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4. If an automatic transmission clutch piston has an area of 16 square inches and the oil pressure is 178 pounds per square inch, what force does the piston exert?

If an automatic transmission clutch piston has an area of [tex]100 \, \text{cm}^2[/tex] and the oil pressure is 121 kPa, what force does the piston exert?

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.

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Rewritten by : Barada