Using a prony brake to determine motor torque

[dotmatrix]

Homework Statement

Hey guys, not much of a physicist. But, I am fairly certain I am right.
We are using a "prony brake" at school to calculate torque in a motor. To me the amount of force supplied should equal the amount of force the motor can turn ie: when the motor stops the force applied on the "prony brake" is 33 oz.
Now my instructor has given us an equation that says that the radius of the shaft of the motor has something to do with the calculation of the force applied.
My problem is a) we did not apply the force to the shaft but instead a coupler which was roughly 4" in diameter (as opposed to a one inch shaft)
b) the force applied was by a belt which squeezed half of the circumference of the shaft
c) it varied with friction (we poured water on the belt to keep it cool and it reduced the amount of "force"}

So I know enough to say that the equation isn't quite right. And I would like to say that the force that I am exerting on the motor is equivalent to the torque (as it is a frictional force that opposes the rotation) but I don't actually know anything for sure. I think that it shouldn't have anything to do with mass times the radius of the shaft or whatever.

Homework Equations

The Attempt at a Solution

 

[NascentOxygen]

Hi dotmatrix. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Torque = force x radial distance (r being measured perpendicular to the line of action of F)

Your instructor is correct. (Edit: thread title changed from "Help prove prof wrong!")

If the coupler expanded the shaft radius to a large enough dimension, you would be able to stall the motor by lightly pressing on the shaft with just one finger (and non-destructively, at that!).

F alone is not an adequate measure of a motor's "strength".

 

[dotmatrix]

Torque= force x radial distance
The radial distance of the shaft is 1'' the force applied at the coupler is at a radial distance of 4'' (this is where we are applying it)
Furthermore the belt that is applying the force is not perpendicular to the coupler it in fact encompasses the lower 180 degrees of the rotating coupler.

 

[dotmatrix]

And P in=P out so the motors "strength" to run something plus the "strength" to run itself for all intensive purposes is fairly accurate representation.

 

[NascentOxygen]

At any point of contact, belt friction is perpendicular to the radial distance. It is the torque produced by this frictional force which opposes the shaft's rotation.

 

[OmCheeto]

Hey guys, not much of a physicist. But, I am fairly certain I am right.
We are using a "prony brake" at school to calculate torque in a motor. To me the amount of force supplied should equal the amount of force the motor can turn ie: when the motor stops the force applied on the "prony brake" is 33 oz.
Now my instructor has given us an equation that says that the radius of the shaft of the motor has something to do with the calculation of the force applied.
My problem is a) we did not apply the force to the shaft but instead a coupler which was roughly 4" in diameter (as opposed to a one inch shaft)
b) the force applied was by a belt which squeezed half of the circumference of the shaft
c) it varied with friction (we poured water on the belt to keep it cool and it reduced the amount of "force"}

So I know enough to say that the equation isn't quite right. And I would like to say that the force that I am exerting on the motor is equivalent to the torque (as it is a frictional force that opposes the rotation) but I don't actually know anything for sure. I think that it shouldn't have anything to do with mass times the radius of the shaft or whatever.

When you said; "So I know enough to say that the equation isn't quite right.", to which equation were you referring to?

According to wiki, the de Prony brake measures the force on a tension belt, from which you can derive both torque and power, knowing other variables.

 

[dotmatrix]

Well that's what I thought?!?
Force x Radial distance
But the force is exerted on a coupling which is much larger than the shaft (4" vs 1") The shaft of the motor is what they're using for the "calculation"
So therefore the force exerted is across a belt which rests upon 180 degrees of the lower circumference of the coupling.
Would this not be a measurement of frictional force in direct opposition to torque?
*Note electrician, not physicist

 

[OmCheeto]

Well that's what I thought?!?
Force x Radial distance
But the force is exerted on a coupling which is much larger than the shaft (4" vs 1") The shaft of the motor is what they're using for the "calculation"
So therefore the force exerted is across a belt which rests upon 180 degrees of the lower circumference of the coupling.
Would this not be a measurement of frictional force in direct opposition to torque?
*Note electrician, not physicist

I'm fairly certain that if you had done the measurement with the belt around the 1" shaft, the force would have been much higher than the 33oz you measured from the 4" coupling.

I will leave that to you as a homework assignment, to determine what the force would be on the 1" shaft.

It's nearly midnight, and I'm off to bed. I'll check your answer in the morning. Please show all your work.

 

[NascentOxygen]

Duplicate threads are not allowed on PF! https://www.physicsforums.com/threads/what-exactly-does-a-prony-brake-measure.775498/

Could a mod join these two identical threads.

Duplicate thread alert. https://www.physicsforums.com/threa...o-determine-motor-torque.775482/#post-4878313

[NOTE: Please note that I have merged your two informational posts re: duplicate threads - gneill]

 

[CWatters]

Torque= force x radial distance
The radial distance of the shaft is 1'' the force applied at the coupler is at a radial distance of 4'' (this is where we are applying it)
Furthermore the belt that is applying the force is not perpendicular to the coupler it in fact encompasses the lower 180 degrees of the rotating coupler.

Any chance of a diagram or photo? Is it similar to...

http://en.wikipedia.org/wiki/De_Prony_brake

In its simplest form an engine is connected to a rotating drum by means of an output shaft. A friction band is wrapped around half the drum's circumference and each end attached to a separate spring balance. A substantial pre-load is then applied to the ends of the band, so that each spring balance has an initial and identical reading. When the engine is running, the frictional force between the drum and the band will increase the force reading on one balance and decrease it on the other. The difference between the two readings multiplied by the radius of the driven drum is equal to the torque. If the engine speed is measured with a tachometer, the brake horsepower is easily calculated.

 

[dotmatrix]

More or less, take the diagram, but instead of using weight, your actually tightening the device and measuring the output with a spring scale. Does that make sense?
Rotary power (in Newton-meters per second, N·m/s) = 2π × lever length (in meters, m) × rotational speed (in revolutions per second) × measured force (in Newtons, N)
Rotary Power being equal to torque

 

[dotmatrix]

i just read that description, feeling a little slow at this hour

 

[gneill]

Duplicate threads are not allowed on PF! https://www.physicsforums.com/threads/what-exactly-does-a-prony-brake-measure.775498/

Could a mod join these two identical threads.

Duplicate thread alert. https://www.physicsforums.com/threa...o-determine-motor-torque.775482/#post-4878313

Done.