Question

An automobile (and its occupants) of total mass M = 2000 kg, is moving through a
curved dip in the road of radius R = 20 m at a constant speed v = 20 m/s. For this analysis, you can
neglect air resistance. Consider the automobile (and its occupants) as the system of interest. Use g =
10 m/s2.


Calculate the normal force exerted by the road on the system (car and its occupants).
A) 60,000 N
B) 20,000 N
C) 40,000 N
D) 50,000 N
E) 30,000 N

Answer 1

Answer:

Normal force, N = 60000 N                      

Explanation:

It is given that,

Mass of the automobile, m = 2000 kg

Radius of the curved road, r = 20 m

Speed of the automobile, v = 20 m/s

Let N is the normal and F is the net force acting on the automobile or the centripetal force. It is given by :

$N-mg=\dfrac{mv^2}{r}$

$N=\dfrac{mv^2}{r}+mg$    

$N=m(\dfrac{v^2}{r}+g)$                

$N=2000\times (\dfrac{(20)^2}{20}+10)$                            

N = 60000 N  

So, the normal force exerted by the road on the system is 60000 Newton. Hence, this is the required solution.