Question

if two forces act in opposite direction then their resultant is 10N. and if they act mutually perpendiicular then their resultant is 50N find magnitudes of both forces

Answer 1

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Answer 2

Answer: The magnitude of the forces are 40N and 30N

Solution:

The blocks in contact with respective forces show resultant force as 10 N when opposite and 50 N when perpendicular, so the respective force is calculated as following,

Given: Resultant force when opposite = 10 N

           Resultant force when perpendicular = 50 N

Let the first force be F1 and second force be F2

So when F1 and F2 are opposite, resultant force is given by F1 – F2 = 10 N

F1 = 10 + F2

And when F1 and F2 are perpendicular, the resultant force is given by –

$\begin{array}{l}{\sqrt{F 1^{2}+F 2^{2}}=50 N} \\ {\sqrt{(10+F 2)^{2}+F 2^{2}}=50 N} \\ {\sqrt{10^{2}+F 2^{2}+2 F 2+F 2^{2}}=50 N} \\ {100+2 F 2^{2}+2 F 2=2500}\end{array}$

$\begin{array}{l}{2 F 2^{2}+2 F 2=2500-100} \\ {2 F 2^{2}+2 F 2-2400=0} \\ {F 2^{2}+F 2-1200=0}\end{array}$

On solving this equation we get F2 = 30 N

Therefore F1 = 10 + F2

F1 = 10 + 30 = 40 N

Therefore, the two forces are 40 N and 30 N respectively.