Question

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?

Answer 1

Answer:

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 $r = d\cos\theta$

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.

$N\cos\theta=mg$....(I)

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

$N\sin\theta=\dfrac{mv^2}{r}$.....(II)

Divided equation (I) by equation (II)

$\tan\theta=\dfrac{v^2}{gr}$

Put the value of g

$\tan\theta=\dfrac{v^2}{g\times d\cos\theta}$

$v^2=\tan\theta\times g\times d\cos\theta$

$v^2=g\times d\sin\theta$

$d=\dfrac{v^2}{g\sin\theta}$

Put the value into the formula

$d=\dfrac{(34.0)^2}{9.8\times\sin40}$

$d=183.51\ m$

Hence, The value of d is 183.51 m.