Solving Statics Problem: Equilibrium of Forces

[619313]

I have having trouble solving this statics problem, I sum up the forces and have

C*cos(30) - B*cos(phi) = 0 in the positive x direction
and
C*sin(30) + B*sin(phi) - D =0 in the positive y direction

B = 275 lbs and D = 300lbs
I need to solve for C and phi, I have tried substitution, division, not matrices because it wouldn't work

 

[rl.bhat]

C*cos(30) = B*cos(phi)...(1)
C*sin(30) = - B*sin(phi) + D ...(2)
Divide (2) by (1).You get
tan(30) = B*cosφ/(B*sinφ - D)
Square both the sides. Write cos^2(φ) = 1 - sin^2(φ) and solve the quadratics to find φ.

 

[619313]

Thanks for the reply,

I divided (2) by (1) but I have

Tan(30) = (-B*sin(φ) + D)/ (B*cos(φ))

Am I missing something?

 

[rl.bhat]

No.
Now square both sides. And simplify.

 

[DeeNos]

I understand your frustration with solving this statics problem. It can be difficult to find the right approach and method to solve a problem like this. However, there are a few things you can try to help you solve this problem.

First, make sure you have the correct values for all the forces involved. Double check your calculations and ensure that you have accounted for all the forces acting on the object.

Next, try drawing a free body diagram to visualize the forces acting on the object. This can help you see the relationships between the forces and how they are balanced.

You can also try using trigonometric identities to simplify the equations and make them easier to solve. For example, you can rewrite the equations as C*cos(30) = B*cos(phi) and C*sin(30) = D - B*sin(phi).

If these methods still do not work, you may want to consider seeking help from a peer or instructor who may have a different perspective on the problem and can offer guidance on how to approach it.

Remember, solving problems in science is all about trial and error and finding the most effective method for each individual problem. Don't get discouraged and keep trying different approaches until you find the solution.