Question

A solid marble of mass m = 35 kg and radius r = 4 cm will roll without slipping along the loop-the-loop track shown in the figure if it is released from rest somewhere on the straight section of track. From what minimum height h 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 = 1.05 m.

Answer 1

Using the floor as the reference position for computing potential energy, mechanical energy conservation leads to release Substitutingmr and -Vcom/ we obtain where we have canceled out mass m in that last step To be on the verge of losing contact with the loop (at the top) means the normal force is vanishingly sma In this case, Newton's second law along the vertical direction +y downward) leads to result vcom-gR-r) into the previous expression stemming from energy consideration:s gives h 2.7*1.05 0.7 0.04 h 2.807 m