IIT JEE , AIEEE Forum - Physics , Mechanics

vteja_06

A horizontal plank having mass m lies on a smooth horizontal surface.A sphere of same mass and radius r is spinned to an angular frequency W(clock wise) and gently placed on the plank.If coefficient of friction between the plank and the sphere is u .Find the distance moved by the plank till the sphere starts pure rolling on the plank.The plank is long enough.

karthik2007

2R²w²/49ug?

waterdemon

I have given you the free body diagrams of the sphere and

the plank in the figure below:

Let "a1" be the acceleration of the plank And

Let "v1" be the --Velocity--of the plank.

Then we have:

F = ma1 = -umg

a1 = -ug

And

v1 = (-ug)T

v1 = -ugT

For the sphere,

acm = ug

and

vcm = ugT

The torque acting on the sphere about the centre of mass

is given by:

= umgr

I

= -umgr

I

Here,

I = (2/5)mr2

Therefore we will get:

= -5ug

2r

Now,

wt = (wo - 5ugt)

2r

For rolling,

V1 = Vcm - wt*r

V1 = Vcm - (wo - 5ugt)r

2r

After solving the above expression we will get:

t = 2wor

9ug

Now the distance travelled by the plank is given by:

s1 = (1/2)(-ug)(2wor/9ug)2

s1 = -2wo2r2/81ug

Hope you find it useful.

Cheers !!!!!! @@@ !!!!!!!

varun.tinkle

hey waterdemon and karthik could u solve sum no 57-64 of anshish 292

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