# A block placed in a horizontal hollow cylinder

• SciencyBoi
In summary, the problem involves a block being placed inside a rotating horizontal hollow cylinder and finding the minimum angular speed of the cylinder for the block to reach the highest point of the cylinder. The solution involves considering the block initially moving with the cylinder until it reaches a 30 degree angle, at which point it starts to slide. The balance of forces at this point determines the minimum angular speed of the cylinder.
SciencyBoi

## Homework Statement

A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center. Find the radius of the cylinder if the coefficient of friction is 0.6, What should be the minimum constant angular speed of the cylinder so that the block reach the highest point of the cylinder?

## Homework Equations

Centrifugal force = mv2 / r
Friction = μN

## The Attempt at a Solution

Picturing a cross section of the hollow cylinder rotating with an angular velocity of 2π radians/sec with forces marked;

Equating forces as the block can be assumed to be in rest (constant slipping);
(There would be no centripetal force because the block isn't moving with the cylinder, or isn't in a circular motion)
Mgcos(30) = μ[Mgsin(30)]
=> μ= √3
Which contradicts the statement made by the question that coefficient of friction is 0.6.
Also, this isn't giving any information about the radius as the radius doesn't even come in the equations.

However, according to the book, the solution is

The solution considers the ω of the block (equation1) to be the ω of the cylinder, when in actuality, the ω of the block is zero (it's at rest), and 5hus there shouldn't be any centrifugal forces acting on it.Please guide as to where I am wrong. I am sure 5to be missing some concept, because the question is correct. Thank you very much.

I think the problem wants you to assume that the block is placed at the bottom of the rotating cylinder such that the block is initially moving with the wall of the cylinder. So, initially the block is not slipping on the wall. The block moves with the wall without any slipping until it reaches the 30 degree position at which point slippage begins.

SciencyBoi
SciencyBoi said:
in actuality, the ω of the block is zero (it's at rest),
The question says
SciencyBoi said:
at which it begins to slide
That is, it was rotating with the cylinder until the given angle was reached. The transition to sliding is determined by the balance of forces just before it started sliding.

SciencyBoi
haruspex said:
The question says

That is, it was rotating with the cylinder until the given angle was reached. The transition to sliding is determined by the balance of forces just before it started sliding.
I have now understood it. It was a language problem apparently. Thank you very much.

TSny said:
So, initially the block is not slipping on the wall. The block moves with the wall without any slipping until it reaches the 30 degree position at which point slippage begins.
Thank you very much, I seem to have understood it now.

## 1. What is the purpose of placing a block in a horizontal hollow cylinder?

The purpose of this experiment is to study the motion of a block placed inside a hollow cylinder and how it is affected by the cylinder's rotation and other external forces.

## 2. What are the variables that can affect the motion of the block?

The variables that can affect the motion of the block include the mass and shape of the block, the diameter and length of the cylinder, the force of gravity, and the rotational speed of the cylinder.

## 3. How does the rotational speed of the cylinder affect the motion of the block?

The rotational speed of the cylinder affects the motion of the block by creating a centrifugal force. This force pushes the block towards the outer edge of the cylinder, causing it to move in a circular path.

## 4. What is the role of friction in this experiment?

Friction plays a key role in this experiment as it acts as a resisting force to the motion of the block. It can also cause the block to slip or slide along the surface of the cylinder, affecting its motion.

## 5. How can this experiment be applied in real-life situations?

This experiment can be applied in various real-life situations, such as understanding the motion of objects on a rotating platform, studying the behavior of satellites in space, and analyzing the motion of vehicles on curved roads.

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