A tannis hall is a hallow sphare with a thin wall. It is sat raling without slip

Question

A tannis hall is a hallow sphare with a thin wall. It is sat raling without slipping at 4.11 m/s on a horizantal section of a track as shown in tha figura hclaw. It rols around tha insida of a vartical drcular lacp af radius the shape of th track deviates trom a perfect circle so that the ball leaves the track at a point -16.0 cm below the horizontal section. 47.2 cm. As the ball naars the battom of tha laop Find the ball's speed in ms) at the top of the loop m/s b) Find its spead (in m) as it leaves tha track at tha hottam. mis

Explanation / Answer

KE_ball = translational KE + rotational KE

= m v^2 /2 + I w^2 /2  

{ I w^2 /2 = (2 m r^2 / 3)(v/r)^2 / 2 = m v^2 /3 }

  
= 5 m v^2 / 6

(A) Applying energy conservation,

PEi + KEi = PEf + KEf

0 + (5 m v0^2 / 6) = m g (2 r) + (5 m v ^2 / 6)

(5 x 4.11^2 / 6) = (9.8 x 2 x 0.472) + (5 v^2 / 6)

v = 2.41 m/s

(B) 0 + (5 m v0^2 / 6) = m g (-h) + (5 m v ^2 / 6)

(5 x 4.11^2 / 6) = (9.8 x - 0.16) + (5 v^2 / 6)

v = 4.33 m/s

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