Single piston engine problem - position of piston

In summary, the conversation discusses a simplified single-piston engine and finding the position of the piston at 2 seconds, with a constant angular speed of 1 rad/s and a wheel radius of 2 m. Various attempts at solving the problem are shared, including taking into account the angle of the connecting rod and drawing a triangle. The final answer is revealed to be x = A cos (omega*t), or in this case, -.83 meters. The conversation also mentions a similar problem with a different wheel radius.
  • #1
grog
23
0

Homework Statement


Consider the simplified single-piston engine in the figure. The wheel rotates at a constant angular speed of 1 rad/s and the radius of the wheel is 2 m. If the piston is fully extended at time t=0, find the position of the piston at 2s. The figure depicts a wheel with a peg that draws a piston in and out of a bore as the wheel rotates (counter clockwise, with the piston horizontal to the right).


Homework Equations


x=A cos (omega*t)
where A is the radius of the wheel



The Attempt at a Solution



omega*t = 2rad
cos 2 * 2m = x.
since 2 > pi/2, I add 2meters to the resulting x.

The answer I get is reportedly wrong. what's wrong with my approach?
 
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  • #2
It would help to see a diagram, but are you taking into account the angle of the connecting rod? When the pin is not at 0 or PI, you lose some of the stroke distance since the pin is above or below the axis of the cylinder.
 
  • #3
Actually it looks like you are trying to include that factor, but the distance x is not cos(2rad*2m). I don't think that's the angle that you should be taking the cos of...
 
  • #4
after doing some searching, I was able to find another problem with an identical diagram.

http://faculty.ksu.edu.sa/alkurtass/Tut102/Tut102-9.pdf

problem number 7 shows the piston and the wheel. my thinking of the angle being 2 rad stems from the piece that catches on the piston assembly following the path of the wheel. Since the piston is fully extended at time t=0, I believe that puts the initial angle at 0. am I wrong in thinking so?
 
  • #5
At t=0, the pin is at the far right. At 2s into rotation, the wheel is 2 radians CCW, which is most of the way to PI radians which is the farthest left. The x displacement to the left of the piston is most of the way to max displacement possible, but a little less. To calc the displacement x, draw a triangle. The theta that you take the cos of is most definitely not 2 radians. Draw the triangle on that figure, and show us your calculation...
 
  • #6
berkeman said:
At t=0, the pin is at the far right. At 2s into rotation, the wheel is 2 radians CCW, which is most of the way to PI radians which is the farthest left. The x displacement to the left of the piston is most of the way to max displacement possible, but a little less. To calc the displacement x, draw a triangle. The theta that you take the cos of is most definitely not 2 radians. Draw the triangle on that figure, and show us your calculation...

And actually, I don't think it's a simple cosine. It's a simple angle calculation, though...
 
  • #7
Sorry to intrude, but what is it? I have the same problem, with the same omega = 1 rad/s, but my r = 1.3m.
I am trying x = Acos(pi - 2rad) but this is not working. I have drawn a little triangle and concluded that the angle is pi minus omega(t), but no bueno! Any suggestions would be greatly appreciated
 
  • #8
livewire852 said:
Sorry to intrude, but what is it? I have the same problem, with the same omega = 1 rad/s, but my r = 1.3m.
I am trying x = Acos(pi - 2rad) but this is not working. I have drawn a little triangle and concluded that the angle is pi minus omega(t), but no bueno! Any suggestions would be greatly appreciated

Can you post a sketch showing your work? That would make it easier to help you.
 
  • #9
For the sake of posterity and future students facing this kind of problem, I thought I'd post an update. It turns out that because the piston is fully extended at time t=0, the answer is simply x=A cos (omega*t). I was making the problem more difficult than it needed to be. In this case, the answer is -.83 meters
 

1. What is a single piston engine?

A single piston engine is a type of internal combustion engine that uses a single piston to convert fuel into mechanical energy. It is commonly used in small aircraft, motorcycles, and other small vehicles.

2. How does a single piston engine work?

A single piston engine works by using a reciprocating motion of the piston to turn a crankshaft. This motion is created by a series of controlled explosions within the engine, which push the piston up and down.

3. What is the position of the piston in a single piston engine?

The position of the piston in a single piston engine can vary depending on the stage of the engine's four-stroke cycle. In the intake stroke, the piston is at the top of the cylinder. In the compression stroke, it moves down. In the power stroke, it moves up again. Finally, in the exhaust stroke, it moves down once more.

4. What happens if the piston is not in the correct position?

If the piston is not in the correct position, it can cause various issues with the engine's performance. For example, if the piston is not at the top of the cylinder during the ignition phase, it can result in a loss of power and inefficient combustion.

5. How is the position of the piston controlled in a single piston engine?

The position of the piston is controlled by the crankshaft and connecting rod, which are connected to the piston. The rotation of the crankshaft determines the up and down motion of the piston, while the connecting rod ensures that the piston stays in the correct position throughout the engine's cycle.

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