Change 66.3 kg/cm 2 to lb/in. 2
The Correct Answer and Explanation is:
To convert (66.3 \, \text{kg/cm}^2) to ( \text{lb/in}^2 ), follow these steps:
- Understand the conversion factors:
- ( 1 \, \text{kg} = 2.20462 \, \text{lb} )
- ( 1 \, \text{cm}^2 = (1/2.54)^2 \, \text{in}^2 = 0.155 \, \text{in}^2 )
- Convert ( \text{kg/cm}^2 ) to ( \text{lb/in}^2 ): The formula for the conversion is:
[
\text{Pressure in} \, \text{lb/in}^2 = \text{Pressure in} \, \text{kg/cm}^2 \times \frac{\text{lb}}{\text{kg}} \times \frac{\text{cm}^2}{\text{in}^2}
] Substituting the values:
[
66.3 \, \text{kg/cm}^2 \times 2.20462 \, \frac{\text{lb}}{\text{kg}} \times \frac{1}{0.155} \, \frac{\text{cm}^2}{\text{in}^2}
] - Perform the calculation:
[
66.3 \times 2.20462 \div 0.155 = 66.3 \times 14.2233 = 943.04 \, \text{lb/in}^2
]
Final Answer:
[
66.3 \, \text{kg/cm}^2 = 943.04 \, \text{lb/in}^2
]
Explanation:
Pressure is a measure of force per unit area. In this problem, the initial pressure is given in ( \text{kg/cm}^2 ), a metric unit. The goal is to convert it into ( \text{lb/in}^2 ), an imperial unit.
- Unit Conversion Details:
- Weight in kilograms needs to be converted into pounds using the factor ( 1 \, \text{kg} = 2.20462 \, \text{lb} ).
- The area in square centimeters is converted to square inches. Since ( 1 \, \text{inch} = 2.54 \, \text{cm} ), the area conversion factor becomes ( (1/2.54)^2 ).
- Why the Formula Works:
By multiplying the given pressure by the conversion factors, the ( \text{kg} ) and ( \text{cm}^2 ) cancel out, leaving the desired units of ( \text{lb/in}^2 ). - Practical Applications:
Understanding such conversions is critical in fields like engineering and physics, where metric and imperial systems are frequently interchanged, particularly in international collaborations or when working with machinery and instruments designed in different regions.
By carefully following each conversion step, the result, ( 943.04 \, \text{lb/in}^2 ), accurately reflects the equivalent pressure in the imperial system.