The subway train shown is travelling at a speed of 30 mih wh

The subway train shown is travelling at a speed of 30 mi/h when the brakes are fully applied on the wheels of car C causing it to slide on the track, but are not applied on the wheels of can a or B. Knowing that the coefficient of kinetic friction is 0.35 between the wheels and the track, determine (a) the distance required to bring the tram to a stop, (b) the force in each coupling.

Solution

a) on car C:
in vertical, N - mC g = 0

N = 40000g

kinetic friction force = uk N = 0.35(40,000g)

this is the only force in horizontal acting on three car system.

a = Fnet / m = 0.35(40000g) / (40000 + 50000 + 40000)

a = 1.06 m/s^2

initial velocity, vi = 30 mi/h = 30 x 1609 m / 3600sec

vi = 13.41 m/s

Applying vf^2 - vi^2 = 2ad

0^2 - 13.41^2 = 2(-1.06)(d)

d = 84.8 m .....Ans

(b) for A-B

on A: Applying Fnet = ma

Fab = mA a = 40000 * 1.06 = 42400 N

on B:

Fbc - Fab = mB a

Fbc - 42400 = 50000 * 1.06

Fbc = 95400 N .....Ans