Answer:
a) The ideal speed = 16.21 m/s
b) Minimum co-efficient of friction = 0.216
Explanation:
From the given information:
The ideal speed can be determined by considering the centrifugal force component and the gravity component.
[tex]\dfrac{mv^2}{r}cos \theta = mg sin \theta[/tex]
[tex]v = \sqrt {gr \ tan \theta}[/tex]
[tex]= \sqrt{(9.8 \ m/s^2) (100) \ tan 15^0}[/tex]
= 16.21 m/s
(b)
Let assume that it requires 25 km/h to take the same curve.
Then, using the equilibrium conditions;
[tex]mg \ sin \theta = \dfrac{mv^2}{r} cos \theta + \mu ((\dfrac{mv^2}{r}) sin \theta + mg cos \theta)[/tex]
[tex]\mu = \dfrac{mg sin \theta - \dfrac{mv^2}{r} cos \theta }{((\dfrac{mv^2}{r}) sin \theta + mg cos \theta) }[/tex]
[tex]\mu = \dfrac{g sin \theta - \dfrac{ v^2}{r} cos \theta }{((\dfrac{v^2}{r}) sin \theta + g cos \theta) }[/tex]
[tex]\mu = \dfrac{(9.8 \ m/s^2 ) sin (15^0) - \dfrac{ \dfrac{(25 \times 10^3}{3600} \ m/s)^2 }{100 \ m } cos (15^0) }{((\dfrac{(\dfrac{25 \times 10^3}{3600} )^2}{100}) sin 15^0 + (9.8 \ m/s^2) cos 15^0 ) }[/tex]
[tex]\mathbf{\mu = 0.216}[/tex]