A weight of 500kg is suspended by two chains 1.5m and 2.7mrespectively.the chains are attached to a beam that is 3.746m in length.
The distance from the suspension to the ground being 900m.
A.Calculate the load.
B.the vertical and horizontal reactions at the suspension points.
To solve this problem, we can use the principles of static equilibrium and the idea that the sum of the forces acting on an object should equal zero.
A. Calculate the load:
The load refers to the weight being suspended by the chains. In this case, the load is given as 500 kg.
B. Calculate the vertical and horizontal reactions at the suspension points:
First, let's label the variables:
- F1: the force acting on the chain with a length of 1.5m
- F2: the force acting on the chain with a length of 2.7m
- L: the length of the beam, which is 3.746m
- H: the horizontal reaction at the suspension points
- V: the vertical reaction at the suspension points
Now, let's break down the forces acting on the system:
1. The vertical forces:
- The weight of the load acts downward and is equal to 500 kg multiplied by the acceleration due to gravity (approx. 9.8 m/s^2). Therefore, the weight of the load is 500 kg*9.8 m/s^2 = 4900 N.
- The vertical reaction at the suspension points, V, balances the weight, so V = 4900 N.
2. The horizontal forces:
- The horizontal reaction at the suspension points, H, balances the horizontal forces acting on the system.
- The horizontal forces present in this case are F1 and F2.
- Since the horizontal force acting on the chains must be equal and opposite to H, we can set up the equation H = F1 + F2.
3. The forces along the length of the beam:
- The forces F1 and F2 act along the lengths of the chains and can be found using similar triangles.
- From the given dimensions, we can create a triangle using the three lengths: 1.5m (length of chain 1), 2.7m (length of chain 2), and 3.746m (length of the beam).
- F1 and F2 must be proportional to the corresponding lengths of the chains, so we can set up the equation F1/L = 1.5/3.746 and F2/L = 2.7/3.746.
- We can solve these equations to find F1 and F2:
- F1 = 1.5/3.746 * L
- F2 = 2.7/3.746 * L
To summarize:
A. The load is given as 500 kg.
B. The vertical reaction at the suspension points, V, is equal to the weight of the load, which is 4900 N. The horizontal reaction at the suspension points, H, is equal to F1 + F2, where F1 = (1.5/3.746)*L and F2 = (2.7/3.746)*L.