## HOLIDAYS AND PHYSICS @ Mt. ABU ##

##Second semester exams just over and it was the time for a nice outing.So me and my friends decided to go to Udaipur(Rajasthan,INDIA).After spending a couple of days there, we left for Mount. Abu(approx. 6000 feet above mean sea level).On reaching there,we experienced a perfect weather at Mt. abu(specially when you come from 40degree C  temp.).It was all in all a mix blend of culture.heritage and nature for us.We didnt noticed how two days passed by. So on third day we decided to return to udaipur.On our journey back to udaipur we have to travel down 22kms of steep slopes of Mt abu.And since we were travelling in  a government bus ,the driver was driving very rashly although he seemed pretty experienced.He turned blindly on the brisk turns of Mt.I still remember we suddenly encountered a bus infront of us after a sharp turn.That journey was a real close shave for all three of us.

After reaching safely to udaipur i thought,that the boundries along that roadside was hardly half a  feet long which is sufficient to encourage toppling of any bus at greater speeds.So to prevent such accidental and fatal topplings on turns(~10m radii) i underwent some calculations.The result I  calculated was for minimum/threshold height of such boundaries.

OBJECTIVE--To calculate minimum height of boundaries of roads on hilly terrains.
Various dimensions are as follows-
1.Mass of bus ~ 10000kgs(average passenger bus of 84 capacity)
2.Speed of bus ~ 60kmph(16.6mps)
3.Track length of bus(distance between two rear wheels) ~ 2.6m
4.Average coefficient of  kinetic friction between road and tyre ~ 0.8
5.Radii of curvature/turn ~ 10m
6.Height of bus ~ 10 feet

Calculations-

Just balancing torques which are applied on bus when get accidently in contact with boundaries.
CENTRIFUGAL FORCE APPLIED ON BUS(F) = mv^2/r
                                                                              = 10000*16.6*16.6/10
                                                                              = 275560 Newtons
FRICTIONAL FORCE ON ONE TYRE(REAR) = coefficient of friction*mass of bus*acceleration due to gravity
                                                                             = 0.8*10000*9.81
                                                                            = 78480 Newtons
WEIGHT OF BUS                                              = mass of bus*acc due to gravity
                                                                            = 10000*9.81
                                                                           = 98100 Newton
Torque equations----
===> (1.5-H)*F-f*H-W*D/2=0
So after putting above values we will obtain a quadratic equation as follows
===>  78480 H^2 - 413340 H^1 + 127530 = 0
SO, the final value of H after solving above equation is
===> H= 0.33 metres/ 1.08 feets

SO THE ABOVE CALCULATED IS THE THRESHOLD HEIGHT THAT I THINK IS REQUIRED FOR PREVENTING ANY SORTS OF ACCIDENTS ESPECIALLY AT HILLY TERRAINS.
                            ## NEXT POST WILL BE UP SOON.......##