A steam engine has mass 3×104 kg, it has two wagons with mass 2×104 kg. These wagons accelerate with 0.2 m/s2, then which of the following option/s is/are correct?

Force exerted by engine is 1 . 4 × 10 4 N

The force experienced by each wagon is 0 . 4 × 10 4 N

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A steam engine has mass $3 \times 10^{4} kg$ , it has two wagons with mass $2 \times 10^{4} kg$ . These wagons accelerate with $0.2 m / s^{2},$ then which of the following option/s is/are correct?

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Force exerted by engine is

1.4 \times 10^{4} N

The force experienced by each wagon is

0.4 \times 10^{4} N

Frictional force between wagons is neglected for easy calculation

All of the above

answer is D.

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Detailed Solution

A steam engine has mass

3 \times 10^{4} kg

, it has two wagons with mass

2 \times 10^{4} kg

. These wagons accelerate with

0.2 m / s^{2}

. Then the force exerted by engine is

1.4 \times 10^{4} N

and force experienced by each wagon is

0.4 \times 10^{4} N

. frictional force is neglected between engine and wagon.
To calculate the force exerted by the engine the total system is taken hence the mass of system m is,

M = m_{1} + m_{2}

Mass of engine

m_{1} = 3 \times 10^{4} kg

Mass of each wagon

m_{2} = 2 \times 10^{4} kg

Total mass of system

M = 3 \times 10^{4} kg + 2 \times (2 \times 10^{4} kg)

M = 7 \times 10^{4} kg

Given that engine provides acceleration

0.2 m / s^{2}

for each wagon. Then the force exerted by each wagon is
From the newton’s second law

F = ma

m is mass and a is acceleration of an object.

F = 7 \times 10^{4} kg \times 0.2 m / s^{2}

F = 1.4 \times 10^{4} kgm / s^{2}

F = 1.4 \times 10^{4} N

The force exerted by engine is

1.4 \times 10^{4} N

.
To calculate the force experienced by each wagon has mass

2 \times 10^{4} kg

with acceleration

0.2 m / s^{2}

F = ma

= > 2 \times 10^{4} kg \times 0.2 m / s^{2}

= > 0.4 \times 10^{4} kgm / s^{2}

F = 0.4 \times 10^{4} N

Hence, the force experienced by each wagon is

F = 0.4 \times 10^{4} N

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