Question

An engine of weight 500 kN pulls a carriage weighing 1500 kN up an incline

of 1 in 100. The train starts from rest and moves with a constant

acceleration against a resistance of 5 N/kN. It attains a maximum speed of

36 km/h in 1 km distance.


a) Determine the tension in the coupling between the carriage and the engine

b) Determine tractive force developed by the engine.
any one can help me please..​

Answer 1

Answer:

Tension in the coupling = 30.14kN

Tractive Force = 40.18kN

Explanation:

Answer 2

a)30.14kN

b)40.16kN

Given,

Weight if engine = 500kN

Weight of carry = 1500kN

initial velocity = 0 (starts from rest)

final velocity = 36km/h = 10m/s

Displacement = 1km.

By using third equation of motion which is,

$v^{2}-u^{2}=2as = 10^{2}-0^{2} = 2(a)(1000) \\100 -0 = 2000a\\ 100 = 2000a\\ 0.05 = a$

So, here we get the acceleration as $0.05m/s^{2}$.

Equating Force(ma) to net force acting parallel to the plane.

Lets assume

$F_{T}$ = Tractive force developed by the engine.

T = Coupling tension.

We can write that,

$F_{T} - 500(\frac{1000}{100})-500(5)-T=(1000)(0.05)(\frac{500}{9.81})\\F_{T}-T-5000-2500= 2548.42\\F_{T}-T=2548.42+5000+2500\\ F_{T}-T=10048.42N$---(1)

For the train,

$T-1500(\frac{1}{100})(1000)-7500=\frac{(1500)(1000)}{9.81}(0.05)\\ T-15000-7500= 7645.23\\T=7645.23+15000+7500\\T=30145.23=30.145kN\\F_{T}= 10.04+30.14=40.18kN$