A uniform rod of 1m long of mass 50g is supported horizontally on two knife edges places 10cm from it ends.what will be reaction of this support when a 100g mass is suspended from the mid point of the rod
I need a solution to the question
To find the reaction at each support when a 100g mass is suspended from the midpoint of the rod, we can use the principle of moments.
1. First, we need to calculate the center of mass of the rod. Since the rod is uniform, it will be located at the midpoint, which is 0.5m from each end.
2. The weight of the rod can be considered as acting through its center of mass. The weight of the rod is given by W_rod = m_rod * g, where m_rod is the mass of the rod (50g = 0.05kg) and g is the acceleration due to gravity (9.8 m/s^2).
W_rod = 0.05 * 9.8 = 0.49 N
3. To calculate the reaction at each support, we need to consider the clockwise and anticlockwise moments about each knife edge.
Let R1 be the reaction at the left support and R2 be the reaction at the right support.
Clockwise moment about the left support: 0.1 * g * 0.5 = 0.05 * 9.8 * 0.5 = 0.245 Nm
Anticlockwise moment about the right support: (0.05 * 9.8) * 1 = 0.49 Nm
Since moments cause rotation, these two moments should be equal to each other for the rod to be in equilibrium.
0.245 Nm = 0.49 Nm
4. Now we can calculate the reaction at each support.
R1 + R2 = W_rod
Since the rod is supported equally from both ends, the reaction at each support will be half of the total weight of the rod.
R1 = R2 = W_rod / 2
R1 = R2 = 0.49 / 2 = 0.245 N
Therefore, the reaction at each support will be 0.245 N when a 100g mass is suspended from the midpoint of the rod.
To find the reaction at each support when a 100g mass is suspended from the midpoint of the rod, we can calculate the forces acting on the rod.
Step 1: Calculate the weight of the rod.
The mass of the rod is given as 50g, so we need to convert it to kilograms:
mass = 50g = 0.05kg
The weight of the rod is given by:
weight of rod = mass x gravity
= 0.05kg x 9.8 m/s^2
= 0.49 N
Step 2: Calculate the weight of the suspended mass.
The mass of the suspended mass is given as 100g, so we also need to convert it to kilograms:
mass = 100g = 0.1kg
The weight of the suspended mass is given by:
weight of suspended mass = mass x gravity
= 0.1kg x 9.8 m/s^2
= 0.98 N
Step 3: Calculate the distance between the midpoint of the rod and each support.
The rod is 1m long, and the supports are placed 10cm (0.1m) from each end. Therefore, the distance between the midpoint of the rod and each support is:
distance = 0.5m - 0.1m
= 0.4m
Step 4: Calculate the reaction forces.
Since the rod is in equilibrium, the sum of the forces acting on it must be zero.
Let R1 be the reaction force at one support and R2 be the reaction force at the other support.
Taking moments about one support, we have:
(R1 x 0.4) - (0.49 x 0.5) - (0.98 x 0.5) = 0
Simplifying the equation, we get:
R1 = (0.49 x 0.5) + (0.98 x 0.5) / 0.4
= 0.245 + 0.49 / 0.4
= 1.225 N
Hence, the reaction at each support will be approximately 1.225 N.