Question

Forces 2N and 1FN act at 45 degrees to give resultant root 10 then F=?? ​

Answer 1

ANSWER :–

▪︎${ \bold{f = - \sqrt{2} \: \: and \: \: {f} = 3 \sqrt{2} }}$

EXPLANATION :–

GIVEN :–

▪︎ Two forces are (2)N and (1F)N act at 45⁰ .

▪︎ Resultant of vectors are √10 N.

TO FIND :–

Value of 'F'.

SOLUTION :–

☞ We know that when two forces a and b act at θ degree angle then resultant is –

$\\ \implies{ \boxed{ \bold{R = \sqrt{ {a}^{2} + {b}^{2} - 2ab \cos( \theta) } }}}$

▪︎ Now put the values –

$\\ \implies{ \bold{ \sqrt{10} = \sqrt{ {(2)}^{2} + {(1f)}^{2} - 2(2)(1f) \cos( {45}^{0} ) }}}$

$\\ \implies{ \bold{ \sqrt{10} = \sqrt{4 + {f}^{2} - 4f( \frac{1}{ \sqrt{2} }) }}}$

$\\ \implies{ \bold{ \sqrt{10} = \sqrt{4 + {f}^{2} - 2 \sqrt{2} f }}}$

• Now square both side –

$\\ \implies{ \bold{10 = 4 + {f}^{2} - 2 \sqrt{2} f }}$

$\\ \implies{ \bold{{f}^{2} - 2 \sqrt{2} f - 6 = 0}}$

$\\ \implies{ \bold{{f}^{2} - 3 \sqrt{2} f + \sqrt{2} f - 6 = 0}}$

$\\ \implies{ \bold{f({f} - 3 \sqrt{2} ) + \sqrt{2}( f - 3 \sqrt{2} )= 0}}$

$\\ \implies{ \bold{(f + \sqrt{2}) ({f} - 3 \sqrt{2} ) = 0}}$

$\\ \implies{ \bold{f = - \sqrt{2} \: \: , \: \: {f} = 3 \sqrt{2} }}$

Answer 2

hope it helps..... .....