How Much Tolerance is Needed for a Windshield to Withstand a 200°F Temperature Change?

[tdusffx]

An automobile windshield 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°F? (The linear expansion coefficient of glass is 9×10-6 (oC)-1.)

I'm thinking of using the area expansion formula but I don't understand the part where it says minumum tolerance in mm...

A = 2a(Tf-Ti)

a = alpha = 9x10^-6

 

[tdusffx]

thanks guys

 

[piercas]

(oC)^-1

Tf = final temperature

Ti = initial temperature

To calculate the minimum tolerance in mm, we need to first determine the maximum change in temperature that the windshield can withstand without breaking. This can be done by using the linear expansion formula:

ΔL = αLΔT

Where:

ΔL = change in length of the windshield
α = linear expansion coefficient of glass
L = original length of the windshield
ΔT = change in temperature

Since we are given the dimensions of the windshield, we can calculate the original length (L) by using the formula for the perimeter of a rectangle:

P = 2a + 2b

Where:

P = perimeter
a = length of one side (60 cm)
b = length of the other side (150 cm)

Therefore, L = 2(60 cm) + 2(150 cm) = 420 cm

Now, we can plug in the values into the linear expansion formula to find the maximum change in length that the windshield can withstand without breaking:

ΔL = (9x10^-6 (oC)^-1)(420 cm)(200°F) = 0.756 cm

To convert this to millimeters, we multiply by 10, so the maximum change in length is 7.56 mm. This means that the minimum tolerance needed in mm to prevent the windshield from breaking is 7.56 mm.

In conclusion, the minimum tolerance in mm needed to prevent the windshield from breaking if the temperature changes by 200°F is 7.56 mm. This calculation is important as it ensures that the windshield can withstand temperature changes without breaking, ensuring the safety of the driver and passengers. It also highlights the importance of considering thermal expansion and contraction in the design and manufacturing of products.