Chapter 64, Problem 1A

To determine

The weight of the steel shaft.

Answer to Problem 1A

  $W=2.5lb$

Explanation of Solution

Given information:

Weight of steel: $w=0.264lb/cubicinch$

The shaft shown in the figure:

  

Calculations:

From the given figure, the shaft is composed of two parts.

  $\begin{array}{l}\therefore V=V_1+V_2\\ where,\\ V_1\to \text{volume of large cylindrical part}\\ V_2\to \text{volume of small cylindrical part}\\ \text{Hence, }\\ V_1=A_1\times l_1=\frac{\pi }{4}{\left(d_1\right)}^2\times l_1\\ substitutingvalues:\\ V_1=\frac{\pi }{4}{\left(1.25\right)}^2\times 6.5=7.976i{n}^3\end{array}$

  $\begin{array}{l}similarly,\\ V_2=A_2\times l_2=\frac{\pi }{4}{\left(d_2\right)}^2\times l_2\\ substitutingvalues:\\ V_2=\frac{\pi }{4}{\left(0.75\right)}^2\times 3=1.325i{n}^3\\ \text{The total volume of the shaft: }V=V_1+V_2=\left(7.976+1.325\right)i{n}^3\\ or,\\ V=9.301i{n}^3\\ \text{Hence, the weight of the shaft:}\\ W=wV\\ W=\left(0.264\frac{lb}{i{n}^3}\right)\left(9.301i{n}^3\right)\\ W=2.455lb\\ \text{Rounding the value to the nearest tenth pound:}\\ W=2.5lb\end{array}$

Conclusion:

The weight of the shaft is $W=2.5lb$