(^612) A Textbook of Engineering Mechanics
and force required to accelerate the engine and train
= ma = 350 × 0.05 = 17.5 kN
∴ Total resisting force = Tractive resistance + Resistance due to inclination
- Force required for acceleration
= 17.5 + 34.3 + 17.5 = 69.3 kN
and work done in one second = Total Resisting force × Distance
= 69.3 × 10 = 693 kN-m/s = 693 kJ/s
∴ Power = 693 kW Ans.
Tension in the coupling
It is the tension which is responsible for driving the train only. We know that tractive resistance
(for train only)
= 50 × 300 = 15 000 N = 15 kN
Similarly, resistance due to inclination (for train only)
= m 2 g sin α = 300 × 9.8 × 0.01 = 29.4 kN
and force required for the acceleration (for train only)
= 300 × 0.05 = 15 kN
∴Tension in the coupling = 15 + 29.4 + 15 = 59.4 kN Ans.
EXERCISE 30.2
- A mass of 50 tonnes is to be pulled up a smooth plane having an inclination of 1 in 50.
Find the work done in pulling up the mass for a distance of 2 metres. (Ans. 19.6 kJ) - A locomotive pulls a train of mass 125 tonnes including its own mass up a slope of 1 in
100 with a velocity of 18 km.p.h. Find the power of the engine, if the frictional resistance
is 50 newtons per tonne. (Ans. 92.5 kW) - A train of mass 300 tonnes moves down a slope of 1 in 200 at 45 km.p.h. with the engine
developing 75 kW. Find the power required to pull the train up the slope with the same
velocity. (Ans. 332.5 kW) - A train of mass 200 tonnes is ascending a track, which has an inclination of 1 in 100, the
resistance being 75 N per tonne. What is the acceleration of the train when its speed has
reached 18 km.p.h. if the power developed by the engine is 450 kW? (Ans. 0.28 m/s^2 )
30.15. ENERGY
The energy may be defined as the capacity to do work. It exists in many forms i.e., mechanical,
electrical chemical, heat, light etc. But in this subject, we shall deal in mechanical energy only.30.16. UNITS OF ENERGY
We have discussed in the previous article, that the energy is the capacity to do work. Since the
energy of a body is measured by the work it can do, therefore the units of energy will be the same as
those of the work.30.17. MECHANICAL ENERGY
Though there are many types of mechanical energies, yet the following two types are impor-
tant from the subject point of view :- Potential energy. 2. Kinetic energy.