A bar is hinged at A and rests on a cylinder at C. The weight of the cylinder is 200 N. The center of the cylinder is connected to the bar by a horizontal wire OE. A weight of 500... A bar is hinged at A and rests on a cylinder at C. The weight of the cylinder is 200 N. The center of the cylinder is connected to the bar by a horizontal wire OE. A weight of 500 N is suspended at B. Find (i) the reaction at hinge A, (ii) the tension in wire OE, (iii) the reactions at C & D. Read more

Steps to Solve

1. Identify the Forces Acting on the System

Start by identifying all the forces acting on the bar, cylinder, and weights. This includes gravitational forces, tension in the wire, and reaction forces at the supports (hinge A, points C, and D).

2. Apply the Equations of Static Equilibrium

For static equilibrium, the sum of all forces and moments must be zero. Therefore, we can start writing the equations:

• $$ \sum F_x = 0 $$
• $$ \sum F_y = 0 $$
• $$ \sum M_{A} = 0 $$ (taking moments about point A)

3. Set Up the Equations Based on the Forces

Using the identified forces, write down equations based on the equilibrium conditions. For example:

• Let the force at hinge A be $R_A$ in the x and y directions.
• Let the tension in the wire be $T$.
• Weight forces can be noted as $W_1$ (weight at the end of the bar) and $W_2$ (weight at another point).

This might look like:

• $$ R_{Ax} + T - W_1 - W_2 = 0 $$
• $$ R_{Ay} + W_1 + W_2 - T = 0 $$

4. Calculate Moments About a Point

Choose a point (usually A for convenience) to take moments and set the sum to zero. This will help solve for the unknown tension $T$ or other reactions. An example equation could be:

• $$ W_1 \cdot d_1 + W_2 \cdot d_2 - T \cdot d_T = 0 $$

Here $d_1$, $d_2$, and $d_T$ are the distances from point A to the lines of action for each force respectively.

5. Solve the System of Equations

Now, you have a system of equations that you can solve using substitution or elimination methods. Solve for the unknowns $R_A$, $T$, $R_C$, and $R_D$ step by step.

6. Check Your Results

Finally, ensure that the results satisfy all equilibrium conditions ($\sum F_x$, $\sum F_y$, and $\sum M_A = 0$). This is essential for confirming that your calculations are correct.