Chapter 7, Problem 75GP

* Loop the loop You are given a loop raceway for your Hot Wheels cars (as shown in Figure P7.75). While playing with the cars, you and your friends notice that you need to release the car from at least a height H of 1.30 diameters of the loop above the ground for the car not to fall off the track at the top of the circular loop. Two of your friends have different explanations for the observed pattern:

Jordan: If there were no friction forces exerted on the car, the minimum height H would be equal to the loop diameter d because the mechanical energy of the car- Earth system is constant in the process.

Leila: The minimum height H is larger than the loop diameter d even if the friction forces are negligible. The car's speed at the top of the loop should be large enough that the force exerted by Earth on the car alone keeps the car moving in a circle determined by the loop.

Analyze the problem and decide which of your friends is correct.