Question

A railway engine of mass 60 tonnes, is moving in an arc of
radius 200 m with a velocity of 36 kmph. Find the force exerted
on the rails towards the centre of the circle.

Answer 1

as force exerted is centripetal force ,
1/2 × M × (V)²
mass is 60 tonnes itwill b 60 ×10² kg 
velocuity will b 36 kmph 
 
1/2 ×60×10² ×36 = ?

Answer 2

The force exerted on the rails towards the center is 30000 N.

Given data:

Mass of the engine, m = 60 tonnes = 60000 kg

Radius of the arc, r = 200 m  

Velocity of the train, v = 36 km/hr

To find:

Force exerted towards the center = ?

Solution:

First, km/hr is to be converted into m/s

$\Rightarrow 36 \times \frac{5}{18}=10 \ \mathrm{m} / \mathrm{s}$

Thereby,  

Force exerted on the rails towards the center is given by the formula given below,

$F=\frac{m v^{2}}{r}$

$F=\frac{60000 \times 10 \times 10}{200}$

$F=30000 \ N$