An astronaut in outer space pushes himself away from his spaceship. About how far does the astronaut go before stopping? What does the astronaut have to do to stop himself?
When an astronaut in outer space pushes themselves away from their spaceship, they will continue moving until an external force acts upon them to change their motion. This is due to the principle of inertia, which states that an object in motion will remain in motion unless acted upon by a force. The distance the astronaut will travel before stopping depends on several factors, such as the amount of force they apply and the mass of the astronaut.
To stop themselves, the astronaut can do the following:
1. Use a thrusting device: If the astronaut has access to a propulsion device, such as a handheld jet or thruster, they can use it to generate thrust in the opposite direction of their motion. This will create an equal and opposite force, effectively bringing them to a stop.
2. Use their spacesuit or body: The astronaut can manipulate their body position or use their spacesuit to create drag or resistance against the surrounding environment. For example, they can extend their arms or legs, which will increase their surface area and create air resistance. This will gradually slow down their motion.
3. Grab onto another object: If there are any structures, tools, or other objects nearby, the astronaut can attempt to reach out and grab onto them. By exerting a force on the object, the astronaut can counteract their own motion and eventually come to a stop.
It is important to note that in outer space, where there is no air or significant gravitational forces, the astronaut will continue to move indefinitely in the absence of an external force.
To determine how far the astronaut goes before stopping, we need to consider the principle of conservation of momentum. According to this principle, in the absence of any external forces, the total momentum of a system remains constant.
Initially, the astronaut and the spaceship are at rest, so the total momentum of the system is zero. When the astronaut pushes himself away from the spaceship, he exerts a force on himself in one direction, creating an equal and opposite force on the spaceship. According to Newton's third law of motion, for every action, there is an equal and opposite reaction.
The astronaut's push propels him in one direction, while the spaceship moves in the opposite direction. Since the spaceship is significantly more massive than the astronaut, its velocity change is small, whereas the astronaut's velocity change is significant.
To calculate how far the astronaut goes, we need to know the mass of the astronaut and the force he exerts while pushing off. Let's assume the astronaut's mass is 70 kilograms and the force he exerts is 100 Newtons.
The momentum of an object is given by the equation: momentum = mass × velocity.
As the astronaut pushes off, he gains velocity. We can use the equation: force = mass × acceleration, to find the acceleration experienced by the astronaut due to the force he exerts on himself.
Since the astronaut is pushing against nothing but empty space, the only force acting on him is the force he applies, and it is equal in magnitude but opposite in direction. Therefore, we can rewrite the equation as: force = mass × (change in velocity / time).
Rearranging the equation, we have: change in velocity = (force / mass) × time.
Given that the force is 100 Newtons, mass is 70 kilograms, and let's assume the astronaut pushes for 1 second, we can calculate the change in velocity: change in velocity = (100 / 70) × 1 = 1.43 meters per second.
Now, let's assume the astronaut's initial velocity was zero. Using the equation: final velocity = initial velocity + change in velocity, we get: final velocity = 0 + 1.43 = 1.43 meters per second.
To determine the distance the astronaut travels, we can utilize the equation: distance = (initial velocity × time) + (0.5 × acceleration × time^2).
Since the initial velocity is zero and the acceleration is force / mass, the equation simplifies to: distance = 0.5 × (force / mass) × time^2.
Plugging in the values, the distance traveled by the astronaut can be calculated as: distance = 0.5 × (100 / 70) × (1^2) = 0.714 meters.
Therefore, the astronaut would go approximately 0.714 meters before stopping.
To stop himself, the astronaut would need to exert an equal and opposite force to bring himself to rest. This can be achieved by exerting another force against a reference point, such as pushing against the spaceship again or using any other object in the vicinity. By exerting a force opposite to his motion, he can gradually reduce his velocity to zero and come to a stop relative to his surroundings.