Problem 1. You are driving a car down a highway when you approach a circular cur

Question

Problem 1. You are driving a car down a highway when you approach a circular curve in the road. For a fun exercise you try to calculate what your maximum velocity can be so that you do not run off the road. You estimate your car to weigh 1500 Kg and you think the road's coefficient of static friction is u=0.75. At a glance you think the radius of this curve to be 15m.

Problem 2. You are still on your trip down the highway and you come across another curve, however, this one is banked so you try to see what your max speed can be for this one as well. The radius of the curve is now 10m and the bank is sitting at a 20 angle. Take the mass and u to be the same as in the last problem.

Explanation / Answer

1.) for maximum speed v => mv2/r = friction force

friction force = uN = 0.75Xmg

so , mv2/r = 0.75Xmg

v2 = 110.25

=> v = 10.5 m/s <------ maximum velocity

2.)here , N = mgcos(20)

so frictional force ,f = 0.75mgcos(20) N

equation for maximum speed , mv2/r =  f + mgsin(20)

mv2/r =  0.75mgcos(20) + mgsin(20)

v2  = 102.51

=> v = 10.12 m/s

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