A constant force F = 3 i ^ − 2 j ^ − k ^ newton has a displacement r = 2 i ^ − 3 j ^ − 3 k ^ metre in 2 second. The work done and the power are respectively

Question

A constant force F = 3 i ^ − 2 j ^ ​ − k ^ newton has a displacement r = 2 i ^ − 3 j ^ ​ − 3 k ^ metre in 2 second. The work done and the power are respectively

TestHub · Accepted Answer

Work done is given by the dot product of force and displacement vectors.

$W = F \cdot r$

$W = (3 \hat{i} - 2 \hat{j} - \hat{k}) \cdot (2 \hat{i} - 3 \hat{j} - 3 \hat{k})$

$W = (3) (2) + (- 2) (- 3) + (- 1) (- 3)$

$W = 6 + 6 + 3 = 15 joule$

Power is the rate of work done.

$P = \frac{W}{t}$

$P = \frac{15}{2} = 7.5 watt$

Answer: 15 joule, $7.5$ watt

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