# Block attached to string, wrapped around hollow cylinder and free to rotate

• Tina20
In summary, a 3.20 kg block attached to a string is released from a height of 1.09 m above the ground, while being wrapped around a 1.17 kg, 4.08 cm diameter hollow cylinder that can freely rotate on an axis through its center. The question asks for the speed of the block as it hits the ground. Using the equations Ui = Kf, Mgh = Kcyl + Kblock, and Mgh = 1/2Iw^2 + 1/2mv^2, where w is angular speed and I is moment of inertia, the solution is found to be 7.64 m/s. However, there may be a missing piece of information in
Tina20

## Homework Statement

A 3.20 kg block is attached to a string that is wrapped around a 1.17 kg, 4.08 cm diameter hollow cylinder that is free to rotate on an axel through the center. The block is released 1.09 m above the ground. What is the speed of the block as it hits the ground?

## Homework Equations

Ui = Kf
Mgh = Kcyl + Kblock
Mgh = 1/2Iw^2 + 1/2mv^2 , where w is angular speed and I is moment of inertia

Moment of Inertia of a hollow cylinder is MR^2
w = v/r

so,

Mgh = 1/2(MR^2)(v^2/r^2) + 1/2mv^2

## The Attempt at a Solution

Mgh = 1/2(MR^2)(v^2/r^2) + 1/2mv^2
(3.2kg)(9.8)(1.09m) = 1/2(1.17kg)(v^2/(0.0204m^2) + 1/2(3.2)v^2
34.182 = 2.434x10-4 (v^2/4.1616x10-4) + 1.6v^2
140435.497 = v^2/4.16x10-4 + 1.6v^2
140435.497 = v^2( 1/4.16x10-4 + 1.6v)
140435.497 = v^2 (2402.92 + 1.6)
140435.497 = v^2 (2404.52)
58.4 = v^2
7.64 m/s = v

The answer is wrong unfortunately. I must be missing a vital piece of information in my equation?

1) On the second line of your solution there is 1 error.

2) Take a while to examine your equations.
Can you simplify this ?
Mgh = 1/2(MR^2)(v^2/R^2) + 1/2mv^2

## What is a block attached to string wrapped around a hollow cylinder?

A block attached to string wrapped around a hollow cylinder is a simple physical system where a block is attached to one end of a string, which is then wrapped around the circumference of a hollow cylinder. The other end of the string is free and the system is able to rotate around the cylinder.

## What is the purpose of this experiment or demonstration?

The purpose of this experiment or demonstration is to study rotational motion and the relationship between the radius of the cylinder, the length of the string, and the time it takes for the system to complete one rotation. It can also demonstrate the concepts of tension, centripetal force, and angular velocity.

## What factors affect the motion of the block attached to string wrapped around a hollow cylinder?

The motion of the block attached to string wrapped around a hollow cylinder is affected by several factors, including the radius of the cylinder, the length and mass of the string, the mass of the block, and the force applied to the string. Other factors such as friction and air resistance may also play a role.

## How can this experiment be modified to study different variables?

This experiment can be modified by changing the radius of the cylinder, the length and mass of the string, the mass of the block, or the force applied to the string. These modifications can help investigate the effects of different variables on the motion of the system.

## What are some real-world applications of a block attached to string wrapped around a hollow cylinder?

A block attached to string wrapped around a hollow cylinder is a simplified version of many real-world systems, such as pulleys, winches, and cranes. The principles and concepts demonstrated in this experiment can be applied to understand and design these types of systems in various industries, including construction, engineering, and transportation.

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