Question

A spoked wheel of radius R=0.56m, that may be modelled as a thin annulus, undergoes a pure rolling motion to the right with a speed of vG=3m/s.

The spring has a stiffness of k=1,040N/m, and has an extension of δ=0.03m at the instant shown.

The spring is connected to the wheel axle by a slip ring that allows it to exert a force on the wheel without restricting its rotation.

The wheel has a mass of m=10kg. g=9.8m/s ².

Answer 1

a)What is the magnitude of the wheel’s angular acceleration ( α) at this instant?
b)What is the magnitude of the friction force ( fs) acting on the wheel from the ground at this instant?
c)What is the minimum possible coefficient of static friction ( μs) that can exist between the ground and wheel such that pure rolling occurs at this instant?

Answer 2

Here is the diagram:

Answer 3

your free body diagram should look like this, which might seem weird but the tension T and the friction F are both acting to the left.....



can you make some equations from here?

Answer 4

PS annulus or ring? think you would need a thickness to treat it as an annulus proper.

Answer 5

Still not entirely sure what equations I can make from the free body diagram? I am aware I have information that may be used in the kinetic energy equation, potential spring energy and obviously moment of inertia but don't understand how they all connect?

Answer 6

Also, as no thickness is given, I assume it may be a ring.

Answer 7

irishboy123 can you help me look at my question

Answer 8

yeah, a ring sounds good

i think you need for this to build a few equations....

you can use energy equations in roundabout way to construct those equations but i doubt that is what you intend.



you are familiar with Newton's second law?

we can say that \(ma = -T - F\)

do you see why?