Chapter 14, Problem 14.1P

Interpretation Introduction

Interpretation:

The cost of material per unit volume is more important in some cases than the cost per unit weight. The cost needs to be determined in terms of $\$/{\text{cm}}^3$. Whether this affects the relationship between the different materials or not needs to be explained.

Concept Introduction:

Specific strength can be calculated as follows:

  $\text{Specific strength =}\frac{\text{ strength }}{\text{ Mass density}}$

It relates the specific strengths of steel, few high strength non-ferrous alloys, and polymer- matrix composites. Additional factor to study in designing with non-ferrous material is their rate, which also differs significantly.

Explanation of Solution

Table no.1

Metal	Density(g/ $c{m}^3$)	Cost per kg($/kg)	Rank
Steels	7.87	0.22	1
Zinc	7.13	0.88	2
Lead	11.36	0.99	3
Aluminium	2.70	1.32	4
Copper	8.93	1.57	5
Magnesium	1.74	3.31	6
Titanium	4.51	8.82	7
Tungsten	19.25	8.82	8
Nickel	8.90	9.04	9
Beryllium	1.85	777.60	10

The cost of a material per unit volume can be converted from ($/kg) to ($/g) by dividing the cost of material by 1000, and multiplying the converted cost value with density.

Table no. 2

Metal	Density	Cost per kg	Cost per gram	Cost per volume	Rank
Steel	7.87	0.22	0.22 $\times {10}^{-3}$	0.0017	1
Aluminium	2.70	1.32	1.32 $\times {10}^{-3}$	0.0036	2
Magnesium	1.74	3.31	3.31 $\times {10}^{-3}$	0.0057	3
Zinc	7.13	0.88	0.88 $\times {10}^{-3}$	0.0063	4
Lead	11.36	0.99	0.99 $\times {10}^{-3}$	0.0013	5
Copper	8.93	1.57	1.57 $\times {10}^{-3}$	0.0140	6
Titanium	4.51	8.82	8.82 $\times {10}^{-3}$	0.0397	7
Nickel	8.90	9.04	9.04 $\times {10}^{-3}$	0.0804	8
Tungsten	19.25	8.82	8.82 $\times {10}^{-3}$	0.1696	9
Beryllium	1.85	771.60	771.60 $\times {10}^{-3}$	1.4247	10

From the above two tables, the different materials are related to each other in terms of cost per kilogram and cost per volume.