In the figure,a very small toy race car of mass m is released from rest on the loop-the-loop track.If it is released at a height 2R above the floor,how high is it above the floor when it leaves the track,neglecting friction?

Question

Quizplus · Accepted Answer

Applying conservation of energy between point A (starting point) and point B (when car leaves the track) we have:
mgh = (1/2)mv^2 + mgh'
where h' is the height of the car above the floor when it leaves the track and v is the speed of the car at the moment it leaves the track. Notice that at point B, the only force acting on the car is gravity, therefore we have:
mgh' = (1/2)mv^2
Using the conservation of energy above, we can eliminate v:
mgh = (1/2)m(2gh') + mgh'
2gh = 2gh' + h'
h' = 2gh/(2g) - h
h' = 1.67 R
Therefore, the answer is A) 1.67 R.

In the Figure,a Very Small Toy Race Car of Mass