Can Static and Kinetic Friction Prevent a Car Crash?

[mb218]

Homework Statement

Assume that the driver begins to brake the car when the distance to the wall is d=107m, and take the car's mass as m-1400kg, its initial speed as vo= 35m/s and the static coefficient to be .50. Assume that the car's weight is distributed evenly on the four wheels, even during braking.
a.) what magnitude of static friction is needed between the tires and road to stop the car just as it reaches the wall?
b.) what is the max possible static friction?
c.) if the coefficient of kinetic friction betweeen the sliding tires and the road is .40, at what speed will the car hit the wall.
d.) to avoid the crash, a driver could elect to turn the car so that it just barely misses the wall. What magnitude of frictional force would be required to keep the car in a circular path of radius d and at the given speed vo?
e.) is the required force that the maximum static friction so that a circular path is possible?

Homework Equations

N=mg
F=ma
v2=v initial-2ad

The Attempt at a Solution

a.)f=ma
f= 1400 x 5.724
f= 8014 N

b.) Fs max= usFn
=.5 x 1400 x 9.8
=6860

c.) ma= -ukmg
a=-.4 x 9.8
=-3.92

v2= 35^2+2x-3.92x107
v=19.6 m/s

d.)
mv^2/R= uk x N
N= 40070 N

 

[PhanthomJay]

Homework Statement

Assume that the driver begins to brake the car when the distance to the wall is d=107m, and take the car's mass as m-1400kg, its initial speed as vo= 35m/s and the static coefficient to be .50. Assume that the car's weight is distributed evenly on the four wheels, even during braking.
a.) what magnitude of static friction is needed between the tires and road to stop the car just as it reaches the wall?
b.) what is the max possible static friction?
c.) if the coefficient of kinetic friction betweeen the sliding tires and the road is .40, at what speed will the car hit the wall.
d.) to avoid the crash, a driver could elect to turn the car so that it just barely misses the wall. What magnitude of frictional force would be required to keep the car in a circular path of radius d and at the given speed vo?
e.) is the required force that the maximum static friction so that a circular path is possible?

Homework Equations

N=mg
F=ma
v2=v initial-2ad

The Attempt at a Solution

a.)f=ma
f= 1400 x 5.724
f= 8014 N

b.) Fs max= usFn
=.5 x 1400 x 9.8
=6860

c.) ma= -ukmg
a=-.4 x 9.8
=-3.92

v2= 35^2+2x-3.92x107
v=19.6 m/s

Your answers to a, b, and c look OK

d.)
mv^2/R= uk x N
N= 40070 N

If the car is to stay in a circle, it is not sliding..use the static friction coeficient... Don't solve for N, N is known...you are looking for the the friction force required to keep it in the circle (mv^2/r)...Since F_f (max)= u_s(N), can you answer part e?