A unuform rod of mass 100g has a length a 1m.it is supported horixontally on two knife edges placed 10cm from its end. what will be the reactions at thise supports when a 50g mass is suspended 30cm from one of the knife edges?
F1 + F2 = 100 + 50 = 150
take moments about knife 1 for example
F2 * 90 = 100 * 40 + 50 * 30 = 5500
so
F2 = 5500/90 = 61.1
F1 = 150 - 61.1 = 88.9
To find the reactions at the supports, we need to consider the equilibrium of the system.
Let's label the supports as Support A (at one end of the rod) and Support B (at the other end of the rod).
First, let's find the center of mass of the uniform rod. Since the rod has a length of 1m, the center of mass will be at the midpoint, which is 0.5m from either end.
Next, we need to calculate the weight of the rod. Given that the mass of the rod is 100g, we can convert it to kilograms by dividing by 1000:
Mass of the rod = 100g / 1000 = 0.1kg
Weight of the rod = Mass of the rod × Acceleration due to gravity (g)
= 0.1kg × 9.8 m/s²
= 0.98 N
Since the rod is uniform and has two supports, the reactions at Support A and Support B will be equal. Let's denote the reaction at Support A as RA and the reaction at Support B as RB.
Now, let's consider the equilibrium of the system.
Horizontally:
Since the rod is supported horizontally on two knife edges, the net horizontal force must be zero.
Sum of horizontal forces = RA + RB = 0 (equation 1)
Vertically:
The weight of the rod and the weight of the suspended mass should be balanced by the reactions at the supports.
Sum of vertical forces = Weight of the rod + Weight of the suspended mass - RA - RB = 0 (equation 2)
Given that the suspended mass is 50g and is suspended 30cm from Support A, we can calculate its weight as follows:
Weight of the suspended mass = Mass of the suspended mass × Acceleration due to gravity (g)
= 50g / 1000 × 9.8 m/s²
= 0.49 N
Substituting the values into equation 2, we get:
0.98 N + 0.49 N - RA - RB = 0
Since RA and RB are equal, we can rewrite the equation as:
1.47 N - 2RA = 0
Now, substituting the value from equation 1 (RA + RB = 0) into the equation above, we have:
1.47 N + RA - RA = 0
Simplifying further, we find:
1.47 N = 0
This equation leads to an inconsistency, which means there is no unique solution.
Therefore, the reaction at each support cannot be determined based on the given information.