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12. The density of oil is [tex]60.3 \, \text{lb/ft}^3[/tex]. What is the specific gravity?

13. The density of lead is [tex]11,300 \, \text{kg/m}^3[/tex]. What is the specific gravity?

14. A 200 lb man rests his weight on a [tex]6.0 \, \text{in}^2[/tex] heel. What is the stress?


Sagot :

Sure! Let's go through each of the questions step by step and find the solutions.

### Question 12: Specific Gravity of Oil

Given:
- Density of oil = 60.3 lb/ft³
- Standard density of water = 62.4 lb/ft³

Formula:
The specific gravity (SG) is calculated as the ratio of the density of the substance to the density of water.

[tex]\[ \text{Specific gravity of oil} = \frac{\text{Density of oil}}{\text{Density of water}} \][/tex]

Solution:

[tex]\[ \text{Specific gravity of oil} = \frac{60.3 \text{ lb/ft}³}{62.4 \text{ lb/ft}³} \approx 0.966 \][/tex]

So, the specific gravity of the oil is approximately 0.966.

### Question 13: Specific Gravity of Lead

Given:
- Density of lead = 11,300 kg/m³
- Standard density of water = 1,000 kg/m³

Formula:
The specific gravity (SG) is calculated as the ratio of the density of the substance to the density of water.

[tex]\[ \text{Specific gravity of lead} = \frac{\text{Density of lead}}{\text{Density of water}} \][/tex]

Solution:

[tex]\[ \text{Specific gravity of lead} = \frac{11,300 \text{ kg/m}³}{1,000 \text{ kg/m}³} = 11.3 \][/tex]

So, the specific gravity of lead is 11.3.

### Question 14: Stress on a Man's Heel

Given:
- Weight of man = 200 lb
- Area of heel = 6.0 in²

Note:
To find stress, we need to convert the area from in² to ft².

1 inch² = 0.00694444 ft².

Convert area from in² to ft²:

[tex]\[ \text{Area in ft}² = 6.0 \text{ in}² \times 0.00694444 \text{ ft}²/\text{in}² \approx 0.04166664 \text{ ft}² \][/tex]

Formula:
Stress is calculated as the force (weight) divided by the area over which the force is applied.

[tex]\[ \text{Stress} = \frac{\text{Weight}}{\text{Area}} \][/tex]

Solution:

[tex]\[ \text{Stress} = \frac{200 \text{ lb}}{0.04166664 \text{ ft}²} \approx 4800.003 lb/ft² \][/tex]

So, the stress on the man's heel is approximately 4800.003 lb/ft².

### Summary
- The specific gravity of oil is approximately 0.966.
- The specific gravity of lead is 11.3.
- The stress exerted by a 200 lb man on a 6.0 in² heel is approximately 4800.003 lb/ft².