F=ma 2011 #24: Effects of Increasing Bearing Width & Radius

[licantroleon]

Homework Statement

A turntable is supported on a Teflon ring of inner radius R and outer radius R+δ (δ  R), as shown in the diagram.
To rotate the turntable at a constant rate, power must be supplied to overcome friction. The manufacturer of the
turntable wishes to reduce the power required without changing the rotation rate, the weight of the turntable, or
the coefficient of friction of the Teflon surface. Engineers propose two solutions: increasing the width of the bearing
(increasing δ), or increasing the radius (increasing R). What are the effects of these proposed changes?


(A) Increasing δ has no significant effect on the required power; increasing R increases the required power.
(B) Increasing δ has no significant effect on the required power; increasing R decreases the required power.
(C) Increasing δ increases the required power; increasing R has no significant effect on the required power.
(D) Increasing δ decreases the required power; increasing R has no significant effect on the required power.
(E) Neither change has a significant effect on the required power.

http://www.aapt.org/physicsteam/2012/upload/exam1-2011-1-3-answers_1.pdf (number 24)

Homework Equations

P=Fv=Tw

The Attempt at a Solution

I have no idea how to start this... Also I don't understand the situation. Is the turntable like a box on top of the ring? Or do they mean they have a vinyl disc on top of the ring? I have no idea what they're talking about.

 

[Simon Bridge]

What difference does it make if the turntable is a vinyl disk or some sort of box?
What matters is how the friction with the teflon ring depends on the dimensions of the ring.

Anyway - the diagram should give you a hint.

 

[licantroleon]

I have no idea where the friction force would be located... Would it be concentrated at the middle of the ring width?

 

[Simon Bridge]

You should have covered friction as part of the course that this exam is for.

Also see:
https://www.physicsforums.com/showthread.php?t=239406
https://www.physicsforums.com/showthread.php?t=561844
https://www.physicsforums.com/showthread.php?t=450861

 

[HalfLostAndSearching]

As a scientist, it is important to first understand the problem before attempting to solve it. In this case, the turntable is most likely referring to a circular disk that rotates on top of the Teflon ring. The power required to rotate the turntable at a constant rate is determined by the friction between the turntable and the Teflon ring.

Now, let's consider the proposed solutions. Increasing the width of the bearing (δ) means that the contact area between the turntable and the Teflon ring will increase. This will result in an increase in the friction force between the two surfaces, which in turn will require more power to overcome. Therefore, increasing δ will increase the required power.

On the other hand, increasing the radius (R) means that the distance between the center of rotation and the point of contact with the Teflon ring will increase. This will result in a decrease in the friction force between the two surfaces, as the force is inversely proportional to the distance between the surfaces. Therefore, increasing R will decrease the required power.

In summary, the correct answer is (B) increasing δ has no significant effect on the required power; increasing R decreases the required power.