Three cylinders with the same size, density, and structure are piled on each oth

Question

Three cylinders with the same size, density, and structure are piled on each otherand on top of a rough surface. Find the minimum angle which the direction of the fforce acting between the cylinders and the rough surface makes with the vertical?
The hint my professor gave: #3 can be solved using F=ma in the x and the y direction. Study, for example, the bottom right cylinder. In the y direction, you have the weight of the cylinder, the y-component of the friction, between the top cylinder and the bottom right cylinder, the y-component of the push caused by the top cylinder on the bottom right cylinder. The sum of the y-component of all these 3 forces is equal to 3W/2. In the x-direction you have the push coming in from the bottom left cylinder and acting on the bottom right cylinder, you have the x-component of the friction between the top cylinder and the bottom right cylinder, the friction from the ground acting on the bottom cylinder and another force. To get a minimum angle set the horizontal force acting by the left cylinder on the right cylinder equal to zero. Three cylinders with the same size, density, and structure are piled on each otherand on top of a rough surface. Find the minimum angle which the direction of the fforce acting between the cylinders and the rough surface makes with the vertical?
The hint my professor gave: #3 can be solved using F=ma in the x and the y direction. Study, for example, the bottom right cylinder. In the y direction, you have the weight of the cylinder, the y-component of the friction, between the top cylinder and the bottom right cylinder, the y-component of the push caused by the top cylinder on the bottom right cylinder. The sum of the y-component of all these 3 forces is equal to 3W/2. In the x-direction you have the push coming in from the bottom left cylinder and acting on the bottom right cylinder, you have the x-component of the friction between the top cylinder and the bottom right cylinder, the friction from the ground acting on the bottom cylinder and another force. To get a minimum angle set the horizontal force acting by the left cylinder on the right cylinder equal to zero.

Explanation / Answer

Can be solved using F=ma in the x and the y direction. Study, for example, the bottom right cylinder. In the y direction, you have the weight of the cylinder, the y-component of the friction, between the top cylinder and the bottom right cylinder, the y-component of the push caused by the top cylinder on the bottom right cylinder. The sum of the y-component of all these 3 forces is equal to 3W/2. In the x-direction you have the push coming in from the bottom left cylinder and acting on the bottom right cylinder, you have the x-component of the friction between the top cylinder and the bottom right cylinder, the friction from the ground acting on the bottom cylinder and another force. To get a minimum angle set the horizontal force acting by the left cylinder on the right cylinder equal to zero.

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