A track consists of two circular pars ABC and CDE of equal radius 100 m and joined smoothly as shown in figure.Each part subtends a right angle at its centre. A cycle weighing 100 kg together with rider travels at a constant speed of 18 km/h on the track. A. Find the normal contact force by the road on the cycle when it is at B and at D. b.Find the force of friction exerted by the track on the tyres when the cycle is at B,C and D. c. Find the normal force between the road and the cycle just before and just after the cycle crosses C. d. What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take `g=10 m/s^2`

Answer

A, B, C, D

Explanation

Radius of the curves =100 m `
Weight = 100 kg
velocity = 18 km/hr=5m/sec
a. At B, mg-(mv^2)/r=N`
`rarrN=(100xx10)-(100xx25/100)`
`=1000-25=975N`
At D,` N=mg+(mv^2)/R`
`=1000+25=1025N`
b.At B & D, the cycle has no tendency to slide.
So at B & D frictioN/Al is zero. At C `mg sintheta=f`
`rarr 1000xx(1/sqrt2)=707N`
`c.i Before C mg costheta-N=(mv^2)/r`
`rarr N=mgcostheta-(mv^2)/r`
=707-25=682N`
ii. `N-mgcostheta=(mv^2)/r`
`rarr N=(mv^2)/r+mgcostheta`
`=25+707=732N`
d. To find out the minimum desired coefficient of frictionwe have to consider a point just before c (where N is minimum).
NOw `muN=mg sintheta`
`rarr muxx682=707`
So, `mu=1.037`