector is,

• $\displaystyle\sf {\vec s=(3\hat i+3\hat j+4\hat k)-(2\hat i+\hat j+3\hat k)}$

• $\displaystyle\sf {\vec s=\hat i+2\hat j+\hat k}$

Then the work done is,

$\displaystyle\longrightarrow\sf {W=\vec F\cdot\vec s}$

$\displaystyle\longrightarrow\sf {W=(6\hat i+8\hat j)\cdot (\hat i+2\hat j+\hat k)}$

$\displaystyle\longrightarrow\sf {W=6\cdot1+8\cdot2+0\cdot1}$

$\displaystyle\longrightarrow\sf {W=6+16}$

$\displaystyle\longrightarrow\sf {\underline {\underline {W=22\ J}}}$