Absolute and Relative Error Exercise Guide #2, True Value
Solve the following exercises
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%
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%
Find the representative value and absolute error expressions for: z = a + b/c²
Find the representative value and absolute error expressions for: w = z/(x – y).
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
What is meant by absolute error?
What is meant by relative error?
What is meant by percentage error?
What is meant by standard error?
What is the difference between measurement error and measurement error?