A rectangular plate has a length of (20.0 ± 0.2) cm and a width of (8.3 ± 0.1) cm. Calculate the area of the plate, including its uncertainty.
To calculate the area of the rectangular plate, we can use the formula:
Area = length × width
Given that the length (L) of the plate is (20.0 ± 0.2) cm and the width (W) is (8.3 ± 0.1) cm, we need to account for the uncertainties when calculating the area.
To include the uncertainty in the area, we will use the method of propagation of uncertainties. This involves adding the absolute uncertainties in the length and width to calculate the maximum possible values, and subtracting the absolute uncertainties to calculate the minimum possible values. Then, we use these values to calculate the maximum and minimum area values.
Let's start with the maximum possible values:
Maximum length (L_max) = L + ΔL = 20.0 cm + 0.2 cm = 20.2 cm
Maximum width (W_max) = W + ΔW = 8.3 cm + 0.1 cm = 8.4 cm
Maximum Area (A_max) = L_max × W_max = 20.2 cm × 8.4 cm
Now, let's calculate the minimum possible values:
Minimum length (L_min) = L - ΔL = 20.0 cm - 0.2 cm = 19.8 cm
Minimum width (W_min) = W - ΔW = 8.3 cm - 0.1 cm = 8.2 cm
Minimum Area (A_min) = L_min × W_min = 19.8 cm × 8.2 cm
The final step is to combine the minimum and maximum values to get the range of area values.
A_range = A_max - A_min
Now you can calculate the area of the plate, including its uncertainty, by using the above calculations.
Please note that when performing such calculations with uncertainties, it is important to keep the same number of significant figures as the original values.