Conservation of Momentum Question

[mfianist]

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A boat of mass m is carrying a load of bricks with a total number of N and mass M, and is floating freely on water. SUPERMAN, in a show of strength, throws the entire load of bricks backward at once with a relative speed of v0. A GENIUS, in a show of intelligence, throws the bricks backward with a relative speed of v0 one at a time. Argue and explain how and why GENIUS achieves a much higher speed than SUPERMAN. Take N >> 1 and M >> m. Neglect the friction between the boat and water, and the mass of GENIUS and SUPERMAN.

I have no clue on how to start this question... Somebody please help me.

 

[Nate810]

The difference in speed can be explained by Newton's Third Law of Motion, which states that "for every action, there is an equal and opposite reaction." When SUPERMAN throws the entire load of bricks at once, the force acting on the boat is the sum of the forces acting on each brick. However, when GENIUS throws the bricks one at a time, the force acting on the boat is the force acting on each brick, multiplied by the number of bricks thrown. Since the force acting on the boat is greater in the latter case, the acceleration of the boat will also be greater, resulting in a larger speed. In addition, since the mass of the bricks is much greater than the mass of the boat, the acceleration of the bricks themselves will be relatively small compared to the acceleration of the boat when they are thrown one at a time. This means that most of the energy imparted by GENIUS will be used to accelerate the boat, whereas with SUPERMAN, much of the energy will be wasted on accelerating the bricks. Therefore, when the bricks are thrown one at a time, the boat will reach a much higher speed than when they are thrown all at once.

 

[wais]

The conservation of momentum states that in a closed system, the total momentum remains constant. In this scenario, the boat, bricks, SUPERMAN, and GENIUS are all part of a closed system. Therefore, the total momentum before and after the bricks are thrown must be equal.

When SUPERMAN throws the entire load of bricks with a relative speed of v0, the momentum of the bricks and the boat will change by a certain amount. However, since the mass of the boat (m) is much smaller than the total mass of bricks (M), the change in momentum will be relatively small. This means that the boat's final speed after the bricks are thrown will not be significantly different from its initial speed.

On the other hand, when GENIUS throws the bricks one at a time with a relative speed of v0, the change in momentum for each brick will be much greater due to the smaller mass of each brick. This means that the boat's final speed after each brick is thrown will be significantly higher than its initial speed. Additionally, throwing the bricks one at a time allows for a continuous transfer of momentum, resulting in a higher overall speed for the boat.

In conclusion, GENIUS achieves a much higher speed than SUPERMAN because of the conservation of momentum and the fact that the bricks are thrown one at a time, allowing for a continuous transfer of momentum.