Chapter 2, Problem 93A

(a)

Interpretation Introduction

Interpretation:

The percent error of measurement $\text{5}\text{.2}\text{m}$ of a steel pipe needs to be determined, if the accepted length is $\text{5}\text{.5}\text{m}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 93A

The percent value of the steel pipe is $5.5\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{5}\text{.2}\text{meters}$ while the accepted value is $\text{5}\text{.5}\text{meters}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{5}\text{.2 m}-\text{5}\text{.5}\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =\left(\frac{\left|-0.3\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =5.45\%\end{array}$

Hence, the percent error is $5.45\%$.

(b)

Interpretation Introduction

Interpretation:

The percent error of measurement $\text{5}\text{.5}\text{m}$ of a steel pipe needs to be determined, if the accepted length is $\text{5}\text{.5}\text{m}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 93A

The percent value of the steel pipe is $0\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{5}\text{.5}\text{meters}$ while the accepted value is $\text{5}\text{.5}\text{meters}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{5}\text{.5}\text{m}-\text{5}\text{.5}\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =\left(\frac{\left|0\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =0\%\end{array}$

Hence, the percent error is $0\%$.

(c)

Interpretation Introduction

Interpretation:

The percent error of measurement $\text{5}\text{.7}\text{m}$ of a steel pipe needs to be determined, if the accepted length is $\text{5}\text{.5}\text{m}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 93A

The percent value of the steel pipe is $3.6\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{5}\text{.7}\text{meters}$ while the accepted value is $\text{5}\text{.5}\text{meters}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{5}\text{.7 m}-\text{5}\text{.5}\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =\left(\frac{\left|0.2\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =3.6\%\end{array}$

Hence, the percent error is $3.6\%$.

(d)

Interpretation Introduction

Interpretation:

The percent error of measurement $\text{5}\text{.1}\text{m}$ of a steel pipe needs to be determined, if the accepted length is $\text{5}\text{.5}\text{m}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 93A

The percent value of the steel pipe is $7.3\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{5}\text{.1}\text{meters}$ while the accepted value is $\text{5}\text{.5}\text{meters}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{5}\text{.1 m}-\text{5}\text{.5}\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =\left(\frac{\left|-0.4\text{m}\right|}{\text{5}\text{.5 m}}\right)\times 100\\ =7.3\%\end{array}$

Hence, the percent error is $7.3\%$.