# Equilibrium cylinder and plank on incline

• joemama69
In summary, the conversation discusses a horizontal stick attached to a free pivot on an inclined plane, with a cylinder resting on the other end of the stick. The coefficient of friction is given and the questions ask for the normal force and the minimum value of μ for the system to not slip. The conversation also mentions a free body diagram and suggests being more careful and complete to avoid errors in the solution. There is also an inquiry about the direction of the bottom friction force.
joemama69

## Homework Statement

A horizontal stick of mass m has its left end attached to a free pivot on a plane (inclined at angle θ), while it’s right end rests on a cylinder also of mass m which in turn rests on the plane, as shown. The coefficient of friction between the cylinder and both the stick and the plane is μ

(a) Assuming that the system is at rest, what is the normal force from the plane on the cylinder?

(b) What is the smallest value of μ (in terms of θ) for which the system doesn’t slip anywhere?

## The Attempt at a Solution

is my free body diagram correct on the attachment. I realize that the Ns and the us are differnt

#### Attachments

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Your free body diagram looks okay. I'd be a little more careful to make the normal forces and frictional forces perpendicular and locate them at the points of contact between the surfaces. I'd make mgcos(Q) perpendicular to the inclined plane, but then I'm a fussy old professor. I'd show the attachment of the horizontal stick to the pivot at the end of the inclined plane.

I guess you can summarize it by I'd be a little more complete and a little more careful. You cut down on errors that way. (Plus it impresses the person who grades your homework.)

I know this is from a few years ago, but can someone explain to me why that bottom friction force is pointed up the plane. It seems strange...

## What is equilibrium in relation to a cylinder and plank on an incline?

Equilibrium refers to a state where the forces acting on an object are balanced, resulting in no net force and thus no change in motion. In the case of a cylinder and plank on an incline, equilibrium occurs when the forces of gravity and friction are balanced by the normal force exerted by the incline.

## How do you determine the equilibrium position of a cylinder and plank on an incline?

The equilibrium position of an object on an incline can be determined by analyzing the forces acting on the object. In the case of a cylinder and plank, the normal force exerted by the incline must be equal and opposite to the force of gravity pulling the object down the incline. This results in a net force of zero and the object will remain in equilibrium.

## What factors affect the equilibrium of a cylinder and plank on an incline?

The equilibrium of a cylinder and plank on an incline can be affected by several factors, including the angle of the incline, the mass and dimensions of the object, and the coefficient of friction between the object and the incline. Any changes in these factors can result in a different equilibrium position for the object.

## What is the significance of finding the equilibrium position of a cylinder and plank on an incline?

The equilibrium position of a cylinder and plank on an incline is important because it allows us to determine the minimum force needed to keep the object in place. This can be useful in designing structures or machines that need to maintain a specific position on an incline.

## How can the equilibrium position of a cylinder and plank on an incline be calculated?

The equilibrium position of a cylinder and plank on an incline can be calculated using the principles of statics, which involves analyzing the forces acting on the object. This can be done by setting up and solving equations based on the forces of gravity, friction, and the normal force, or by using graphical methods such as free body diagrams and vector addition.

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