Question

A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is half the cart's mass, how fast is cart moving in m/s?

Answer 1

The speed of cart is 5.5 m/s.

Step-by-step explanation:

Given that,

Mass of cart = 100 kg

Distance = 3 m

Speed = 6 m/s

We need to calculate the speed of cart

Using relation of centripetal force and normal force

`N+mg=(mv^2)/(r)`

`(m)/(2)+mg=(mv^2)/(r)`

Put the value into the formula

`(1)/(2)+9.8=(v^2)/(3)`

`v=\sqrt{3((1)/(2)+9.8)}`

`v=5.5\ m/s`

Hence, The speed of cart is 5.5 m/s.