in the following figure w = 20 n, f = 25 n. find the value of angle θ. find the tension in the string.

Question

in the following figure w = 20 n, f = 25 n.

.

 (i) find the value of angle θ. 

 (ii) find the tension in the string.

Answer 1

It is obvious from figure that angle between T and W is (180-theta). Again the angle between T and  F will be (90+theta)

So by Lami's theorem

T/sin90 = F/sin(180-theta)= W/sin(90+theta)

=> T=F/sin (theta)=W/cos(theta)

Tsin(theta)= F andTcos(theta)=W

Hence tan(theta)=F/W

So (theta) = arctan(F/W)

And T= √(F^2+W^2) N