2007-12-05 - More examples
Today's nonsense
- Homework due Friday. pg 146 #91-95,97-99,101,110
- Classwide church-based support-the-needy gift plans
ex 4) In a skid test, a recent-model BMW 530i was able to travel in a circle of radius 45.7 m in 15.2 sec without skidding. (a) What was its average speed? (b) Assuming v to be constant, what was the centripetal acceleration? (c) Again assuming v to be constant, what is the minimum value for the coefficient of static friction?
a = v^(2) / r
v = 2 * pi * r / T
2 * pi * r = distance
(a) v = 18.891 m/sec.
(b) a_(c) = v^(2) / r = 7.809 m/sec^2
(c) Do a freebody diagram.
Static friction is the centripetal force here (f_(n)), and it moves inward here. Imagine that your car is out of control on a curve-turn, and so the friction is pointing inwards towards the circle, while you're still moving outwards from the circle.
Sum of F_(y) = F_(n) - mg = 0
Sum of F_(radial direction) = -f_(s) = ma_(radial)
Coefficient of static friction
mu_(s) * mg = mv^(2) / r
mu_(s) = 0.796
ex 5) A curve of radius 30 m is banked at an angle theta. Find theta for which a car can round the curve at 40 km/h even if the road is frictionless.