Final answer:
To find the difference in length between a 30-foot measuring tape and its correct length at a temperature of 100℉, we can use the coefficient of linear expansion and the temperature change.
Step-by-step explanation:
To find the difference in length between a 30-foot measuring tape and its correct length, we need to understand the temperature effect on the tape. When the temperature increases, the measuring tape expands, and when the temperature decreases, the tape contracts.
First, let's convert the temperature from Fahrenheit to Celsius. To do this, we subtract 32 from the Fahrenheit temperature and then multiply by 5/9. So, (100℉ - 32) × 5/9 = 37.8℃.
The change in length of a measuring tape can be calculated using the formula:
ΔL = αLΔT,
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the temperature change.
The coefficient of linear expansion for most materials is constant. Assuming the coefficient of linear expansion for the measuring tape is α = 1.2 × 10^-5 /℃, we can plug in the values:
ΔL = (1.2 × 10^-5 /℃)(30 ft)(37.8℃),
ΔL = 0.01359 ft.
Therefore, the 30-foot measuring tape is approximately 0.01359 feet longer than its correct length when the temperature is 100℉.