Question

Four forces are exerted on the eyebolt as shown. If the net effect on the bolt is a direct pull of 600 lb in the y-direction, determine the necessary values of T and ø

Answer 1

the net effect:

$R=240cos\theta+Tcos30\degree+400cos60\degree=600$ lb

$0=400cos30\degree+Tcos60\degree-240sin\theta-360$

$240cos\theta+\sqrt{3}T/2=400$

$T/2-240sin\theta=360-200\sqrt{3}$

$T/2=(400-240cos\theta)/\sqrt{3}$

$(400-240cos\theta)/\sqrt{3}-240sin\theta=360-200\sqrt{3}$

$400-240cos\theta-240\sqrt3sin\theta=360\sqrt3-600$

$6cos\theta+6\sqrt3sin\theta=25-9\sqrt3$

$36(1-sin^2\theta)=625-450\sqrt3+243-12\sqrt3sin\theta(25-9\sqrt3)+108sin^2\theta$

$144sin^2\theta-12\sqrt3sin\theta(25-9\sqrt3)+832-450\sqrt3=0$

$sin\theta=\frac{195.6-\sqrt{38265-4\cdot144(832-450\sqrt3)}}{288}=\frac{195.6-\sqrt{38265-30284}}{288}=\frac{195.6- 89.3}{288}=0.3691$

$\theta=21.66\degree$

$T=2(400-240cos21.66\degree)/\sqrt3=204$ lb