Three cylinders with the same size, density and structure are piled on each other on top of a rough surface. Find the minimum angle which the direction of the force acting between the cylinders and rough surface makes with the vertical?
To find the minimum angle at which the force between the cylinders and the rough surface makes with the vertical, we need to consider the forces acting on the cylinders.
Let's call the three cylinders stacked on top of each other as A, B, and C, with A at the bottom, B in the middle, and C on top. The vertical direction will be upwards, and we'll assume that the force of gravity acts downwards.
There are two main forces acting on the cylinders: the force of gravity and the normal force exerted by the rough surface on the bottom cylinder.
The force of gravity on each cylinder is given by the equation F = mg, where m is the mass of each cylinder and g is the acceleration due to gravity. Since the cylinders have the same size, density, and structure, they will have the same mass, so the force of gravity on each cylinder will be the same.
The normal force is the force exerted by a surface perpendicular to it. In this case, the rough surface exerts a normal force on the bottom cylinder. Since the cylinders have the same size, density, and structure, and they are stacked vertically on top of each other, the normal force exerted on the bottom cylinder will be equal to the force of gravity acting on that cylinder.
Due to the rough surface, there will be a frictional force acting between the bottom cylinder and the rough surface. This frictional force opposes the motion or impending motion between the cylinders and the surface. We want to find the minimum angle at which the frictional force prevents the cylinders from sliding down.
The minimum angle occurs when the frictional force is at its maximum, which is when the angle of the surface is at its critical angle. At the critical angle, the frictional force is equal to the normal force, which is equal to the force of gravity acting on the bottom cylinder.
Therefore, to find the minimum angle, we need to calculate the critical angle using the formula:
μ = tan(θ)
Where μ is the coefficient of friction between the surface and the cylinders, and θ is the angle of the surface with the vertical.
Once you know the coefficient of friction between the surface and the cylinders, you can substitute it in the formula to solve for the minimum angle (θ).
Remember to use appropriate units and constants in your calculations.