Question

A particle is displaced from A = (2, 2, 4) to B= (5, -3, -1). A constant force of 34 N acts in the
direction of AP, where P=(10,2,-11). (Coordinates are in m).
(1) Find the F. (ii) Find the work done by the force to cause the displacement.
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Answer 1

(1) A constant force of 34N acts in the direction of AP.

so, unit vector of force = unit vector of AP (Let r)

$\frac{\vec{F}}{|F|}=\frac{\vec{r}}{|r|}$

first of all, find $\vec{r}$ ,

$\vec{r}=(10-2)\hat{i}+(2-2)\hat{j}+(-11-4)\hat{k}$

or, $\vec{r}=8\hat{i}-15\hat{k}$

magnitude of r = √{8² + 15²} = 17 unit.

now, $\vec{F}=|F|\frac{\vec{r}}{|r|}$

= 34 × (8i - 15k)/17

= 16i - 30k

hence, force , F = 16i - 30k

(ii) workdone by force to cause displacement , W = F.x

= (16i - 30k).[(5-2)i + (-3-2)j + (-1-4)k]

= (16i - 30k).(3i - 5j - 5k)

= 48 + 150

= 198 J

hence, workdone by the force to cause the displacement is 198 J

Answer 2

Answer:

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Explanation:

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