Inelastic Sphere Collision!

A uniform rigid sphere having radius RR moving with velocity vo{ v }_{ o } and angular velocity ωo=voR{ \omega }_{ o } =\cfrac { { v }_{ o } }{ R } strikes a horizontal rough surface having coefficient of friction μ\mu . If coefficient of restitution for collision is e=1/2e=1/2.
Let angular velocity and Velocity of centre of sphere after immediately after the collision is in 'x' and 'y' direction will be expressed as :

vx=ab×μvovy=cd×voω"=(αβ×μ)γR×vo \begin{aligned} { v }_{ x } &= \cfrac { a }{ b } \times \mu { v }_{ o }\\ { v }_{ y }&= \cfrac { c }{ d } \times { v }_{ o }\\ { { \omega } }^{ " }&= \cfrac { (\alpha -\beta \times \mu ) }{ \gamma R } \times { v }_{ o } \end{aligned}


Then find the value of :

a+b+c+d+α+β+γ.a + b + c + d + \alpha +\beta +\gamma.


Details and assumptions

\bullet gcd (a , b ) = 1

\bullet gcd (c,d ) = 1

\bullet gcd (α\alpha , β\beta ) = 1

\bullet gcd ( γ\gamma , β\beta ) = 1

\bullet All are positive integers.

\bullet Take clockwise direction as positive.

This is part of my set Deepanshu's Mechanics Blasts

Source : My Friend give me as challange , Unfortunately He is not on Brilliant .

×

Problem Loading...

Note Loading...

Set Loading...