a heavy rod AB of length of 5m weighs 50N.The bar is supported in a horizontal position by two vertical strings X and Y.If string X is 0.6m from B and string Y is 1.8 from A,find the tension in the strings.
To find the tension in strings X and Y, we need to consider the equilibrium of forces acting on the rod AB.
1. Draw a free-body diagram for the rod AB:
- At point A, there is tension in string Y (TY) acting vertically upward.
- At point B, there is tension in string X (TX) acting vertically upward and the weight of the rod (W = 50N) acting vertically downward.
2. Resolve the vertical forces:
- At point A: TY - W = 0 (since the rod is in equilibrium, the net vertical force at A is zero).
- At point B: TX - W = 0 (since the rod is in equilibrium, the net vertical force at B is zero).
3. Let's calculate the distances:
- Distance of string X from B = 0.6m
- Distance of string Y from A = 1.8m
- Total length of the rod = 5m
4. Calculate the weights supported by each string:
- Weight supported by string X (WX) = (distance of X from B / total length) * weight of the rod = (0.6m / 5m) * 50N
- Weight supported by string Y (WY) = (distance of Y from A / total length) * weight of the rod = (1.8m / 5m) * 50N
5. Substitute the values into the equations:
- At A: TY - (1.8/5) * 50N = 0
- At B: TX - (0.6/5) * 50N = 0
6. Solve the equations simultaneously to find the tensions in the strings:
- TY - 18N = 0 (1)
- TX - 6N = 0 (2)
From equation (2), we get TX = 6N.
Substituting this value in equation (1), we get TY - 18N = 0.
Therefore, TY = 18N.
The tension in string X is 6N, and the tension in string Y is 18N.