The x and y components of a certain force are measured and found to be Fx = (68 ± 3)N and Fy =(42 ± 2) N, respectively. Calculate the magnitude of this force? expressing your result to the proper number of significant figures.
To calculate the magnitude of the force, we can use the Pythagorean theorem. The magnitude (F) of the force can be calculated using the formula:
F = sqrt(Fx^2 + Fy^2)
Let's plug in the given values:
Fx = 68 ± 3 N
Fy = 42 ± 2 N
First, we need to determine the uncertainties in Fx and Fy. Since we're performing addition and subtraction, we can simply add the uncertainties:
ΔFx = 3 N
ΔFy = 2 N
Now, let's calculate the magnitude. We'll assign a range of values to the uncertainties and calculate the magnitude for each possibility in order to find the minimum and maximum values:
Minimum magnitude: Fmin = sqrt((Fx - ΔFx)^2 + (Fy - ΔFy)^2)
= sqrt((68 - 3)^2 + (42 - 2)^2)
= sqrt(65^2 + 40^2)
Maximum magnitude: Fmax = sqrt((Fx + ΔFx)^2 + (Fy + ΔFy)^2)
= sqrt((68 + 3)^2 + (42 + 2)^2)
= sqrt(71^2 + 44^2)
Now, we can find the range of the magnitude by taking the minimum and maximum values:
Minimum magnitude = sqrt(65^2 + 40^2)
Maximum magnitude = sqrt(71^2 + 44^2)
Using a calculator, we find:
Minimum magnitude ≈ 76.2 N
Maximum magnitude ≈ 82.6 N
Therefore, the magnitude of the force is approximately 76.2 N to 82.6 N, expressing the result to the proper number of significant figures.
the magnitude is
√(Fx^2 + Fy^2)
So, figure the min and max values for F and use the average ± something