Uniform cylinder force diagram

In summary, the conversation discusses a problem involving a uniform cylinder resting on an inclined rough plane and supported by a cord under constant tension. The objective is to find the minimum coefficient of friction for the cylinder to remain in equilibrium. Two diagrams are provided, and the need for three equations to solve for the unknown forces is mentioned. One potential error in the second diagram is identified.
  • #1
diorific
19
0

Homework Statement



A uniform cylinder of mass m and radius R rests in equilibrium against a
rough plane that is inclined at an angle α to the horizontal. The cylinder
is supported by a cord under a constant tension, wrapped round it, so that
the cord leaves the surface of the cylinder tangentially and is horizontal;
the plane of the cord is perpendicular to the axis of the cylinder. The axis
of the cylinder is horizontal, and all the forces act in the same vertical
plane.
Model the cord as a model string, and take the coefficient of static friction
between the cylinder and the plane as μ. The object of this question is to
find the minimum value of the coefficient of friction for the cylinder to be
in equilibrium.
https://skydrive.live.com/redir?resid=4CDF33FFA97631EF!1040
I'm having problems drawing the force diagram.


The Attempt at a Solution



I've made two diagrams, but I think they are both wrong.
https://skydrive.live.com/redir?resid=4CDF33FFA97631EF!1041
Can you help?
 
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  • #2
Pics

http://sdrv.ms/Rz5gnF
http://sdrv.ms/VhVbS8
 
  • #3
You have four unknown forces. You only need to figure out (in principle) the ratios between them, so that's 3 degrees of freedom. That means you need three equations. Horizontal and vertical force balance gives two, and torque balance gives the third. So you will be needing the second diagram.
The only problem I see with it is how you've drawn N. The direction looks a bit off (maybe just a drawing inaccuracy) and the line of action is not right.
The line of action of W isn't quite clear, but it's probably OK.
 

1. What is a uniform cylinder force diagram?

A uniform cylinder force diagram is a visual representation of the forces acting on a cylinder that has a constant cross-sectional area and consistent distribution of mass. This diagram can help to analyze and understand the behavior of the cylinder under different conditions.

2. How is a uniform cylinder force diagram drawn?

A uniform cylinder force diagram is typically drawn by first identifying and labeling the forces acting on the cylinder, such as its weight, normal force, and any external forces. Then, the magnitude and direction of each force are represented by arrows on the diagram. The length of the arrows is proportional to the magnitude of the force, and the direction of the arrows indicates the direction of the force.

3. What can a uniform cylinder force diagram tell us?

A uniform cylinder force diagram can provide information about the forces acting on a cylinder, including the net force, resulting acceleration, and equilibrium conditions. It can also help to determine the stability and motion of the cylinder under different conditions.

4. How is a uniform cylinder force diagram used in engineering?

In engineering, a uniform cylinder force diagram is often used to analyze and design structures or machines that involve cylinders, such as pipes, pistons, or hydraulic systems. It can also be used to determine the strength and stability of structures that are subjected to external forces, such as bridges or towers.

5. What are some common mistakes when drawing a uniform cylinder force diagram?

Some common mistakes when drawing a uniform cylinder force diagram include forgetting to include all the forces acting on the cylinder, mislabeling or miscalculating the magnitude and direction of the forces, and not considering the effects of friction or other factors that may affect the behavior of the cylinder. It is important to carefully consider all the forces involved and accurately represent them in the diagram to ensure accurate analysis.

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