The drawing shows a version of the loop-the-loop trick for a small car. If the car is given an initial speed of 4.5 m/s, what is the largest value that the radius r can have if the car is to remain in contact with the circular track at all times?
1 answer
The largest value that the radius r can have is determined by the centripetal force, which is equal to the mass of the car multiplied by its velocity squared, divided by the radius. Therefore, the largest value for the radius r is equal to the mass of the car multiplied by its velocity squared, divided by the centripetal force. In this case, the mass of the car is 1 kg, the velocity is 4.5 m/s, and the centripetal force is 9.8 N. Therefore, the largest value for the radius r is 1 kg x (4.5 m/s)^2 / 9.8 N, which is equal to 0.23 m.