A small solid marble of mass m and radius r will roll without slipping along the

Question

A small solid marble of mass m and radius r will roll without slipping along the loop-the-loop track shown in Fig. 12-35 if it is released from rest somewhere on the straight section of track. For the following answers use m for the mass, r for the radius of the marble, R for the radius of the loop-the-loop and g for the acceleration due to gravity. Figure 12-35 (a) From what minimum heighth above the bottom of the track must the marble be released to ensure that it does not leave the track at the top of the loop? (The radius of the loop-the-loop is R. Assume R r.) h= (b) If the marble is released from height 6R above the bottom of the track, what is the horizontal component of the force acting on it at point Q? Ex=

Explanation / Answer

(a) let the height is h

Let velocity at top of loop is v

m*v*v/r=mg

v=sqrt(rg)

Conserving energy

0.5*m*v*v+0.5I*w*w+2mgR=mgh

h=2R+0.7R=2.7R

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