What are the Newton’s Laws that are at work here and why?

Question

An astronaut of mass 52 Kg, pushes against the space craft door and flies away with an

acceleration of 1.3 m/s2. What was the force applied in the push? What are the Newton’s Laws

that are at work here and why?

Answer 1

To find the force applied in the push, we use Newton's second law of motion.

Newton's Second Law:

Newton's second law states that the force applied to an object is equal to its mass times its acceleration F=ma.

F=ma=(52 kg)×(1.3 m/s2)=67.6 N

Therefore, the force applied by the astronaut in the push is 67.6 N.

Newton’s Laws at Work:

1. Newton's First Law (Law of Inertia):
2. Before the push: The astronaut is at rest relative to the spacecraft, meaning they have a constant velocity of 0 m/s.
3. During the push: An external force (the push) acts on the astronaut, causing a change in their state of motion.
4. After the push: Once the push ends, no additional external forces act on the astronaut (assuming we neglect space resistance), and they continue to move with a constant velocity (inertia).
5. Newton's Second Law (Law of Acceleration):
6. This law helps us calculate the force exerted by the astronaut using the relationship F=ma. The force is the product of the astronaut's mass (52 kg) and their acceleration (1.3 m/s²), resulting in a force of 67.6 N.
7. Newton's Third Law (Action and Reaction):
8. When the astronaut pushes against the spacecraft, the spacecraft pushes back with an equal and opposite force. If we define the direction the astronaut moves as positive, then: F_astronaut_on_spacecraft = −F_spacecraft_on_astronaut
9. Since the force exerted by the spacecraft on the astronaut is 67.6 N, the force exerted by the astronaut on the spacecraft is -67.6 N (equal in magnitude but opposite in direction).

Answer 2

Of course, all of newton's laws apply to this situation, but let's look at them individually.

Newton's first law:

Before the astronaut pushed on the spacecraft, they were at rest (constant velocity v = 0 m/s).

While the astronaut was pushing on the spacecraft, an external force F was applied to the astronaut (a > 0) which caused a change in the astronaut's speed.

After the astronaut pushed on the spacecraft, they will travel with a constant velocity v > 0 since no external forces are acting on them anymore.

Newton's second law:

F = ma = (52 kg)*(1.3 m/s²) = 67.6 N

Newton's third law:

If we define the positive direction to be the direction in which the astronaut moves, then newton's second law tells us that F_{astronaut on spacecraft} = -F_{spacecraft on astronaut} , and since we know that the force exerted by the spacecraft on the astronaut is 67.6 N, we also know that the force exerted by the astronaut on the spacecraft is -67.6 N.