Question

two persons are raising a load pulling at an angle of each other. If they exert forecs of `30 N` and ` 60 N` respectively and their effective pull is at right angles to the direction of the pull of the first person, what is the angle between their pulling forces ? What is the effective pull

Answer 1

Here, `A= 30 N, B= 60 N beta = 90^@`
Let ` theta` be the angle between two foreces ,Then
` tan beta = ( b sin theta) /( A + B cos theta)`
` or ` tan 90^@= ( 60 sin theta)/( 30 + 60 cos theta)` ltBrgt or ` prop = ( 60 sin theta)/( 30 + 60 cos theta)`
or ` 30 + 60 cos theta= 0`
or ` 30 + 60 cos theta=0`
or ` cos theta =- 30//60 =- 1//2 = cos 120^@` ltbRgt or ` theta 120^@`
Effective pulling force is
` R = sqrt ( a^2 + B^2 + 2 30 xx 60 xx cos 120 ^@` )`
` = sqrt( 900 + 3600 + 2 xx 30 xx 60 xx ( - 1//2)` ltbRgt `= 30 sqrt 3 N` .