Question

A scooter weighing 150kg together with its Rider moving at $36\,km/hr$ is to take a turn of radius $30\,m$. What force on the scooter towards the center is needed to make the turn possible? Who or what provides this?

Answer 1

Hint: The force required to make a particle move in a circular path is the centripetal force.
Centripetal force is a force that always acts towards the center of a circular path. It is given by the equation
\[F = \dfrac{{m{v^2}}}{r}\]
Where $m$ is the mass $v$ is the velocity $r$ is the radius of the circular path.

Complete step by step answer:
Given the total weight of the scooter along with its Rider
$m = 150\,kg$
The speed of the scooter is
$v = 36\,km/hr$
We need to convert kilometers per hour into meters per second.
We know that $1\,km$ is $1000\,m$ and $1\,hr$ is $3600\,s$.
Therefore
$v = 36\, \times \dfrac{{1000}}{{3600}} = 10\,m/s$
The radius of the turn is given as
$r = 30\,m$
We need to find the force acting on the scooter towards the centre which makes the turn possible.
In a circular motion, there is a force called centripetal force. Centripetal force is a force acting towards the center of a circular path. It is given by the equation
\[F = \dfrac{{m{v^2}}}{r}\]
Where $m$ is the mass $v$ is the velocity $r$ is the radius of the circular path.
Centripetal force is what makes a particle continue to move in a circular path.
Let us calculate this force by substituting the given values.
\[F = \dfrac{{150 \times {{10}^2}}}{{30}} = 500\,N\]

Therefore, the force which is required to make the turn possible is the centripetal force and its value is \[500\, N\].

Note:
There is another force connected with circular motion which is the centrifugal force. Don't confuse between centripetal and centrifugal force. Centripetal force always acts towards the center. It is the force required to keep the particle moving in a circle. Whereas, centrifugal force is a force that acts away from the center.