Question

A small toy is hanging from a string attached to the dome light of a car. The car is traveling with speed v on a level highway going around a turn with radius R. Find the angle that the string makes with the roof of the car.

Answer 1

let theta is the angle made by the string with the roof.

let m is the of the toy and T is the tension in the string.

As the toy is inequilirbium in y-direction,
Fnety = 0

T*sin(theta) - m*g = 0

T = m*g/sin(theta)

Net force acting towards the center of the turn, Fnetx = T*cos(theta)

m*a = T*cos(theta)

m*(v^2/R) = (m*g/sin(theta))*cos(theta)

v^2/R = g/tan(theta)

v^2 = R*g/tan(theta)

v = sqrt(R*g/tan(theta) ) <<<<<<<<<------------Answer