What is the Constant Torque Applied in a Simple Piston Engine?

[Jrak11]

Homework Statement

Find the constant Torque being applied.
We are given a diagram of a piston engine, along with the masses of piston, flywheel and rod connecting the two. I know that the expanding gas in the piston does 4 kJ of work. I know that at the beginning of each rotation the engine is at 350 rpm. I know that a constant torque is being applied on the fly wheel.

Homework Equations

work=Torque*Angular displacement

The Attempt at a Solution

4kJ = T*2pi
T=4000/2Pi

I feel this is wrong however because I have not taken into account that the piston has been moved back and forth, and we knew it's mass. I can easily calculate the force on the piston at any point in the rotation so I would have thought there is some work done by its movement. Or does this do no net work since the net displacement is zero??
Thanks a heap for any help

 

[Redbelly98]

Welcome to Physics Forums.

It is difficult to understand without seeing the actual figure. If you could attach a copy of it, that would be helpful. To attach a figure, click the "Go Advanced" button below, then click the paper clip icon just to the right of the smiley-face icon.

 

[Jrak11]

Ok Here is an image:

I also have a question about when I am calculating the rotaitonal KE of the rod. Does it rotate around an axis through its centre, or the axis where it connects to the piston?

 

[Redbelly98]

Well, I'm still perplexed by this one. Have you posted all the given information? Copying the problem statement exactly, word-for-word, is generally a good idea.

To answer two of your questions: the work done by the piston in one cycle is not zero if there is any net heat either added or taken away during a cycle. As for the KE of the rod, you can calculate the total KE as rotational KE about the center-of-mass, plus the translational KE of the center-of-mass. Since the end point is not actually fixed in place, I would not use it as a reference point for the rotation.

Meanwhile, I have asked some of our designated "Homework Helpers" if they have any ideas.

 

[Jrak11]

I guess I should have been more specific. I meant, is there any work done in moving the mass of the piston back and forth. Not turning the wheel or accelerating the engine, just moving the piston.

And as to the other part, Is there a reason why it would be better to use the CM of the rod as the zero point? It too is moving, so why is it not better to choose the lesser of two evils and use the rotation around the piston joint instead.

 

[ideasrule]

I think that your initial calculation is correct. Think about it this way: each cycle, the piston supplies 4kJ of new energy, yet the flywheel's speed never increases. This means that the constant torque must be draining 4 kJ every cycle. If it drained any more or less, the flywheel would be rotating faster or slower than 350 rpm at the start of the next cycle.

I guess I should have been more specific. I meant, is there any work done in moving the mass of the piston back and forth. Not turning the wheel or accelerating the engine, just moving the piston.

Yes, the gas does positive work when pushing the piston forwards. However, it also does negative work when the rod pushes the piston backwards and compresses the gas. The sum of the positive work done during expansion and the negative work done during compression is 4kJ.

And as to the other part, Is there a reason why it would be better to use the CM of the rod as the zero point? It too is moving, so why is it not better to choose the lesser of two evils and use the rotation around the piston joint instead.

(You don't need to do this for the question; I'm just responding to clear up any misconceptions.)

You could, and that would give you the rotational energy with respect to that point. However, how do you plan on calculating kinetic energy? If you choose the CM as the reference point, kinetic energy is just 1/2*mv^2, where m is the mass of the entire rod and v is the speed of that point. This is not true for any other point.

 

[ideasrule]

By the way, I assumed that the constant torque was done by an external force on the flywheel, and not by the rod on the flywheel. Is this assumption right?

 

[Jrak11]

Indeed that is correct.
I realized to calculate the energy in the Rod at any point If i was to use the center of mass I would need its horizontal KE, vertical KE and rotational KE.

However, I decided I would use the horizontal KE of the rod at the center of mass, then the rotation around the piston. This makes the calculation easier as I don't have to take into account vertical KE

 

[Redbelly98]

Okay, I'm understanding the question better now. I hadn't realized "the constant Torque being applied" referred to an external torque.

I think that your initial calculation is correct.

I agree.

I guess I should have been more specific. I meant, is there any work done in moving the mass of the piston back and forth. Not turning the wheel or accelerating the engine, just moving the piston.

No, and we can use the work-energy theorem here:

W_net = ΔKE​

Since the KE of anything after a complete cycle is the same as it was at the start of the cycle, ΔKE is zero.

That probably makes the following discussion a moot point:

And as to the other part, Is there a reason why it would be better to use the CM of the rod as the zero point? It too is moving, so why is it not better to choose the lesser of two evils and use the rotation around the piston joint instead.

I realized to calculate the energy in the Rod at any point If i was to use the center of mass I would need its horizontal KE, vertical KE and rotational KE.

However, I decided I would use the horizontal KE of the rod at the center of mass, then the rotation around the piston. This makes the calculation easier as I don't have to take into account vertical KE

I don't think that will work, but I am many years removed from studying this in school. Do you have information from your class lectures or textbook that says the KE may be calculated this way?

I do know that KE can be calculated either by:

(1) Adding the CM translational KE to the CM rotational KE; or
(2) Taking the rotational KE about a fixed point.

Since the piston-rod joint is not fixed (it moves horizontally), method (2) would certainly not work. I'm not sure if adding the CM horizontal KE, as you said, would take care of the problem.

 

[Vespa71]

Rotational Energy of the Rod..

sounds like a movie I might have seen..

Anyways: If we imagine that the rod itself has no mass, all the mass is in the end bolts, connecting the flywheel and piston, respectively. Would you agree that the flywheel bolt rotates, and that the reciprocating piston bolt doesn't? And if we then distribute the mass from the heavy bolts, evenly onto the rod, that then the rotational energy of the rod does not change, as CM is indentical?

I'm not certain, and I've spent some time thinking about it, but I think we calculate half the rod's mass as the rotating mass centered in the flywheel joint. The ellips at rod's CM is far to complex for me to compute. Anyone better?