Errors and Measurements

# Absolute and Relative Error Exercise Guide #2, True Value

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%
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?

### 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?