Answers and Solutions

Answer

1. Given information:

• Two identical prismatic bars PQ and RS, each weighing 75 N, are welded together to form a tee.

• The structure is suspended in a vertical plane.

• A load of 100 N is applied at point S.

• We need to find the angle θ that bar PQ makes with the vertical when the load is applied.

2. Analysis:

• When the load is applied at S, the structure will experience both vertical and horizontal forces.

• The vertical forces will be the weight of the bars (acting downwards) and the applied load (acting downwards).

• The horizontal forces will be the reactions at points P and R (both acting inwards).

• Since the structure is in equilibrium, the sum of forces in both the vertical and horizontal directions must be equal to zero.

3. Free Body Diagram (FBD):

• In the FBD, we have:

• W1 and W2 represent the weights of bars PQ and RS, respectively (each equal to 75 N).

• P and R represent the horizontal reactions at points P and R, respectively.

• 100 N represents the applied load at point S.

• θ represents the angle that bar PQ makes with the vertical.

4. Equations of Equilibrium:

• Vertical direction:

∑Fy = 0
W1 + W2 + 100 N - Psinθ - Rsinθ = 0

• Horizontal direction:

∑Fx = 0
Pcosθ + Rcosθ = 0

5. Solving for θ:

• We have two independent equations and two unknowns (θ and either P or R).

• Since we are interested in finding θ, we can eliminate P or R from the equations.

• One way to do this is to solve the horizontal equilibrium equation for P:

P = -Rcosθ

• Substitute this expression for P in the vertical equilibrium equation:

W1 + W2 + 100 N - (-Rcosθ)sinθ - Rsinθ = 0

• Simplify and solve for sinθ:

sinθ = (W1 + W2 + 100 N) / (R(cosθ + sinθ))

• We can now substitute the given values:

W1 = W2 = 75 N
R = P (since the structure is symmetrical)

• This gives us:

sinθ = (75 N + 75 N + 100 N) / (P(cosθ + sinθ))

• Unfortunately, we still have two unknowns (θ and P). To solve for θ, we need one more equation or relationship.

6. Additional information:

The problem statement doesn't provide any additional information about the structure or the forces acting on it. Without this information, we cannot solve for the specific value of θ.

7. Possible approaches:

• If we knew the value of one reaction (P or R), we could substitute it into the equation and solve for θ.

• If we knew the relationship between the horizontal and vertical components of the reactions (e.g., if they were equal), we could use this relationship to eliminate one unknown and solve for θ.

8. Conclusion:

While I can explain the general approach to solve this problem, I need more information about the structure or the forces acting on it to find the specific value of angle θ. Please provide any missing information if you want me to help you solve for θ.

Answer

Sum of moments about point P is zero

75 *l* Sinθ +75* 2l* Sinθ -100(l Cosθ - 2l Sinθ) = 0

75Sinθ +150Sinθ-100Cosθ + 200Sinθ=0

425 Sinθ =100Cosθ

Sinθ/Cosθ = 100/425

tanθ=0.2353

θ = tan^-1 (0.2353)

=13.24 degrees