02. Comic-strip hero Superman meets an asteroid in outer space and hurls it at 800 m/s, as fast as a bullet. The asteroid is a thousand times more massive than Superman, yet in the comic strip, he remains stationary after releasing the asteroid. Say, his mass is 107 kg, what is not right in this scene? Consider the law of conservation of momentum. Support your answer by providing a numerical proof.
In this scene, there are a couple of aspects that are not consistent with the law of conservation of momentum. Let's analyze the situation step by step to understand what's happening.
According to the law of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. Momentum is the product of an object's mass and velocity.
In this case, Superman meets an asteroid in outer space and hurls it at 800 m/s. Let's denote the mass of the asteroid as "mA" and its initial velocity as "vA." Superman's mass is given as 107 kg, and his initial velocity is 0 m/s since he remains stationary after releasing the asteroid.
To ensure the conservation of momentum, the total initial momentum before the asteroid is thrown should be equal to the total final momentum after the asteroid is thrown.
The total initial momentum is the sum of Superman's initial momentum (which is zero) plus the asteroid's initial momentum:
Initial momentum = Superman's initial momentum + Asteroid's initial momentum
= 0 kg * 0 m/s + mA * vA
The final momentum is the sum of Superman's final momentum (since he is stationary) plus the asteroid's final momentum after it is thrown:
Final momentum = Superman's final momentum + Asteroid's final momentum
= 0 kg * 0 m/s + mA * (vA - 800 m/s)
By the law of conservation of momentum, the initial momentum should be equal to the final momentum:
Initial momentum = Final momentum
0 + mA * vA = 0 + mA * (vA - 800)
Now, let's substitute the given values. The mass of Superman, mS, is 107 kg:
107 kg * 0 m/s = 107 kg * (0 m/s - 800 m/s)
0 = -107 kg * 800 m/s
0 = -85,600 kg*m/s
As we can see, the equation doesn't balance and leads to an inconsistency. The left side of the equation is zero, while the right side is a negative value. This implies that the conservation of momentum doesn't hold in this scene.
Therefore, the situation described in the comic strip is not physically possible according to the law of conservation of momentum.