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

Answer:

The speed of cart is 5.5 m/s.

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

$N+mg=\dfrac{mv^2}{r}$

$\dfrac{m}{2}+mg=\dfrac{mv^2}{r}$

Put the value into the formula

$\dfrac{1}{2}+9.8=\dfrac{v^2}{3}$

$v=\sqrt{3(\dfrac{1}{2}+9.8)}$

$v=5.5\ m/s$

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