Percentage error in displacement time and mass are 2%, 1% and 3%. Find percentage error in the measurement of force.
to determine the force acting on each mass it was assumed that g=9.80
To find the percentage error in the measurement of force, we need to apply the principle of error propagation, also known as the chain rule. According to the chain rule, the percentage error in a calculated quantity that depends on several variables can be determined by summing the percentage errors for each individual variable.
In this case, the force depends on three variables: displacement (x), time (t), and mass (m). The given percentage errors for each variable are 2% for displacement, 1% for time, and 3% for mass.
Let's denote the force as F, the percentage error in F as ΔF, the percentage errors for displacement, time, and mass as Δx, Δt, and Δm respectively. The formula for calculating the percentage error using the chain rule is:
ΔF/F = [(Δx/x)^2 + (Δt/t)^2 + (Δm/m)^2]^0.5
Now we can substitute the given percentage errors into the formula:
ΔF/F = [(0.02)^2 + (0.01)^2 + (0.03)^2]^0.5
ΔF/F = [0.0004 + 0.0001 + 0.0009]^0.5
ΔF/F = 0.0014^0.5
ΔF/F = 0.0374
To express this as a percentage, we multiply by 100:
ΔF/F = 0.0374 * 100
ΔF/F = 3.74%
Therefore, the percentage error in the measurement of force is approximately 3.74%.