Question

A space ship that is out of fuel is traveling through space with a speed 10 m/s. The total mass of the space ship and its empty fuel tank is 900 kg. What is the momentum of the space ship (with the empty fuel tank attached)? What is the total kinetic energy of the space ship (with the empty fuel tank attached)? Since there is no more fuel, the 200 kg fuel tank is disconnected and released in the opposite direction at 4 m/s. At what speed is the rest of the space ship now traveling? What is the total kinetic energy of the system after the fuel tank is disconnected? Was this process (the fuel tank being released) elastic or inelastic?

Answer 1

What is the momentum of the space ship (with the empty fuel tank attached)

p = mv

p = 900 * 10

p = 9000 Kg.m/s

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What is the total kinetic energy of the space ship (with the empty fuel tank attached)

K.E = 1/2 * m * v²

K.E = 1/2 * 900 * 10²

K.E = 45000 J

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At what speed is the rest of the space ship now traveling

suppose initially spaceship ( with tank) was moving in + direction, then

using conservation of momentum

mv = m (tank) * v ( tank) + m ( spaceship) * v ( spaceship)

9000 = 200 * -4 + 700 * v ( spaceship)

so,

v ( spaceship) = 14 m/s ( in initial direction of motion

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What is the total kinetic energy of the system after the fuel tank is disconnected

1/2 * 700 * 14²

K.E = 68600 J

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