Question

A child of mass 40 kg is in a roller coaster car that travels in a loop of radius 11 m. At point A the speed of the car is 12.8 m/s, and at point B, the speed is 13.1 m/s. Assume the child is not holding on and does not wear a seat belt. What minimum speed is required to keep the child in his seat at point A?

Answer 1

To keep the child in his seat at point A, the minimum speed required is when the net force acting on the child is equal to the centripetal force required to keep the child moving in a circular path.

Step-by-step explanation:

To keep the child in his seat at point A, the minimum speed required is when the net force acting on the child is equal to the centripetal force required to keep the child moving in a circular path.

The net force is the difference between the gravitational force and the normal force. At point A, the gravitational force is acting downwards and the normal force is acting upwards.

Since the child is not holding on and does not wear a seat belt, the normal force at point A is equal to zero. Therefore, the net force at point A is equal to the gravitational force.

Gravitational force = mass of the child x acceleration due to gravity

Centripetal force = mass of the child x (velocity squared / radius of the loop)