Question

a constant force f = 3i + j - k newton has a displacement r = 2i + 2j - 3k meters in 2 seconds. find the work done and the power. [11 Joules, 5.5 Watt] ​

Answer 1

Given ,

Force (F) = 3i + j + k

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

Time (t) = 2 sec

We know that ,

Work done is defined as the dot product or scalar product of force and displacement

$\boxed{ \sf{Work \: done = F.S \: cos(Φ)}}$

Where ,

Φ = angle b/w force and displacement

Thus ,

Work = (3i + j - k) . (2i + 2j - 3k)

Work 3(2) + 1(2) + (-1)(-3)

Work = 6 + 2 + 3

Work = 11 J

Therefore ,

The work done is 11 J

Now , The rate of work done is known as power

$\boxed{ \sf{Power = \frac{Work \: done}{Time} }}$

Thus ,

Power = 11/2

Power = 5.5 Watt

Therefore ,

The power is 5.5 Watt

Answer 2

Answer:

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