Calculus III Question

Question

A weight of 100 pounds is suspended by two ropes A and B. Rope A makes an angle of 30 degrees with the ceiling and rope B makes an angle of 45 degrees with the ceiling. What are the magnitudes of the forces in each of the ropes?

Answer 1

This is not a calculus problem.  It is a problem in elementary statics.  Set up force equilibrium in the x and y directions, which will give you 2 equations in the 2 unknown forces, and then solve for the 2 forces.

 

x direction:

 

F_Acos30° - F_Bcos45° = 0

 

y direction:

 

F_Asin30° + F_Bsin45° = 100 lbs

 

Solve for F_A and F_B in

 

0.8660F_A - 0.7071F_B = 0

0.5F_A + 0.7071F_B = 100

 

You should get

 

F_A = 73.21 lbs

F_B = 89.66 lbs