Right Angle Cable
What is the angle theta with given tension and weight?
Hint: sin^2x + cos^2x = 1.
Consider the 699 N weight held by two cables. The left hand cabke had tension 450 N and makes an angle of theta2 with the ceiling. The right hand cable had tension 520 N and makes an angle theta1 with the ceiling.
A) What is the angle theta1 which the right hand cable makes with respect to the ceiling? Answer in units of degrees.
B) What is the angle theta2 which the lefy hand cable makes with respect to the ceiling? Answer in units of degrees.
Thanks for the help!!!!!
We form a triangle with sides a = 450, b = 520 and c = 699
θ1 = 90- A and θ2= 90 – B.
s = [450 +520 + 699] / 2 = 834.5
s-b = 314.5; s-c = 135.5; s-a = 384
————————————————-
tan A/2 = √ {[s-b] [s-c] / s[s-a]}
tan A/2 = √ {[314.5* 135.5] / [834.5 *384.5]} = 0.3644
A = 40.04°
————————————————-
tan B/2 = √ {[s-c] [s-a] / s[s-b]}
tan B/2 = √ {[135.5* 384.5] / [834.5 *314.5]} = 0.4455
B = 48.03°
—————————————————–
θ2 = 90 – 48.03 = 41.97°
θ1 = 90 – 40.04°= 49.96°
================================
Alternatively,
Since 450^2 + 520^2 = 687.7^ 2 , and 699 ~687.7,
cos θ1 = 450/699 and cos θ2 = 520/ 699 and hence
θ1 = 49.9 ° and θ2 = 41.9°
—————————————————-
Summer NAMM ’09 – Lava Cable Right Angle Cable and VOVOX
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