Force needed to hold a wheel with axle still against cord tension

[thepanda]

Homework Statement

My friend wanted me to explain this problem, it seems pretty simple but I can't get the back of the book answer.

a wheel 60 cm in radius is connected to an axle that is 1.5 cm in radius. Someone pulls with a force of 50 N on a thin cord wrapped around the axle. How much force do you have to exert on the wheel's rim to hold it still?

The Attempt at a Solution

First I tried a simple torque balancing but that doesn't work: 60cm * x N = 1.5 cm * 50 N -> x = 1.25 N.

Then I thought, maybe the wheel has friction with the ground, because torque AND force must be balanced in static equilibrium, so:

x (the force) * 60 cm - (50N - x) (frictional force that prevents slipping) * 60 cm = 50 N * 1.5 cm. But that makes an answer near 25ish N, obviously because these torques are large compared to the one around the axle.

So the correct answer is supposed to be 6.1 N but I can't get it, can anyone explain it to me? I really like this friend and I would appreciate it :)

 

[christensen]

My interpretation of the question is the exact same as your first attempt, and likewise i get the same answer. Is anything else given to you in the problem? Width of the cord, angle a force is applied and diagrams you can provide?

 

[thepanda]

No, just this text ;) I think the first one is wrong because the forces are not balanced, so it should move forward unless there was something pushing back... but yeah this problem seems pretty odd.

 

[christensen]

Well, assuming it is rotating on an axle, i would assume the normal for between the axel and the wheel would counter any transverse motion... making your solution of 1.25N correct again. I don’t know what to tell you other than maybe we're interpreting the question wrong or there is a mistake in the back of the book.

 

[thepanda]

Can anyone else please help? I really need an answer, I REALLY like this friend ;)