Physics.. question. Help me

Question

A 200kg cart with passengers is travelling in a vertical circle on a Ferris wheel amusement ride. The cart is at a fixed distance of 12m from the axis of rotation and it is set to travel at 15m/s. If the maximum tension force for supporting the cart can be 5000N, can the cart safely travel around the entire circular path? Explain with calculations.

Answer 1

Mass of the cart, m = 200 kg

Distance of cart from axis of rotation ,R = 12 m

Speed of the cart, v = 15 m/s

Maximum tension , T max = 5000 N

Acceleration due to gravity ,g = 9.81 m/s^2

Calculate the tension force for supporting of the cart by using the formula:

T = (mv^2/R)-(mg)

    =((200)(15)^2/12)-((200)(9.81))

    =3750-1962

    = 1788  N < T max = 5000 N

Therfore, the cart safely travel around the entire circular path.