Balance of the cylinder on the rod

In summary, the problem asks for three equations for equilibrium, and provides information about one possible equation.
  • #1
Innoko
9
0
It is told, that all homework-like threads should be posted there. So, here I go.
Imagine such a situation: there is a vertical rod and a cylinder, with the hole diameter sightly larger than the diameter of rod. There is also a second rod, attached to the cylinder perpendicularly. There is a friction between the main rod and the cylinder. It is known, that if we put a cylinder on the rod (watch picture) and apply a force at the edge of the second rod, the system stays rest, i.e. there is lack of rotational and translational motion in it.
On the picture frictional forces are colored with red, normal forces with green.
attachment.php?attachmentid=44192&stc=1&d=1329845120.jpg

The question is:
-What can we say about frictional forces in the system, if the geometry of the problem is fully known?
-Can we find their quantities, if the mass of the cylinder and the force applied are known?
-Can we answer at least a qualitative question: which one is bigger - applied to the right or to the left corner?
-May they be equal before reaching their maximal quantities (kN, where k is coefficient of friction)?
-Can it be so, that one of them is always reaches it's maximal value and the other doesn't? Under which conditions?
-Can the boundary conditions be founded?
That's clear for me, that we can write down three equitations: protections of the second Newton's law on vertical (here we can fund sum of friction forces) axis, on horizontal axis (here we from here we can clearly understand, that both normal forces are equal!) and the equation, that tells us: the total momentum is equal zero. But this way we get 3 equations with 4 variables (both frictional forces and both normal forces, which are claimed to be equal). Have you got any ideas of how can we find out one more equation?
All bodies are solid.
The force applied is vertical.
PS: it isn't some kind of a homework or other stuff. I just wonder, what is the answer and can't find it myself. You won't find this problem in any book!
PSS: Sorry for my English. Write it down, if you've found some mistakes here, but remember, that it's not the point of the conversation!
Thank you for attention!
 
Last edited:
Physics news on Phys.org
  • #2
No ideas? (making the thread to go up)
 
  • #3
The cylinder must have mass, draw it, too.
You need to answer the questions and they suggest that you might not find all forces.
Write up the equations for equilibrium you mentioned, and find out what information can be obtained of them. Consider the case when one frictional force has the maximum value, what it means on the other one.

ehild
 
  • #4
Torque Equation?
 
  • #5


I would approach this problem by first analyzing the forces acting on the system. From the given information, there are two main forces at play: the normal forces and the frictional forces.

The normal forces are equal and opposite between the rod and the cylinder, as well as between the two rods. This means that they cancel each other out and do not contribute to any rotational or translational motion in the system.

The frictional forces, on the other hand, are responsible for keeping the cylinder in place on the rod. They act in opposite directions, with one pointing to the left and the other to the right. The direction of these forces will depend on the direction of the applied force on the second rod.

In order to find the quantities of the frictional forces, we would need to know the mass of the cylinder and the magnitude of the applied force. With this information, we can use the equations of motion to solve for the frictional forces.

As for which force is bigger, it would depend on the specific geometry and conditions of the system. It is possible for one force to reach its maximum value before the other, depending on the coefficient of friction and the angle of the applied force.

To find another equation to solve for the unknown variables, we would need to consider the torque on the system. This would require knowing the distance between the point of application of the applied force and the center of the cylinder. With this information, we can set up an equation for the net torque and solve for the unknown variables.

In conclusion, with the given information, we can find the quantities of the frictional forces and determine their relative magnitudes. However, to fully solve for all the unknowns, we would need more information such as the distance between the point of application and the center of the cylinder. The boundary conditions can also be determined by considering the forces and torques acting on the system.
 

What is the balance of a cylinder on a rod?

The balance of a cylinder on a rod refers to the equilibrium state in which the cylinder is able to remain stable and not topple over when placed on top of the rod.

How is the balance of a cylinder on a rod determined?

The balance of a cylinder on a rod is determined by various factors such as the mass and dimensions of the cylinder, the length and diameter of the rod, and the distribution of weight on the cylinder.

What is the importance of understanding the balance of a cylinder on a rod?

Understanding the balance of a cylinder on a rod is important in various fields such as engineering, physics, and architecture. It allows for the design of stable structures and accurate predictions of the behavior of objects in equilibrium.

What are some common methods used to achieve balance of a cylinder on a rod?

Some common methods used to achieve balance of a cylinder on a rod include adjusting the position of the cylinder on the rod, varying the length or diameter of the rod, and adding counterweights to the cylinder.

What are some real-world applications of the balance of a cylinder on a rod?

The balance of a cylinder on a rod is used in various real-world applications such as balancing mechanisms in machinery, construction of stable structures such as towers and bridges, and even in sports equipment such as balancing beams in gymnastics.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
3
Replies
97
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
927
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
821
  • Introductory Physics Homework Help
2
Replies
41
Views
2K
Back
Top