Decelerating Car?

Question

On a level road with its brakes on, the shortest distance in which a car traveling with 81 km/hr can stop is 94 m. This shortest distance occurs when the driver uses anti-lock brakes which means that that the car brakes without skidding.

a) What is the magnitude of the acceleration of the car?

|a| = 2.69 m/s2


b) What is the coefficient of friction between the tires and the pavement?

µ =

c) How steep a hill can the car park on? (Give the angle to horizontal).

Angle =


I can't get parts b and c for this problem. Can anybody show me how to calculate µ and the maximum angle?

Answer 1

Yea, I know how you feel!

F=ma
W=Ke
W=F S
maS=0.5mV^2
a=0.5V^2/S
a=0.5 (81 / 3.6)^2/94
a=2.7 m/s^2 (confirmed)

b)
f=µ mg
again
f S=Ke
µ mg S=0.5mV^2
µ =0.5V^2/(gS)
µ =0.5 (81 / 3.6)^2/(9.8 x 94)
µ =0.274 a bit slick

c)Aha... The max angle problem!
Fd=f if Fd is more then f th ecar will slide.
Fd=mgsin(A)
f= µ mg cos(A)
mgsin(A)=µ mg cos(A)
sin(A)/cos(A) =tan(A)= µ
A=arcTan(µ)
A=15.4 degrees

Answer 2

it could be because the question is flawed.
anti-lock brakes are designed to keep your steering ability, and they usually increase best stopping distance a small amount.

what is gravity acceleration ?

2.69m/s2 / gravity acceleration = µ
the computer of the car actually calculates µ as your stopping.

please someone else help with the last part, I really don't like math.