Two children float motionlessly in a space station. The 20-kg girl pushes on the 40-kg boy and he sails away at 1.0m/s.
What happens to the girl?
The girl floats away in the opposite direction at 2.0m/s
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the girl pushes on the boy, the boy will move in one direction, and the girl will move in the opposite direction. This means that the girl will also move away from the spot she was originally floating. The girl's speed after pushing the boy will depend on their respective masses and the speed at which the boy moves away.
To understand what happens to the girl, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction, assuming no external forces act on the system.
Given that the initial momentum of the girl and the boy together is zero (since they are motionless), we can write this as:
Initial momentum = Final momentum
The initial momentum is the sum of the individual momenta of the girl and the boy. Since they are initially at rest, their momenta are both zero:
Initial momentum = (mass of the girl) × (velocity of the girl) + (mass of the boy) × (velocity of the boy)
= (20 kg) × (0 m/s) + (40 kg) × (0 m/s)
= 0 kg·m/s
After the girl pushes the boy, the boy sails away at a velocity of 1.0 m/s. The girl, on the other hand, will experience a reaction force pushing her in the opposite direction. This reaction force will cause her to move in the opposite direction with a lower velocity.
Assuming no external forces act on the system, the final momentum of the system is still zero:
Final momentum = (mass of the girl) × (final velocity of the girl) + (mass of the boy) × (final velocity of the boy)
= (20 kg) × (final velocity of the girl) + (40 kg) × (-1.0 m/s)
= 0 kg·m/s
Since the final momentum is zero, the final velocity of the girl can be calculated:
(20 kg) × (final velocity of the girl) + (40 kg) × (-1.0 m/s) = 0 kg·m/s
Now we can solve for the final velocity of the girl:
(20 kg) × (final velocity of the girl) = (40 kg) × (1.0 m/s)
final velocity of the girl = (40 kg) × (1.0 m/s) / (20 kg)
= 2.0 m/s
Therefore, the girl will move in the opposite direction with a final velocity of 2.0 m/s.