Find the tension in each cable necessary to keep the block from moving (either sideways or downward)

Question

A 900-lb block is being suspended and held stationary by two steel cables as shown.  The first cable (to the left of the block) makes a 70 degree angle with the horizontal, while the second cable (to the right of the block) makes a 65 degree angle with the horizontal.  At point B (where the weight is being held), there are three forces acting: R, S, and W.  Find the tension in each cable necessary to keep the block from moving (either sideways or downward).

 

So, so far I have this - this is how my professor says it "should be done".  I also do have a program on my calculator called, "System of Equations" that I can plug in 2 variables and have it solve it for me.

 

                                                       L              R

W (weight) = -900j     70 degree angle\             /65 degree angle

- W = 900j                                         \ _____ /

                                                     -900-lb block

 

L = |L| (cos theta i + sin theta j)

R = |R| (cos theta i + sin theta j)

 

l + r + w = 0 or l + r = -w

 

If you could, please help me solve this - showing me step by step would be most beneficial into helping me understand this for my final! :) Thank you!

 

 

Answer 1

Given the 900lb weight suspended by two cables, resolve the tension forces R and L (assuming S is a typo) into horizontal and vertical components in the x and y directions.

In the x or horizontal direction: Rcos65° - Lcos70° = 0 

In the y or vertical direction Rsin65° + Lsin70° - W = 0

or Rsin65° + Lsin70° = 900

 

Now you have two equationa which you can use to solve for the two unknowns R and L