When gasoline is burned in the cylinder of an engine, it creates a high pressure that pushes on the piston. If the pressure is 150 pound-force per square inch, and it moves the 3-inch diameter piston a distance of 6 centimeters in 0.1 seconds, how much horsepower does this action produce?
Well, if we're talking about horsepower, I have to say that horses are probably not the best measure of engine power these days. I mean, have you ever seen a horse try to start a car? It's not pretty. But I'm here to entertain, so let's do some calculations anyway.
To calculate horsepower, we'll need to take into account the force and the distance traveled. First, let's convert the piston diameter from inches to centimeters. The diameter is 3 inches, which is around 7.62 centimeters. So, the radius of the piston is approximately 3.81 centimeters.
Now, let's calculate the force exerted by the pressure on the piston. The pressure is 150 pounds per square inch, but since we're using metric units, let's convert that to Newtons per square centimeter. Roughly speaking, 1 psi is around 6894.76 pascals, and 1 pascal is equivalent to 1 Newton per square meter. Therefore, 150 psi is about 1034219.905 pascals or Newtons per square meter. Since there are 10,000 square centimeters in a square meter, the force exerted on the piston is approximately 103.42 Newtons per square centimeter.
To calculate the total force, we'll need to multiply the force per square centimeter by the area of the piston. Using the formula for the area of a circle (A = πr^2), the area of the piston is roughly 45.55 square centimeters. So, the total force exerted on the piston is approximately 4711.28 Newtons (103.42 N/cm^2 * 45.55 cm^2).
Now, let's calculate the work done by this force. The work done is equal to the force multiplied by the distance traveled. The distance traveled is 6 centimeters, so the work done is approximately 28267.68 Newton-centimeters (6 cm * 4711.28 N).
Finally, let's calculate the power, which is the work done divided by the time taken. The time taken is 0.1 seconds, so the power is approximately 282,676.8 Newton-centimeters per second (28267.68 N / 0.1 s). Since 1 horsepower is equivalent to 745.7 watts, this action would produce approximately 378.92 horsepower (282,676.8 N-cm/s / 745.7 W/hp).
And there you have it! Approximately 378.92 horsepower from a little bit of piston-pushing action. Please note that these calculations are rough estimates and may not reflect the true power of an engine. Now, let's hope no horses were harmed in the process!
To calculate the horsepower produced, we need to gather some additional information. Specifically, we need to know the volume of the cylinder and the rate at which the piston is being pushed.
1. Calculate the area of the piston, using the formula for the area of a circle:
- The radius of the piston is half of its diameter, so the radius is 3 inches / 2 = 1.5 inches.
- Convert the radius to centimeters by multiplying by 2.54: 1.5 inches * 2.54 cm/inch = 3.81 cm.
- Calculate the area of the piston using the formula: area = π * radius^2.
- area = π * 3.81 cm * 3.81 cm = 45.48 cm^2.
2. Calculate the force exerted by the pressure on the piston, using the formula: force = pressure * area.
- Convert the pressure from pounds-force per square inch to pascals (Pa) by multiplying by 6895 (1 lb/in^2 = 6895 Pa).
- force = 150 lb/in^2 * 6895 Pa/lb/in^2 = 1,034,250 Pa.
- Convert the force to newtons (N) by dividing by 1.0E5 (1 N = 1.0E5 Pa).
- force = 1,034,250 Pa / 1.0E5 N/Pa = 10.3425 N.
3. Calculate the work done, using the formula: work = force * distance.
- Convert the distance from centimeters to meters by dividing by 100 (1 m = 100 cm).
- work = 10.3425 N * 6 cm / 100 cm/m = 0.62055 Nm.
4. Calculate the power, using the formula: power = work / time.
- Convert the time from seconds to hours by dividing by 3600 (1 hour = 3600 seconds).
- Convert the power from watts (W) to horsepower (hp) by multiplying by 0.00134 (1 hp = 0.00134 W).
- power = 0.62055 Nm / 0.1 s / 3600 s/h * 0.00134 hp/W = 0.00495 hp.
Therefore, the action of the burning gasoline produces approximately 0.00495 horsepower.
To calculate the horsepower produced by this action, we need to use the following formula:
Horsepower = (Force × Distance) ÷ (Time × Conversion Factor)
First, let's calculate the force exerted on the piston:
Force = Pressure × Area
The area of the piston can be determined using its diameter:
Area = π × (Radius)²
Given that the diameter is 3 inches, the radius (r) can be calculated as half the diameter:
Radius = 3 inches / 2 = 1.5 inches
Now, we need to convert the radius from inches to centimeters since the given distance is in centimeters:
Radius = 1.5 inches × 2.54 centimeters/inch = 3.81 centimeters
Next, we can calculate the area of the piston using the radius:
Area = π × (3.81 cm)²
Since π (pi) is a constant with a value of approximately 3.1416, we can compute the area:
Area = 3.1416 × (3.81 cm)²
Now, we have the force and we can substitute it into the formula:
Force = Pressure × Area
Force = 150 lb/in² × (3.1416 × (3.81 cm)²)
Now, we have the force exerted on the piston. To solve for horsepower, we need to convert the units:
1 lb = 0.453592 kg (kilograms)
1 inch = 0.0254 meters
1 horsepower = 745.7 watts
We can express the force in newtons:
Force = (150 lb/in²) × (0.453592 kg/lb) × (9.81 m/s²) × (0.0254 m/in)²
(distance is in inches, and we need to convert it to meters)
Now, we have the force in newtons, the distance in meters (since 1 cm = 0.01 m), and the time in seconds. We can substitute these values into the horsepower formula.
Horsepower = (Force × Distance) ÷ (Time × Conversion Factor)
Horsepower = (Force × Distance) ÷ (Time × 745.7 watts/hp)
Finally, we can calculate the horsepower using the given values.
Please provide the value of distance in meters and the given time in seconds so that I can proceed with the calculation.
Power = Work/time = Force*distance/time
The force, of course, is pressure*area
Now just put things into the proper units and it all falls out.