A solid sphere of radius 39 cmis positioned at the top of an incline that makes

Question

A solid sphere of radius 39 cmis positioned
at the top of an incline that makes 24 ! angle
with the horizontal. This initial position of
the sphere is a vertical distance 2.8 m above
its position when at the bottom of the incline.
The sphere is released and moves down the
incline.
Calculate the speed of the sphere when it
reaches the bottom of the incline if it rolls
without slipping. The acceleration of gravity
is 9.8 m/s2 . The moment of inertia of a sphere
with respect to an axis through its center is
2/5 MR2

Calculate the speed of the sphere if it reaches
the bottom of the incline by slipping frictionlessly
without rolling.

A solid sphere of radius 39 cmis positioned at the top of an incline that makes 24 ! angle with the horizontal. This initial position of the sphere is a vertical distance 2.8 m above its position when at the bottom of the incline. The sphere is released and moves down the incline. Calculate the speed of the sphere when it reaches the bottom of the incline if it rolls without slipping. The acceleration of gravity is 9.8 m/s2 . The moment of inertia of a sphere with respect to an axis through its center is 2/5 MR2 Calculate the speed of the sphere if it reaches the bottom of the incline by slipping frictionlessly without rolling.

Explanation / Answer

mg(h+Rcos) =Iw2/2 + mv2/2

mg(h+Rcos) = 2mR2*v2/5*2*R2 +mv2/2

7v2/10 =g(h+Rcos24)

v =10*9.8(2.8+0.39*0.913)/7 =6.64 m.s

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