Answer to Question #176554 in Physics for Grey

Question

the drawing shows a version of the loop the loop trick for small car. If car is given an initial speed of 4.0 m/s what is the largest value that the radius can have if the the car is to remain in contact with the circular track at all times

Answer 1

According to conservation of energy, the car must go upward and the difference between the centripetal acceleration and acceleration due to gravity must be greater than 0:

$$a_c-g>0,\\\space\\ a_c=\frac{v^2}{R},\\\space\\ \frac{v^2}{R}-g>0,\\\space\\ R<\frac{v^2}{g}.$$