Torque requirements to roll vertically?

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Discussion Overview

The discussion revolves around calculating the torque required for a wheel to roll up a wire at a constant speed. Participants explore the relationship between torque, energy, and the forces involved, including friction and gravity. The conversation includes theoretical considerations and assumptions related to energy conservation and the non-slip condition during the rolling motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Ian seeks assistance in modeling the torque required to roll a wheel up a wire, noting the importance of coefficients of friction, normal forces, and weight.
  • One participant suggests using an energy approach, asserting that the wheel gains potential energy as it rises, requiring an input of energy equal to mgv, where v is the velocity of the wheel's center.
  • This participant explains that while torque is not power, a constant torque must be applied to maintain the necessary power output for climbing.
  • Another participant questions the initial assumptions about energy, suggesting that the equation should reflect the relationship between kinetic energy, torque input, and potential energy, and asks about the relevance of peak height in this context.
  • A different participant disagrees with the previous phrasing of the energy equation, emphasizing that in a steady state, the energy provided by torque equals the potential energy gained, and that kinetic energy can be disregarded in this scenario.
  • This participant clarifies that the power required to raise the wheel is dependent on the mass being raised and the speed of ascent, reiterating that the power delivered by torque must equal mgv to maintain constant velocity.

Areas of Agreement / Disagreement

Participants express differing views on the formulation of the energy equations and the relevance of kinetic energy and peak height in the context of the problem. There is no consensus on these points, and the discussion remains unresolved regarding the best approach to model the torque requirements.

Contextual Notes

Assumptions about energy conservation, the non-slip condition, and the steady state of the wheel's motion are discussed but not fully resolved. The relationship between torque, power, and energy is a central theme, with varying interpretations presented by participants.

imathieson
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Hi,

I'm trying to model a problem about rolling up a wire. I don't know how to go about setting it up to calculate the Torque required to climb at a given speed. Obviously coefficients of friction, normal forces, and weight will all play a roll but am hoping I can get a hand setting up the problem.

Any help would be greatly appreciated.

Thanks

Ian
 
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I would start with an energy approach. Let’s assume that the wheel is rolling up the wire without slipping at constant speed. That means constant linear and angular velocity. So no kinetic energy is being added or removed. No slipping means no loss of energy to friction or heat. (that’s an idealization of course) However, as the wheel rises against the force of gravity, it gains potential energy. At a constant speed, the wheel requires an input of potential energy every second equal to mgv where v is the velocity of the center of the wheel. The units are of power (Newton-meters per second). The torque you apply must provide this power. But torque is not power. Its Newton-meters. However, if constantly applied, torque is units of power. (Applying a torque of 10 Newton-meters for a full second is exactly what you get from an engine that delivers 10 Newton-meters per second power.) So you need a constant torque of magnitude mgv.

But you’re not finished. You need to assure the non-slip condition that was previously assumed. To get a non-slip condition, you need to generate friction between the wheel and wire. That is, you need to press the wheel to the wire. Given a wheel radius, torque and static coefficient of friction, are you comfortable calculating the normal force?
 
Last edited:
Hi everyone, I'm just a new member and have been trying to post a question in the forum but couldn't find no link to do this. Can anyone tell me how to do this please... Any direct link or instructions to the post page will be ok...

Thanks
 
Hi Mike,

Thanks for your reply. I'm comfortable getting the normal force give that data, however I have a question on the initial assumptions. With the kinetic energy being constant, it is the potential energy that is increasing correct. Therefore the equation essentially becomes kinetic energy+torque input=potential energy correct? If this is correct that is it correct to take the potential energy value at it's peak height?

Thanks for the reply!
 
No, I don't think you phrased that last equation right.

Kinetic Energy + Energy provided by Torque = Kinetic Energy + Potential Energy.

Or, Energy provided by Torque = Potential Energy

The potential energy comes from the constantly applied torque.
You can really leave Kinetic Energy out of the equation.

As for peak height, it does not come into play either. You are thinking of potential energy as mgh, right? But I described a steady state problem. When, or if, the wheel stop does not matter. What matters is power while the wheel is moving. ***Energy per unit time*** And the amount of that power depends upon the amount of mass you are raising and how fast you are raising it. Its mgv where v is the velocity of the center of the wheel.
 
Last edited:
us001007 said:
Hi everyone, I'm just a new member and have been trying to post a question in the forum but couldn't find no link to do this. Can anyone tell me how to do this please... Any direct link or instructions to the post page will be ok...

Thanks

Welcome us001007. I suppose the options for posting a question is different for different browsers. But on my machine there is a button at the top of the list of topics for Mechanical Engineering forum that says "New Topic". That's what I use to post a question.
 
To imathieson,

As I reviewed my posting, I’m thinking it is not clear. I started out talking about energy but moved to talking about power. The determining equation really is,

Power delivered by the Torque = Power required to raise the wheel

Potential Energy, as you know, is mgh (units Newton-meters)
Power is Energy per unit time, in this case, mgv (units Newton-meters/second)

where m is the mass of the wheel,
g is gravity
and v is the velocity of the center of the wheel.

The power delivered by any torque (in units of Newton-meters) is the magnitude of the torque as long as that torque is being applied continuously (Newton-meters/second). That’s what you have to do to maintain a constant velocity for the wheel. You have to apply a torque of mgv continuously.

Does that make more sense? Or is it more confusing?
 

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