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A freight train consists of two 8.00x104 kg engines and 45 cars with average masses of 5.50x104 kg.  What force must each engine exert backward on the track to accelerate the train at a rate of 5.00x10-2 m/s2 if the force of friction is 7.50x105 N, assuming the engines exert identical forces?Group of answer choices882 kN441 kN221 kN110 kN

Question
A freight train consists of two 8.00x104 kg engines and 45 cars with average masses of 5.50x104 kg.  What force must each engine exert backward on the track to accelerate the train at a rate of 5.00x10-2 m/s2 if the force of friction is 7.50x105 N, assuming the engines exert identical forces?
Group of answer choices
882 kN
441 kN
221 kN
110 kN
check_circleAnswer
Step 1

Let F be the force with which the engines pull the cars, f be the frictional force acting backwards on the track, m be the mass of the car, M be the mass of the engines, and a be the acceleration of freight train.

Write the values given in the question.

f =
M 8 x10 kg
7.5x103 N
m 5.5 x10 kg
a 5x10 m/s
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f = M 8 x10 kg 7.5x103 N m 5.5 x10 kg a 5x10 m/s

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Step 2

Draw the kinetic diagram of the motion of the freight train.

a
F
M
M
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a F M M

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Step 3

Write the expression for Newton’s second...

2F - f (2M 45m)a
1
((2M 45m)a+f
F
2
1
(2(8x10 kg)+ 45(5.5x 10 kg)(5x10 m/s')+(7.5x10 N))
1
(1.3175 x 10 N+7.5 x10 N
2
1
(8.8175x10' N
2
=4.408x 103 N
= 441 kN
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2F - f (2M 45m)a 1 ((2M 45m)a+f F 2 1 (2(8x10 kg)+ 45(5.5x 10 kg)(5x10 m/s')+(7.5x10 N)) 1 (1.3175 x 10 N+7.5 x10 N 2 1 (8.8175x10' N 2 =4.408x 103 N = 441 kN

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