Work done by torque: wheel turning about a curb

[Taulant Sholla]

Homework Statement

Homework Equations

work-kinetic energy theorem

The Attempt at a Solution

 

[TSny]

You've assumed that it is possible for W_net to equal zero when F is constant. Try to see why this can't be true.

Can you figure out how much force is required to get the wheel to start to rise?

 

[haruspex]

Further to TSny's hints...
You write that you have to solve it by the Work-KE theorem. I suspect you have misunderstood the requirement. As TSny writes, you have no guarantee that $\Delta KE=0$.
You can solve statics problems using virtual work. Maybe that is what you are supposed to be using? But that method considers infinitesimal changes in position, not integrating over a substantial change.

 

[Taulant Sholla]

You've assumed that it is possible for W_net to equal zero when F is constant. Try to see why this can't be true.

Can you figure out how much force is required to get the wheel to start to rise?

Ah, yes. Thank you. It would take a variable force to result in a final kinetic energy of 0. I know torque equilibrium yields the constant force required to offset the torque produced by gravity. Thank you again.

 

[Taulant Sholla]

Further to TSny's hints...
You write that you have to solve it by the Work-KE theorem. I suspect you have misunderstood the requirement. As TSny writes, you have no guarantee that $\Delta KE=0$.
You can solve statics problems using virtual work. Maybe that is what you are supposed to be using? But that method considers infinitesimal changes in position, not integrating over a substantial change.

Right. Thank you. I need to find the rotational kinetic energy of the wheel once it rises to the top of the curb.

 

[Hamal_Arietis]

You assumed that $ds=Rd\theta$ but $ds>0$ and $d\theta <0$. So it is wrong
If you assumed that $ds=-Rd\theta$ I think you will get answer

 

[Monsterboy]

Isn't that angle = 30^o ?

 

[haruspex]

You assumed that $ds=Rd\theta$ but $ds>0$ and $d\theta <0$. So it is wrong
If you assumed that $ds=-Rd\theta$ I think you will get answer

Taulant's error was to calculate a funny kind of average force (averaged over horizontal distance, which is not what is meant by "average force") necessary to provide the PE gain. Instead, the force to be found is the minimum constant force that will get it over the step. The next stage is to find the residual KE that results. That could be done by integration, but it is not necessary.

Isn't that angle = 30^o ?

Taulant set θ as the angle to the vertical, the 60^o. That reduces as the wheel rises.