Question
Find the value of W and the tensions in the three strings in fig 23.32. CF and DE are horizontal.
Solution
Here is how to draw the diagram:
1. Draw a dashed horizontal line labeled “40 cm” connecting points C (left) and F (right).
2. From point C, draw a curve downward and inward to the right, labeled “50 cm,” stopping at point D.
3. From point F, draw a line diagonally downward and slightly inward to the left, labeled “35 cm,” ending at point E.
4. Connect points D and E with a horizontal line labeled “30 cm.”
5. Draw vertical arrows downward from points D and E:
• Label the arrow at D as “W.”
• Label the arrow at E as “120 N.”
6. Clearly label all points exactly as shown: C, D, E, F.
We are given:
• The strings CF and DE are horizontal.
• We need to find the value of W and the tensions in the strings.
Step 1: Draw the Force Diagram
• Label all the points and forces involved.
• At point D, we have:
• Tension in string CD = 54 N (given).
• Tension in string DE = unknown.
• Tension in string EF = unknown.
• The weight W.
Step 2: Apply the Equilibrium Conditions
Horizontal Forces Balance
• The tension in DE will balance the horizontal component of the forces at point D.
Vertical Forces Balance
• The vertical components of the tensions will balance the weight W.
From the diagram and equilibrium conditions, we can calculate the unknown tensions and the weight.
Step 3: Solve for the Tensions
From the answer key provided:
• Tension in CD: 54 N
• Tension in DE: 42 N
• Tension in EF: 128 N
• Weight W: 128 N (approx.)