Finding Horsepower given Pressure, Diameter, and Distance

[Oannes]

Homework Statement

When gas is burned in a cylinder of an engine it creates a high pressure that pushes a piston. If the pressure is 100psi and it moves a 3 inch in diameter piston a distance of 5cm every .1 seconds. How much horsepower does this action produce?

Homework Equations

Pressure = Force/ Area
HP = Force * distance / time
Area of Cylender = 2pieR² (H) + 2pie R²
Kinetic Energy = 1/2 (mass) (velocity)²

The Attempt at a Solution

Im honestly not sure where to start. I can find Force by multiplying Pressure by area, however I can't find the area of a cylinder without it's height. We have only looked at equations for power in the form of Kinetic Energy and Potential Energy, so I assume the problem is solved with the Kinetic Energy equation, however, without mass I do not see how I can solve for kinetic energy. I either need force or mass and I am not sure how I could go about finding either one.

 

[billy_joule]

The Attempt at a Solution

Im honestly not sure where to start. I can find Force by multiplying Pressure by area,

That's the right approach, and you have enough information and the correct equations to do this.

however I can't find the area of a cylinder without it's height.

The area of the cylinder is irrelevant.
The gas does work on the piston, not the cylinder.

 

[Oannes]

That's the right approach, and you have enough information and the correct equations to do this.
The area of the cylinder is irrelevant.
The gas does work on the piston, not the cylinder.

Would my Force be pressure? If so that would mean distance and time was given so :

HP = 100psi * 5cm/.1sec

That would make things very simple, but I don't think pressure is the force is it? I mean it makes sense that it is a force, but in the context of the equations the class I am in is going over right now it just seems very puzzling. Is this the right train of thought? Thanks as well.

 

[Oannes]

That's the right approach, and you have enough information and the correct equations to do this.
The area of the cylinder is irrelevant.
The gas does work on the piston, not the cylinder.

Alright so I've gotten a bit further but still not where I need to be. So I have pressure, diameter, and acceleration and here is the following:

Power = energy/time
Pressure = Force/area
Energy = Force * Distance
Force = mass * acceleration

I have pressure, I have a distance (from velocity), and I have the diameter of a cylinder. From this I know that I need to get a value for energy. To get energy, however, I need to find force. I can't find force, however , because I do not have mass. How do I find force given what I have been given? I just don't see it. I got pressure which can be split up into Force/area, but I don't have one or the other to complete the equation. From what I see I don't have 2 of the three values needed to complete any of the equations above. Power lacks energy, Pressure lacks area and force, energy lacks force, and force lacks mass. I am stuck at a dead end and I do not see a way out. I've been going over this in my head constantly because I know I'm missing something but I just can't figure out what.

 

[Oannes]

That's the right approach, and you have enough information and the correct equations to do this.
The area of the cylinder is irrelevant.
The gas does work on the piston, not the cylinder.

Wait... should I be looking for the area of a circle and not the area of a cylinder since the pressure is only pushing down on the surface?

So I've gotten force which turns out to be 124071 Newtons, but this is only true if I find it by getting the area of a circle whose diameter is 3inches. Unfortunately, I still am not sure how to solve for anything else. I tried to get mass by usein Force = mass * acceleration, but if I do that I get kg/s which makes no sense to me.

 

[billy_joule]

You have the right approach for force but your value is wrong, you must have made an error in your calculation.
You have a force, a time and a distance...look at your relevant equations.