Is the Acceleration of the Sphere with Respect to the Plank Correct?

[coldblood]

Hi friends,
Please help me in solving this problem, I'll appreciate the help.

The problem is as:

https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q71/s720x720/1503374_1461728057387633_909744247_n.jpg

Attempt -

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1506899_1461728417387597_658199054_n.jpg



Thank you all in advance.

 

[haruspex]

a = Rα is for rolling contact.

 

[coldblood]

a = Rα is for rolling contact.

Yes But centre of mass of the sphere woild be going with Translational acceleration,
Whose value would come from the bottom point in contact using, a = rα
Isn't it?

 

[haruspex]

Yes But centre of mass of the sphere woild be going with Translational acceleration,
Whose value would come from the bottom point in contact using, a = rα
Isn't it?

No, as I said, that's only for rolling contact. When the spinning cylinder is placed on the plank it will skid at first. Suppose frictional force is F. What linear acceleration will that produce? What torque? What angular acceleration?

 

[coldblood]

No, as I said, that's only for rolling contact. When the spinning cylinder is placed on the plank it will skid at first. Suppose frictional force is F. What linear acceleration will that produce? What torque? What angular acceleration?

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-ash4/1506955_1462163254010780_1540770628_n.jpg

 

[haruspex]

That's all correct, but what you are asked for is a. Your remaining step is to figure out what f is in terms of m, g and mu.

 

[coldblood]

That's all correct, but what you are asked for is a. Your remaining step is to figure out what f is in terms of m, g and mu.

Well, here a is f/m and f will be, μmg/m = µg(i)
and acceleration of plank would be µg(-i)

so acceleration of sphere w.r.t. plank would be 2µg.

Is that correct?

 

[haruspex]

Well, here a is f/m and f will be, μmg/m = µg(i)
and acceleration of plank would be µg(-i)

so acceleration of sphere w.r.t. plank would be 2µg.

Is that correct?

That's it. You didn't need to worry about the rotations at all!