A racetrack has the shape of an inverted cone, as the drawing shows. On this surface the cars race in circles that are parallel to the ground. For a speed of 34.0 m/s, at what value of the distance d should a driver locate his car if he wishes to stay on a circular path without depending on friction?

The value of d is 183.51 m.

Explanation:

Given that,

Speed of car = 34.0 m/s

Suppose The car race in the circle parallel to the ground surface is at an angle 40°

The radius of circular path

Normal force acting on the car = N

We need to calculate the value of d

Using component of normal force

The horizontal component of normal force is equal to the gravitational force.

....(I)

The vertical component of normal force is equal to the centripetal force

.....(II)

Divided equation (I) by equation (II)

Put the value of g

Put the value into the formula

Hence, The value of d is 183.51 m.