You are driving your car uphill along a straight road. Suddenly, you see a car r

Question

You are driving your car uphill along a straight road. Suddenly, you see a car run a red light and enterthe intersection just ahead of you. You slam on your brakes and skid in a straight line to a stop,leaving skid marks 100 feet long. A policeman observes the whole incident and gives a ticket to theother car for running a red light. He also gives you a ticket for exceeding the speed limit of 30 mph.When you get home, you read your physics book and estimate that the coefficient of kinetic frictionbetween your tires and the road was 0.60, and the coefficient of static friction was 0.80. Youestimate that the hill made an angle of about 10o with the horizontal. You look in your owner'smanual and find that your car weighs 2,050 lbs. Will you fight the traffic ticket in court?Known:Unknown:Strategy:

Explanation / Answer

We are provided with the following data

Mass, m=2050 lb,

Skidding or stopping distance, x=100ft

Angle theta 10 degree

And coffeccient of kinetic friction   k=0.6

Now let us calculate the work done by frictional force which is given by
W = Fd = Nd = (m*g*cos(theta))x

Where N is the normal reaction

g is the acceleration due to gravity = 32.174 ft/s2

now using conservation of energy, we have:

work done = change in KE – change in PE

=>0.5mv2= mg(xsin(theta))+*m*g*xcos(theta)

=>v = sqrt (2*g*x(sin(theta) +cos(theta)))

= 912383708 feet /sec

= 48mph

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