Pressure is a quantity that tell the average force per unit area. Its unit is Newton per meter square [N/m2] or Pascal [Pa]. When you fill the air for your car’s tires, the convention unit is pound force per square inch [psi]. Given 1 pound force = 4.5 N, and 2.5 cm = 1inch, convert the pressure of 1 [psi] to [Pa].
The Correct Answer and Explanation is:
To convert 1 psi (pound-force per square inch) to pascals (Pa):
Step 1: Understand the units
- 1 psi=1 pound-force1 inch21 \, \text{psi} = \frac{1 \, \text{pound-force}}{1 \, \text{inch}^2}1psi=1inch21pound-force
- We are given:
- 1 pound-force=4.5 N1 \, \text{pound-force} = 4.5 \, \text{N}1pound-force=4.5N
- 2.5 cm=1 inch2.5 \, \text{cm} = 1 \, \text{inch}2.5cm=1inch
- Convert inches to meters: 1 inch=0.025 m1 \, \text{inch} = 0.025 \, \text{m}1inch=0.025m
Step 2: Convert square inches to square meters
1 inch2=(0.025 m)2=0.000625 m21 \, \text{inch}^2 = (0.025 \, \text{m})^2 = 0.000625 \, \text{m}^21inch2=(0.025m)2=0.000625m2
Step 3: Compute pressure in pascals
1 psi=4.5 N0.000625 m2=7200 Pa1 \, \text{psi} = \frac{4.5 \, \text{N}}{0.000625 \, \text{m}^2} = 7200 \, \text{Pa}1psi=0.000625m24.5N=7200Pa
✅ Final Answer:
1 psi=7200 Pa1 \, \text{psi} = 7200 \, \text{Pa}1psi=7200Pa
Explanation
Pressure is a measure of how much force is applied over a specific area. In the metric system, pressure is measured in pascals (Pa), where one pascal equals one newton per square meter. In some practical applications like automobile tires, the unit used is pounds per square inch (psi). To compare or convert between these units, we need to understand the relationship between the quantities involved.
We begin by converting the force unit. One pound-force is equal to 4.5 newtons. This means that if a force of one pound is applied, it is equivalent to applying a force of 4.5 newtons in the metric system.
Next, we convert the unit of area from square inches to square meters. We are told that 2.5 centimeters is equal to one inch. Since there are 100 centimeters in a meter, one inch equals 0.025 meters. To find the area in square meters, we square this number. Squaring 0.025 meters gives 0.000625 square meters.
Now, we compute the pressure in pascals by dividing the force in newtons by the area in square meters. Dividing 4.5 newtons by 0.000625 square meters gives 7200 pascals. Therefore, one psi is equal to 7200 pascals. This large number shows that psi is a unit for relatively high pressures, which is appropriate for things like tire inflation.
Understanding how to convert between psi and pascals allows for clear communication and consistency across different measurement systems used in engineering and science.
