A uniform plank AB which is 75m long and has a weight of 350N and is supported horizontally by two vertical ropes A and B. A weight of 100N rest on the plank at C where AC=4m. Find the tension in each rope A and B
To find the tension in each rope, we can use the principles of equilibrium. In order for the plank to be balanced horizontally, the sum of the forces acting on it must be zero.
Let's start by considering the forces acting on the plank. We have:
1. Weight of the plank (350N) acting vertically downwards at its midpoint (point E).
2. The tension in rope A (let's call it T_A) acting upwards at point A.
3. The tension in rope B (let's call it T_B) acting upwards at point B.
4. The weight of the 100N load acting vertically downwards at point C.
Now, we can break down the forces acting on the plank in the horizontal and vertical directions.
Horizontal Forces:
1. The only horizontal force acting on the plank is the tension in rope B (T_B).
2. Since there are no other horizontal forces, the sum of the horizontal forces must be zero. Therefore, T_B = 0.
Vertical Forces:
1. The vertical forces acting on the plank are the weight of the plank, the tension in rope A (T_A), and the weight of the load.
2. Since the plank is in equilibrium, the sum of the vertical forces must be zero.
3. We can write the equation as follows: 350N + T_A - 100N = 0.
4. Simplifying the equation, we get T_A - 100N = -350N.
5. Adding 100N to both sides of the equation, we get T_A = -350N + 100N.
6. T_A = -250N.
Since the tension in rope B (T_B) is zero, the entire weight of the plank and load is being supported by rope A (T_A). Therefore, the tension in rope A is 250N (upwards).
Hence, the tension in rope A is 250N (upwards) and the tension in rope B is 0N (no tension).