A uniform rod 1.8m long and of mass 10kg rest horizontally on support at its ends. If a weight of mass 3kg is attached at a point 1.2m from one end, find the reactions from the support
F1 + F2 = 10 g + 3 g = 13 g
0.9 (10 g) + 1.2 (3 g) = 1.8 (F2)
so
1.8 F2 = 9 g + 3.6 g = 12.6 g
F2 = 7 g Newtons
F1 = 13 g - 7 g = 6 g Newtons
g is gravitational acceleration about 9.81 m/s^2 on earth
A uniform rod 1.8m long am of mass10kg rest horizontal on support at it ends.If weight of mass 3kg is attached at a point 1.2m from one ends find reaction from the support
To find the reactions from the support, we need to analyze the forces acting on the rod.
Let's denote the reactions from the support as R1 and R2. Since the rod is at rest and in equilibrium, the sum of all forces and the sum of all moments acting on the rod must be zero.
First, let's consider the forces acting on the rod in the vertical direction:
At the left end (R1): The reaction force R1 acts upward.
At the right end (R2): The reaction force R2 acts upward.
At the point where the weight is attached: The weight force acts downward, which is given by the formula: weight = mass × acceleration due to gravity.
Now, let's consider the moments acting on the rod:
A moment is the rotational equivalent of force, and it depends on the force and its distance from a reference point. In this case, the reference point is the left end of the rod.
The moment caused by the weight (W) about the left end of the rod is calculated as: moment = weight × distance from the left end of the rod (1.2 m).
Now, since the rod is in equilibrium, the sum of the moments about the left end of the rod must be zero.
Using the principle of moments:
Sum of moments about the left end (R2 × distance from the left end) - (W × distance from the left end) = 0.
We can now substitute the known values into the equation:
(R2 × 1.8 m) - (3 kg × 9.8 m/s^2 × 1.2 m) = 0.
Simplifying the equation, we get:
R2 = (3 kg × 9.8 m/s^2 × 1.2 m) / 1.8 m.
Now, we have the value of R2. To find R1, we can use the fact that the sum of all vertical forces must be zero:
R1 + R2 - weight = 0.
Substituting the known values:
R1 + R2 - (3 kg × 9.8 m/s^2) = 0.
Simplifying the equation, we get:
R1 = (3 kg × 9.8 m/s^2) - R2.
By substituting the value of R2, we can calculate R1.
Please note that R1 and R2 are the magnitudes of the reaction forces exerted by the support on the rod. The direction of these forces will be opposite to their respective magnitudes so that the rod remains at rest.