# What is the optimal speed for a tumble dryer to gently tumble clothes?

• BOAS
In summary, the conversation is about a question regarding a tumble dryer and the conditions for it to work properly. The question involves calculating the number of revolutions per second for the dryer's cylinder to ensure that clothes tumble gently as they dry. The conversation also includes the correct equations and reasoning used to find the solution. The final conclusion, however, is incorrect as it does not provide the correct units for revolutions per second.
BOAS
Hello,

I have a question regarding a tumble dryer and the conditions that must be met for it to work as described in the following question.

I'm not totally convinced by my reasoning so would like to run it by somebody.

## Homework Statement

In an automatic clothes dryer, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.32m). The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle θ above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. How many revolutions per second should the cylinder make in order that the clothes lose contact with the wall when θ = 70°?

## The Attempt at a Solution

I have drawn diagrams to illustrate my answer, but hopefully my working is clear to you without them.

Centripetal force $$F_{c} = \frac{mv^{2}}{r}$$

Weight of the clothes $$W = mg$$

If you imagine a triangle with the hypotenuse being Fc and the vertical component equal to the weight of the clothes, with an angle of 70° between the horizontal and the hypotenuse then we can say that $$mg = F_{c} \sin \theta$$.

The condition for which the clothes will fall is when $$mg > F_{c} \sin \theta$$.

$$\frac{mv^{2}}{r} \sin \theta = mg$$

Cancel the mass and rearrange for v to find;

$$v = \sqrt{\frac{gr}{\sin \theta}} = 1.85$$ms-1

The circumference of the cylinder is ~2m, so the number of revolutions per second must be less than 2m/1.85ms-1 = 1.08s-1.

I'm just concerned that my reasoning is incorrect... I have used the value for g = 10 ms-2.

Thanks!

For what it's worth: reasoning is correct, final conclusion is not: if you divide meters by meters/second you cannot expect to get s-1. (By the way: I get 1.09 seconds/revolution -- but remember: they want revolutions per second !)

BvU said:
For what it's worth: reasoning is correct, final conclusion is not: if you divide meters by meters/second you cannot expect to get s-1. (By the way: I get 1.09 seconds/revolution -- but remember: they want revolutions per second !)

Oh of course, thanks!

## 1. How do tumble dryers work?

Tumble dryers use a combination of heat and airflow to remove moisture from wet clothing. The dryer heats up the air, which then circulates through the drum and absorbs the moisture from the clothes. The hot, damp air is then vented out of the dryer, and the process repeats until the clothes are dry.

## 2. How does the size of a tumble dryer affect its performance?

The size of a tumble dryer can affect its performance in several ways. A larger drum allows for more clothes to be dried at once, but it also means that there is more space for the clothes to move around and get evenly dried. However, a larger dryer may use more energy, so it's important to consider your needs and energy efficiency ratings when choosing a size.

## 3. What is the difference between gas and electric tumble dryers?

The main difference between gas and electric tumble dryers is the source of heat used to dry the clothes. Gas dryers use natural gas or propane to generate heat, while electric dryers use electricity. Gas dryers tend to be more energy-efficient and cost less to operate, but they require a gas line and proper ventilation. Electric dryers are more convenient to install, but they may have a higher operating cost.

## 4. Can tumble dryers damage clothes?

Tumble dryers can potentially damage clothes if they are not used correctly. Over-drying clothes can cause shrinkage, fading, and wear and tear. It's important to read the care labels on clothing and follow the recommended drying settings. Using a lower heat setting or removing clothes while still slightly damp can help prevent damage.

## 5. Are there any safety concerns when using a tumble dryer?

There are a few safety concerns to be aware of when using a tumble dryer. It's important to regularly clean the lint trap and exhaust vent to prevent potential fire hazards. It's also recommended to never overload the dryer and to avoid putting items that are flammable or have been exposed to flammable substances in the dryer. Additionally, it's important to follow the manufacturer's instructions and never attempt to repair or modify the dryer yourself.

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