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Instantaneous Force and Impulse

An engine can...

Question

An engine can pull four coaches at a maximum speed of $20 m s^{- 1}$ . The mass of the engine is twice the mass of every coach. Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine, when it pulls $12$ and $6$ coaches, are

8.5 m s^{- 1}

and

15 m s^{- 1}

, respectively

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6.5 m s^{- 1}

and

8 m s^{- 1}

, respectively

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8.5 m s^{- 1}

and

13 m s^{- 1}

, respectively

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10.5 m s^{- 1}

and

15 m s^{- 1}

, respectively

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Solution

The correct option is A $8.5 m s^{- 1}$ and $15 m s^{- 1}$ , respectively
Let the mass of every coach is $m$ , the mass of the total system when $4$ coaches are connected will be $6 m$ and the mass of the total system when $12$ coaches are connected will be $14 m$ .

According to conservation of linear momentum, when $12$ coaches are connected, it can be written as,

$6 m \times 20 = 14 m \times v_{1}$

$v_{1} = 8.57 m / s$

Since, the mass of the total system when $6$ coaches are connected will be $8 m$ .

According to conservation of linear momentum, when $6$ coaches are connected, it can be written as,

$6 m \times 20 = 8 m \times v_{2}$

$v_{2} = 15 m / s$

Thus, when engine pulls $12$ coaches, the speed is $8.57 m / s$ and when engine pulls $6$ coaches, the speed is $15 m / s$ .

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An engine can pull four coaches at a maximum speed of 20 ms−1. The mass of the engine is twice the mass of every coach. Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine, when it pulls 12 and 6 coaches, are

An engine can pull four coaches at a maximum speed of $20 m s^{- 1}$ . The mass of the engine is twice the mass of every coach. Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine, when it pulls $12$ and $6$ coaches, are