SOLUTION OF EME-102; EQUILIBRIUM OF FORCES

EQUILIBRIUM OF FORCES IN 2D

A light string ABCDE whose extremity A is fixed, has weights W₁ & W₂ attached to it at B & C. It passes round a small smooth pulley at D carrying a weight of 300 N at the free end E as shown in figure. If in the equilibrium position, BC is horizontal and AB & CD make 150° and 120° with BC, find (i) Tensions in the strings and (ii) magnitudes of W₁ & W₂

Although ABCDE is a single string/rope but still the tensions in the string/rope will be different at different segments like in the segment AB the tensions will be T₁ , but in BC segment it will be different as the weight is attached at a fixed point (point B) on the string, hence it will be T₂ here and in CD it will be T₃  there. As at point D the string is not attached rather passes over a smooth pulley hence the tension in DE and CD will be same ie. T₃  again.

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To solve for equilibrium of forces in 2D, follow these steps:

1. Draw a free body diagram: Draw a diagram of the object in question and identify all the forces acting on it. This will help you visualize the problem and identify any unknown forces or angles.

2. Break forces into components: Resolve all forces into their x- and y-components. This is done by using trigonometry to determine the horizontal and vertical components of each force.

3. Apply Newton's second law: For the object to be in equilibrium, the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. This gives you two equations to solve simultaneously.

4. Solve the equations: Solve the equations for the unknown forces or angles by using algebraic methods. This will give you the values of the unknown forces or angles required for the object to be in equilibrium.

5. Check for consistency: Check that the forces and angles you have calculated are consistent with the problem and the free body diagram. For example, make sure that the direction of the forces makes sense and that the angles are reasonable.

6. Interpret the results: Interpret the results and explain what they mean in the context of the problem. This might involve calculating the tension in a rope, the force required to lift an object, or the angle required for an object to remain stationary.