Mechanical problem related to materials

[racer]

Homework Statement

Use calculations to determine what could happen to the 215mm wide glass window if it is tightly fitted into teh aluminum frame.

The temperature in the mechanical wrokshop was 20 C
The Maximum temperature in Bahrain = 55 C
THe Minimum temperature in Bahrain = 5 C
Thermal Expansion Alluminum = 24x10-6/K
Thermal Expansion Glass = 9x10-6/K

2- Calculate the weight ( grams ) of the glass window.
Use a glass size of 215mm * 155mm * 2.8mm

Homework Equations

No relevant equation

The Attempt at a Solution

I was not given any equation or any hint about how to solve it on purpose to make me research, I tried to search about an equation that I can plug these values in or anything related, the closest I got was with tensile stress but I have not found anything useful, I do not need someone to solve it for me, I need to know how to solve it and by what equation.

Thank you so much

 

[nvn]

racer: The PF rules state we are not allowed to tell you how to solve your assignment. A large part of the learning process is to read and study your textbook enough to find and list some relevant equations yourself. Keep trying; list some relevant equations. And you must show your work; then someone might check your math.

Hint: Look up the density of your glass. Look for an equation relating temperature and strain, using coefficient of thermal expansion. Look for an equation relating stress and strain. Look for the tensile and compressive strength properties of your glass and aluminum materials.

You did not list the cross-sectional dimensions of your aluminum frame yet. Generally, I think window frames probably do not grip the glass rigidly enough to put the glass in significant tension (maybe I'm wrong). Therefore, you could probably just work the problem for compressive stress on the glass. But you could work it for tensile stress on the glass, also, if you wish.

 

[Mene]

for your question. it is important to understand the problem and how to approach it in a systematic manner. In this case, we can use the principles of thermal expansion to determine what could happen to the glass window if it is tightly fitted into the aluminum frame.

Firstly, we need to understand that when materials are heated, they expand in size and when they are cooled, they contract. In this case, the aluminum frame and the glass window will both experience thermal expansion due to the change in temperature from 20°C to 55°C.

To calculate the potential expansion of the aluminum frame, we can use the equation: ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the change in temperature. Plugging in the values for the aluminum frame, we get:

ΔL = (24x10^-6/K)(215mm)(55°C-20°C) = 0.15mm

This means that the aluminum frame will expand by 0.15mm when the temperature increases from 20°C to 55°C.

Similarly, we can calculate the potential expansion of the glass window using the same equation. However, we need to take into account that the glass window is tightly fitted into the aluminum frame, which means that it cannot expand freely. This will result in compressive stress being applied to the glass window.

To calculate the compressive stress, we can use the equation: σ = EαΔT, where σ is the stress, E is the Young's modulus, α is the coefficient of thermal expansion, and ΔT is the change in temperature. Plugging in the values for the glass window, we get:

σ = (70x10^9 Pa)(9x10^-6/K)(215mm)(55°C-20°C) = 0.067 MPa

This means that the glass window will experience a compressive stress of 0.067 MPa when the temperature increases from 20°C to 55°C.

Now, to determine what could happen to the glass window, we need to compare the compressive stress to the strength of the glass. If the stress is greater than the strength of the glass, it could potentially crack or break. However, if the stress is within the strength of the glass, it may only experience some deformation.

As for the weight of the glass