A uniform rod (AB) of mass 80kg and 1.0m lenght is supported on the 2 knife edges placed 15.0cm from its ends. what will be the reactions at these support when a 20kg mass is suspend 10cm from the mid-point of the rod.(workings and diagram)
sum vertical forces. Let fl be the knife edge left support, and fr be the right support.
fl+fr=80+20 in kg
sum moments about the left knife edge.
0=20kg(50-15-10)+80(50-15)-Fr*70
solve for the force right. then in the other equation lf.
Now in newtons, multiply by 9.8, kg is not a force.
To solve this problem, we can use the principle of moments, which states that the total sum of moments acting on an object in equilibrium is zero.
First, let's draw a diagram to visualize the scenario:
```
------------------------A---------------------B-------------------------
<---------x1----------><-----------------x2------------------------>
```
Here, the rod AB has a length of 1.0 m. The knife edges are placed 15.0 cm (0.15 m) away from each end of the rod, denoted by distances x1 and x2, respectively. A 20 kg mass is suspended 10 cm (0.10 m) away from the midpoint of the rod.
Now, let's calculate the reactions at the supports:
Step 1: Calculate the weight of the rod
The weight of the rod can be calculated by multiplying its mass by the acceleration due to gravity (9.8 m/s^2):
Weight of the rod = mass * acceleration due to gravity
Weight of the rod = 80 kg * 9.8 m/s^2
Step 2: Calculate the weight of the suspended mass
The weight of the suspended mass can be calculated in the same way:
Weight of the mass = mass * acceleration due to gravity
Weight of the mass = 20 kg * 9.8 m/s^2
Step 3: Calculate the moments about the supports
The total moment about the left support (A) is equal to the clockwise moment (due to the rod) plus the anticlockwise moment (due to the mass). We can express this mathematically as:
Clockwise moment = Reaction at A * Distance x1
Anticlockwise moment = Weight of the rod * Distance from A to the midpoint + Weight of the mass * Distance from the midpoint to the mass
Total moment about A = Clockwise moment - Anticlockwise moment
Total moment about A = 0 (because the system is in equilibrium)
Similarly, we can find the total moment about the right support (B):
Total moment about B = Clockwise moment - Anticlockwise moment
Total moment about B = 0 (because the system is in equilibrium)
Step 4: Solve the equations
Now, we need to solve the equations for the unknown reactions at the supports (Reaction at A and Reaction at B).
The equation for the total moment about A:
0 = Reaction at A * Distance x1 - (Weight of the rod * Distance from A to the midpoint + Weight of the mass * Distance from the midpoint to the mass)
The equation for the total moment about B:
0 = Reaction at B * Distance x2 - Weight of the rod * Distance from B to the midpoint
From these equations, we can calculate the reactions at the supports (Reaction at A and Reaction at B).
I hope this explanation helps you understand how to approach this problem. Follow the steps and calculations provided to find the reactions at the supports.