Answer :
Sure, let's break down the problem step by step for each scenario.
### Scenario 1: Area in square inches and pressure in pounds per square inch (psi)
1. Identify the given values:
- Area of the piston: 16 square inches
- Oil pressure: 178 pounds per square inch (psi)
2. Apply the formula to calculate the force:
The formula to calculate the force exerted by the piston is:
[tex]\[
\text{Force} = \text{Area} \times \text{Pressure}
\][/tex]
3. Perform the calculation:
[tex]\[
\text{Force} = 16 \, \text{square inches} \times 178 \, \text{psi}
\][/tex]
[tex]\[
\text{Force} = 2848 \, \text{pounds-force}
\][/tex]
So, the piston exerts a force of 2848 pounds-force.
### Scenario 2: Area in square centimeters and pressure in kilopascals (kPa)
1. Identify the given values:
- Area of the piston: 100 square centimeters (cm²)
- Oil pressure: 121 kilopascals (kPa)
2. Convert the area to square meters:
Since 1 square centimeter (cm²) is equal to 0.0001 square meters (m²):
[tex]\[
\text{Area} = 100 \, \text{cm}^2 \times 0.0001 \, \left(\frac{\text{m}^2}{\text{cm}^2}\right) = 0.01 \, \text{m}^2
\][/tex]
3. Convert the pressure to pascals:
Since 1 kilopascal (kPa) is equal to 1000 pascals (Pa):
[tex]\[
\text{Pressure} = 121 \, \text{kPa} \times 1000 \, \left(\frac{\text{Pa}}{\text{kPa}}\right) = 121000 \, \text{Pa}
\][/tex]
4. Apply the formula to calculate the force:
The formula to calculate the force exerted by the piston is:
[tex]\[
\text{Force} = \text{Area} \times \text{Pressure}
\][/tex]
5. Perform the calculation:
[tex]\[
\text{Force} = 0.01 \, \text{m}^2 \times 121000 \, \text{Pa}
\][/tex]
[tex]\[
\text{Force} = 1210 \, \text{newtons}
\][/tex]
So, the piston exerts a force of 1210 newtons.
### Summary
- For the first scenario, the piston exerts a force of 2848 pounds-force.
- For the second scenario, the piston exerts a force of 1210 newtons.
### Scenario 1: Area in square inches and pressure in pounds per square inch (psi)
1. Identify the given values:
- Area of the piston: 16 square inches
- Oil pressure: 178 pounds per square inch (psi)
2. Apply the formula to calculate the force:
The formula to calculate the force exerted by the piston is:
[tex]\[
\text{Force} = \text{Area} \times \text{Pressure}
\][/tex]
3. Perform the calculation:
[tex]\[
\text{Force} = 16 \, \text{square inches} \times 178 \, \text{psi}
\][/tex]
[tex]\[
\text{Force} = 2848 \, \text{pounds-force}
\][/tex]
So, the piston exerts a force of 2848 pounds-force.
### Scenario 2: Area in square centimeters and pressure in kilopascals (kPa)
1. Identify the given values:
- Area of the piston: 100 square centimeters (cm²)
- Oil pressure: 121 kilopascals (kPa)
2. Convert the area to square meters:
Since 1 square centimeter (cm²) is equal to 0.0001 square meters (m²):
[tex]\[
\text{Area} = 100 \, \text{cm}^2 \times 0.0001 \, \left(\frac{\text{m}^2}{\text{cm}^2}\right) = 0.01 \, \text{m}^2
\][/tex]
3. Convert the pressure to pascals:
Since 1 kilopascal (kPa) is equal to 1000 pascals (Pa):
[tex]\[
\text{Pressure} = 121 \, \text{kPa} \times 1000 \, \left(\frac{\text{Pa}}{\text{kPa}}\right) = 121000 \, \text{Pa}
\][/tex]
4. Apply the formula to calculate the force:
The formula to calculate the force exerted by the piston is:
[tex]\[
\text{Force} = \text{Area} \times \text{Pressure}
\][/tex]
5. Perform the calculation:
[tex]\[
\text{Force} = 0.01 \, \text{m}^2 \times 121000 \, \text{Pa}
\][/tex]
[tex]\[
\text{Force} = 1210 \, \text{newtons}
\][/tex]
So, the piston exerts a force of 1210 newtons.
### Summary
- For the first scenario, the piston exerts a force of 2848 pounds-force.
- For the second scenario, the piston exerts a force of 1210 newtons.
