Two forces F 1 - i -2 j -2 k - N and F 2 -3 i - j -3 k - N acts on a body and causes it to displace from position s 1 - i - j - m to s 2 -2 j - ak - m- Findthe value of - a - if the amount of net work done by the forces is 5 J during the displacement-A- -4B- 8C- 6D- -5

Net force acting of body is given by: F→=F1→+F2→=i^ 2j^+2k^+( 3i^+j^ 3k^)⇒F→= 2i^ j^ k^ Displacement of body while moving from initial to final position: S→= ...

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Standard XII

Physics

Work Done as Dot Product

Two forces F ...

Question

Two forces $_{1} = ˆ i - 2 ˆ j + 2 ˆ k$ $N$ and $_{2} = - 3 ˆ i + ˆ j - 3 ˆ k$ $N$ acts on a body and causes it to displace from position $_{1} = ˆ i - ˆ j$ $m$ to $_{2} = 2 ˆ j - a ˆ k$ $m$ . Find the value of $^{'} a^{'}$ if the amount of net work done by the forces is $5 J$ during the displacement.

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Solution

The correct option is C $6$
Net force acting of body is given by:
$\to F =_{1} +_{2} = (ˆ i - 2 ˆ j + 2 ˆ k) + (- 3 ˆ i + ˆ j - 3 ˆ k) \Rightarrow \to F = - 2 ˆ i - ˆ j - ˆ k$
Displacement of body while moving from initial to final position:

$\to S =_{2} -_{1} = (2 ˆ j - a ˆ k) - (ˆ i - ˆ j) \Rightarrow \to S = - ˆ i + 3 ˆ j - a ˆ k m$
Work done by force given by:
$W = \to F . \to S$
$W = (- 2 ˆ i - ˆ j - ˆ k) . (- ˆ i + 3 ˆ j - a ˆ k) \Rightarrow 5 = (2 - 3 + a) \Rightarrow a = 6$

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Work Done as Dot Product

Standard XII Physics

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Two forces −→F1=ˆi−2ˆj+2ˆk N and −→F2=−3ˆi+ˆj−3ˆk N acts on a body and causes it to displace from position →s1=ˆi−ˆj m to →s2=2ˆj−aˆk m. Find the value of ′a′ if the amount of net work done by the forces is 5 J during the displacement.