A train with a total mass of 1.1 × 106 kg rises 819 m while traveling a distance

Question

A train with a total mass of 1.1 × 106 kg rises
819 m while traveling a distance of 75 km at
an average speed of 9 km/h. The frictional
force is 0.8 percent of the weight.
Find the kinetic energy of the train. The
acceleration of gravity is 9.81 m/s2 .
Answer in units of MJ
75 km = 75e3 m or 75,000 m


a) answer: 3.437 MJ or 3.437e6 or 3.437 x 10^6

b) Find the total change in its potential energy.
Answer in units of J
answer is 8.828e9 or 8.828 x 10^9

c) Find the energy dissipated by friction.
Answer in units of J
answer is 6.468 * 10^9 J

d) Find the power output of the train’s engines.
Answer in units of MW

Note: a through c are all correct answers, need d.

Explanation / Answer

a)v = 9 km/h = 2.5 m/s

kinetic energy of the train = 1/2(m)v2

                            = 1/2(1.1 X 106 ) X (2.5)2 = 3.437 X 106 J = 3.437 MJ

b) change in potential energy = mgh

                                 = 1.1 X 106 X 9.81 X 819 = 8828 X 106 J = 8.828 X 109 J

c) friction is 0.8 % of weight = 0.008 X 1.1g X 106 = 8.8g X 103 N

energy = work done = F.d = 8.8g X 103 X 75,000 = 660g X 106 = 6.468 X 109 J

d) net energy by engine = total energy dissipated

                              = 3.437 + 8828 + 6468 = 15299.437 MJ

this energy is dissipated in 75/9 = 8.333 hours= 29988 sec.

POwer is energy dissipated per hour = 15299.437 / 29988 = 0.51 MW

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