Linear Expansion related to area expansion

In summary, the minimum tolerance needed to prevent an automobile windshield from breaking due to a 200 degree Fahrenheit temperature change is approximately 4.5 mm. This is calculated by finding the area of the windshield (900,000 mm^2) and multiplying it by the linear expansion coefficient (9 x 10^-6) and the change in temperature (111 degrees Celsius). It is important to only consider linear expansion in this problem and to use the larger dimension (150 cm) when calculating the area.
  • #1
student 1
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0

Homework Statement


An automobile windshild has dimensions of 60 cm by 150 cm. What minimum tolerance in mm is needed to prevent the windshield from breaking if the temperature changes by 200 degrees Farenheight? (The linear expansion coeffecient of galss is 9 x 10[tex]^{}-6[/tex]
(C)-1

Homework Equations


area expansion = Ai(Area expansion coefficient)(Change in Temp)
Area expansion coefficient=2(Linear expansion coefficient)

The Attempt at a Solution


I found my area to be 900,000 mm2 The change in temperature 111 Degrees Celsius. but I'm not getting the right answer when I multiply 2(Linear expansion coefficient)
I'm getting a huge number for my final answer when it should be really small.
 
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  • #2
You don't need to consider anything beyond linear expansion. They are looking for an answer in mm.
 
  • #3
So do I use the 60 mm or the 150 mm? I figured I was trying to over think it.
 
  • #4
student 1 said:
So do I use the 60 mm or the 150 mm?
Good question. Each dimension would have a different answer. If I had to pick, I'd go with the larger dimension. (Note that those measurements are in cm, not mm.)
 
  • #5
ok, I'll try them both! Thanks!
 

FAQ: Linear Expansion related to area expansion

1. What is linear expansion and how is it related to area expansion?

Linear expansion is the increase in length of an object when it is heated. It is related to area expansion because when an object expands in length, its width and height also increase, causing an overall increase in area.

2. What factors affect the linear expansion and area expansion of an object?

The main factor that affects linear and area expansion is temperature. When an object is heated, the particles within it vibrate faster, causing them to take up more space and resulting in expansion. Other factors that can affect expansion include the material of the object and its initial dimensions.

3. How is linear expansion measured and calculated?

Linear expansion can be measured using a device called a micrometer, which measures the change in length of an object. The linear expansion coefficient (α) is used to calculate the amount of expansion, and is equal to the change in length divided by the original length and the change in temperature. The formula for linear expansion is ΔL = αLΔT, where ΔL is the change in length, α is the linear expansion coefficient, L is the original length, and ΔT is the change in temperature.

4. Can linear expansion and area expansion be prevented or controlled?

While linear and area expansion cannot be completely prevented, it can be controlled to some extent. Using materials with a lower coefficient of linear expansion, such as steel, can help reduce expansion. Additionally, designing objects with expansion joints or incorporating flexible materials can also help control expansion.

5. What are some real-world applications of linear and area expansion?

Linear and area expansion have many practical applications in everyday life. For example, they are used in the design of bridges and buildings to account for temperature changes. They are also utilized in the design of various household items, such as thermostats and thermometers. In industrial settings, linear and area expansion are important considerations in the manufacturing of machinery and equipment.

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