Absolute and Relative Error Exercise Guide #2, True Value
Solve the following exercises
problem #1
For a cube whose edge is 10.5 ± 0.5 cm, calculate the relative and percentage error of the area and volume.
Answer: E rS = 0.095 and 9.52%
E rV = 0.143 and 14.3%
problem #2
A simple pendulum is used to calculate the gravitational acceleration. The period of oscillations can be expressed as:
T = 2 π √ l/g
Where L = 1 m, is the length of the pendulum, measured with an experimental uncertainty of 1 cm. The period T is measured with a stopwatch and with an experimental uncertainty of 0.2 s, resulting in 2 seconds for the time of a complete oscillation.
a) Solve for g and determine the relative error of L and T .
b) Calculate the percentage relative error of the length of the pendulum.
c) Determine the minimum number of complete oscillations, so that the percentage relative error of the period is 0.05%.
d) Calculate the representative value of the gravitational acceleration and its experimental uncertainty, if the period was calculated with the number of oscillations calculated in c.
Answer: a) 0.01 and 0.1; b) 1%
Problem #3
Find the representative value and absolute error expressions for: z = a + b/c²
Problem #4
Find the representative value and absolute error expressions for: w = z/(x – y).
Problem #5
The mass of a body is 37.5 ± 0.02 g, and its volume is 13.89 ± 0.01 cm³
a) Calculate the mean density of the body with its corresponding absolute error.
b) Knowing that the density of aluminum is 2.7 g/cm³ and that of copper is 8.92 g/cm³, what material could the body be made of?
Answer: 2.7 ± 0.000035g/cm³
Answer the following questionnaire
Question #1
What is meant by absolute error?
Question #2
What is meant by relative error?
Question #3
What is meant by percentage error?
Question #4
What is meant by standard error?
Question #5
What is the difference between measurement error and measurement error?
