Two cylinders having weights of 100 kN and 200 kN with radii of 100 mm and 200 mm are placed with heavier weight above the lighter weight and both of them are placed in a container having a width of 500 mm. Assuming that the length of the container and cylinder to be the same. What is the reaction, R , between cylinders?
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To find the reaction, R, between the cylinders, we need to consider the equilibrium of forces acting on the system.
The weight of the upper cylinder (200 kN) will be acting downwards, and the weight of the lower cylinder (100 kN) will be acting upwards.
Let's denote the reaction force at the contact point between the cylinders as R.
According to Newton's third law of motion, the force exerted by the lower cylinder on the upper cylinder is equal in magnitude and opposite in direction to the force exerted by the upper cylinder on the lower cylinder.
Therefore, we can say that the reaction force R is equal in magnitude to the weight of the upper cylinder (200 kN).
Hence, the reaction force R between the cylinders is 200 kN.
To find the reaction force (R) between the cylinders, we need to consider the forces acting on them.
In this case, there are three forces involved:
1. The weight of the upper cylinder (acting downward).
2. The weight of the lower cylinder (acting downward).
3. The reaction force between the cylinders (acting upward).
We'll calculate the weight of each cylinder first:
Weight of upper cylinder = 100 kN
Weight of lower cylinder = 200 kN
Next, we need to calculate the areas of the cylinder ends to determine the pressures involved:
Area of upper cylinder end = π * r^2
Area of lower cylinder end = π * R^2
Given:
Radius of upper cylinder (r) = 100 mm = 0.1 m
Radius of lower cylinder (R) = 200 mm = 0.2 m
Width of the container = 500 mm = 0.5 m
Now, we can calculate the reaction force (R) between the cylinders using Pascal's Law, which states that the pressure is the same at all points on a confined fluid:
Pressure on the upper cylinder = Pressure on the lower cylinder
Pressure = force/area
Weight of upper cylinder/Area of upper cylinder end = Weight of lower cylinder/Area of lower cylinder end
(100 kN)/ (π * 0.1^2) = (200 kN)/ (π * 0.2^2)
To solve this equation, we can simplify the equation by removing the constants from both sides:
1/0.01 = 1/0.04
Both sides of the equation are now equal to 100. Therefore, the reaction force (R) between the cylinders is 100 kN.
So, the reaction force (R) between the cylinders is 100 kN.