Question

You are driving your car uphill along a straight road. Suddenly, see a car cross a red light and enter the intersection, just ahead of you. Immediately apply your brakes and skid in a straight line to stop, leaving a mark of 100 ft long by sliding. A policeman observes the whole incident, gives a ticket to the driver of the car for passing a red light. It also gives a ticket to you for exceeding the 30 mph speed limit. When you arrive at your house, you read your physics book and you may notice that the coefficient of kinetic friction between the tires and the road was 0.60, and the coefficient of static friction was 0.80. You estimate that the hill forms an angle of approximately 10 ° with the horizontal. You check the owner's manual and find that your car weighs 2,050 lbs. Are you going to claim the traffic ticket in court? Support your argument.

A) It shows a detailed diagram (design) of the situation, where it shows the conditions before and after. THIS IS VERY IMPORTANT!

B)It shows a correct procedure of conservation laws and the mathematical calculations that support their arguments.

C)It gives a final conclusion of its found results.

Answer 1

We are provided with the following data

Mass, m=2050 lb,

Skidding or stopping distance, x=100ft

Angle theta 10 degree

And coffecient of kinetic friction μk=0.6

Now let us calculate the work done by frictional force which is given by
W = Fd = μNd = μ(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))+μ*m*g*xcos(theta)

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

= 912383708 feet /sec

= 48mph