Given: the linear expansion coefficient of glass is 9 x 10^-6 ('C)^-1.
An automobile windshield has dimensions of 59 cm by 390 cm. What minimum spacing around the windshield is needed to prevent the windshield from breaking if the temp. changes by 146' F?
answer should be in units of mm.
The 390 changes most and is 3900 mm
delta L =9*10^-6 (146 *5/9) (3900)
Divide that by two because it is the total change in length and you get half of that on each side.
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sorry for repeating it, but i was hoping to get a better answer because i didn't understand the one drwls gave last time...
To determine the minimum spacing around the windshield needed to prevent it from breaking, we need to calculate the change in length of the glass due to the temperature change and then convert it to millimeters.
1. Calculate the change in temperature:
Since the given temperature change is in Fahrenheit, we need to convert it to Celsius. The temperature change of 146' F can be converted to Celsius using the formula:
ΔT (°C) = (ΔT (°F) - 32) × 5/9
ΔT (°C) = (146 - 32) × 5/9
ΔT (°C) = 78.888 °C (rounded to the nearest thousandth)
2. Calculate the change in length:
The change in length can be determined using the formula:
ΔL = α * L * ΔT
where ΔL is the change in length, α is the linear expansion coefficient of glass, L is the initial length, and ΔT is the change in temperature.
Given:
α = 9 x 10^-6 (°C)^-1
L = 390 cm (initial length converted to centimeters)
ΔT = 78.888 °C
ΔL = (9 x 10^-6) * (390 cm) * (78.888 °C)
ΔL = 2.749 cm (rounded to the nearest thousandth)
3. Convert the change in length to millimeters:
Since the answer should be in millimeters, we need to convert the change in length from centimeters to millimeters by multiplying by 10:
ΔL (mm) = 2.749 cm * 10
ΔL (mm) = 27.49 mm
Therefore, the minimum spacing around the windshield needed to prevent it from breaking should be 27.49 mm.