Solving the Stuck Ring Problem Using Expansion Coefficients

In summary, the conversation discusses heating a brass ring with a diameter of 10.00 cm at 19.5C and slipping it over an aluminum rod with a diameter of 10.01 cm at the same temperature. The question is asked of what temperature the combination must be cooled to in order to separate them, and if it is possible. It is also asked what the required temperature would be if the aluminum rod had a diameter of 10.03 cm, and if it is possible. The conversation also mentions the average coefficients of linear expansion for both metals and the possibility of contracting when the temperature is reduced. Ultimately, the suggestion is made to use the length equation to solve for the temperature that will make both metals the same
  • #1
skwerl
4
0
A brass ring of diameter 10.00 cm at 19.5C is heated and slipped over an aluminum rod of diamter 10.01 cm at 19.5C. Assume the average coefficients of linear expansion are constant.

a) To what temperature must this combination be cooled to separate them? is this possible?
b) If the aluminum rod were 10.03 cm in diameter, what would be the required temperature? Is this possible?

B(brass) = 19x10^-6
B(alum) = 24x10^-6

Well...let's see... first I thought of heating the brass until it was wide enough to slip over the tube, and then I tried to set up some kind of relationship and failed miserably.

oh and by the way I'm new! hi guys!
 
Last edited:
Physics news on Phys.org
  • #2
skwerl said:
Well...let's see... first I thought of heating the brass until it was wide enough to slip over the tube, and then I tried to set up some kind of relationship and failed miserably.
Welcome to Physics Forums!

When the temperature is reduced, both metals will contract. The question is will they contract enough to separate?

The length is given by: L = L0(1 + α ΔT). Set it up and solve for the temperature that will make both metals the same diameter.

Hints: You know the "unstressed" diameter of both metals at 19.5°C, so start there. Also, what is the maximum possible ΔT?
 
  • #3
neat. so much more elegant than what I thought of

thanks!
 

FAQ: Solving the Stuck Ring Problem Using Expansion Coefficients

What is the "stuck ring problem"?

The stuck ring problem refers to the difficulty of removing a ring that is stuck on a finger. This can be caused by a variety of factors, such as swelling of the finger, skin irritation, or the ring being too small for the finger.

How can expansion coefficients be used to solve the stuck ring problem?

Expansion coefficients, also known as thermal expansion coefficients, are used to determine the change in size of an object due to temperature changes. By understanding the expansion coefficient of the ring and the finger, a solution can be found to safely and effectively remove the stuck ring without causing damage.

What is the process for using expansion coefficients to remove a stuck ring?

The process for using expansion coefficients to remove a stuck ring involves heating the ring and/or finger to increase their size, making it easier to slide the ring off. This can be done by submerging the hand in warm water or using a lubricant, such as oil or hand lotion, to reduce friction. The expansion coefficient for both the ring and finger can be used to determine the appropriate temperature and amount of force needed for successful removal.

Are there any risks or potential complications when using expansion coefficients to remove a stuck ring?

As with any method for removing a stuck ring, there are potential risks and complications. Heating the ring and finger may cause discomfort or burns if not done carefully. Additionally, if the ring or finger has an abnormal expansion coefficient, the method may not be effective. It is always recommended to seek professional help if the ring cannot be safely removed.

Is this method effective for all types of rings and fingers?

The effectiveness of using expansion coefficients to remove a stuck ring may vary depending on the materials and sizes of the ring and finger. It may be more effective for metal rings and larger fingers, while it may not work as well for smaller or non-metallic rings. It is important to understand the properties of both the ring and finger before attempting to use this method.

Similar threads

How Does Temperature Affect the Fit Between a Brass Ring and an Aluminum Rod?
Replies
1
Views
2K
Thermal Expansion Aluminium Problem
Replies
1
Views
3K
Thermal Expansion Problem Involving a Brass Ring
Replies
4
Views
7K
Ring and Sphere Linear Expansion
Replies
4
Views
8K
Thermal expansion of brass and iron rings
Replies
2
Views
4K
Heat and work. Fit ring over rod, remove ring from rod
Replies
1
Views
5K
Thermal coefficients of expansion
Replies
5
Views
1K
Thermal elongation-ring on a shaft
Replies
7
Views
2K
Iron Ring Expansion: Solve for Δθ to Find Temp Increase
Replies
2
Views
2K
How Cold to Separate a Heated Brass Ring from an Aluminum Rod?
Replies
4
Views
6K

Hot Threads

Recent Insights

Back
Top