Solve Rotational Problem Homework: Force to Hold Wheel Still at 60 cm Radius

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In summary, if someone exerts a force of 50 N on a wheel that is 60 cm in radius and 1.5 cm in axle diameter, they will need to exert a force of 6.1 N to keep the wheel from moving.
  • #1
thepanda
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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 :)
 
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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
Can anyone else please help? I really need an answer, I REALLY like this friend ;)
 

What is rotational problem homework and how is it solved?

Rotational problem homework is a type of physics problem that involves calculating the forces and torques acting on a rotating object. It can be solved by using the principles of rotational motion, including torque, angular acceleration, and moment of inertia.

What is the force needed to hold a wheel still at a given radius?

The force needed to hold a wheel still at a given radius can be calculated using the equation F = ma = mrω^2, where F is the required force, m is the mass of the wheel, a is the angular acceleration, r is the radius, and ω is the angular velocity.

How do you determine the radius of a wheel for a given force?

The radius of a wheel for a given force can be determined by rearranging the equation F = mrω^2 to solve for r. This will give you the radius needed to produce the desired force, given the mass and angular velocity of the wheel.

What factors affect the force needed to hold a wheel still?

The force needed to hold a wheel still is affected by several factors, including the mass of the wheel, the radius of the wheel, and the angular velocity of the wheel. Additionally, external forces such as friction can also impact the required force.

How can this problem be applied in real-world scenarios?

This type of problem can be applied in real-world scenarios, such as designing and testing rotating machinery, calculating the forces needed to keep a car or bike wheel from slipping, or determining the stability of a rotating object in space.

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