/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 An astronaut, inside an earth sa... [FREE SOLUTION] | 91Ó°ÊÓ

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An astronaut, inside an earth satellite, experiences weightlessness because (1) no external force is acting on him (2) he is falling freely (3) no reaction is exerted by the floor of the satellite (4) he is far away from the earth's surface

Short Answer

Expert verified
The astronaut experiences weightlessness because (3) no reaction is exerted by the floor of the satellite.

Step by step solution

01

Understanding Weightlessness

Weightlessness occurs when an object or person is in a state of free fall, such that they do not feel the effects of gravity pulling them towards the ground. This happens because there is no contact force acting opposite to the direction of gravity.
02

Consider the Forces Acting on the Astronaut

Inside a satellite, the astronaut and the satellite are both under the influence of Earth's gravitational pull. However, they are both in free fall towards Earth at the same rate due to the satellite's orbit.
03

Analyze the Motion of the Satellite

The satellite is in orbit around Earth, which means it is constantly falling towards Earth due to gravity, but it also has a horizontal velocity that keeps it moving around Earth. This creates a constant state of free fall for everything inside the satellite.
04

Resulting Feeling of Weightlessness

As the astronaut is in free fall along with the satellite, there is no normal force exerted by the floor of the satellite against him/her. Without this normal force, the astronaut experiences a sensation of weightlessness.
05

Identify the Correct Statement

The correct reason for the astronaut experiencing weightlessness is (3) no reaction is exerted by the floor of the satellite, which is due to free fall.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Free Fall
When we talk about free fall, we're discussing a situation where an object is moving freely under the gravitational pull without any other forces acting on it. Imagine dropping a ball in the air. As it falls, it's influenced only by gravity, not air resistance or any other force. This is exactly what's happening with an astronaut in a satellite. The satellite orbits Earth, and both the astronaut and satellite are in a continuous state of free fall. Since they're falling together at the same rate, it feels as if there's no gravity affecting them, hence the sensation of weightlessness.

The key aspect of free fall is that there is no contact force to counteract gravity. This lack of a counteracting force is what makes the astronaut feel as though they are floating.
  • The astronaut and satellite are falling under gravity.
  • They're moving at the same speed, so it feels like floating.
  • No opposing force means no sense of weight.
Gravitational Force
Gravitational force is the attractive force between two masses, like Earth and an astronaut. This force is what keeps planets in orbit and gives us weight here on Earth. If you weigh yourself, it's the gravitational pull of the Earth that's affecting you.

In the case of the astronaut inside the satellite, Earth's gravitational force is still acting upon both the astronaut and the satellite. This force pulls them towards Earth's center. However, because they are orbiting, the gravitational pull does not simply drag them down but ensures that their path curves around the planet.
  • Gravity pulls objects towards each other.
  • The astronaut and satellite are both affected by Earth’s gravity.
  • Gravity causes the orbit path around the Earth.
Despite this constant pull, the lack of the normal force inside the satellite makes the astronaut feel weightless.
Orbital Motion
The fascinating aspect of orbital motion is how it allows objects to "fall around" a planet rather than directly towards it. This means that while a satellite, and anything within it, is indeed falling due to gravity, it moves forward at a velocity that matches the rate of this fall. This creates a stable orbit around Earth.

For the astronaut, this constant state of orbital motion means they're always in free fall. This continuous motion around Earth means the gravitational pull is balanced by the orbital path, keeping them above Earth.
  • Orbit is created by a balance of falling and forward motion.
  • Free fall results in weightlessness due to the orbit.
  • Satellite and its contents are in constant motion around Earth.
Normal Force
The normal force is what we usually feel when we stand on solid ground. It's the counteracting force exerted by a surface to support the weight of an object. Think of it as the force the ground pushes back against you, which stops you from sinking through it.

In a satellite, the absence of this normal force is the reason behind the sensation of weightlessness. Since the floor of the satellite does not exert a force against the astronaut (because both the floor and astronaut fall together), the astronaut does not feel any weight.
  • Normal force counteracts gravitational pull.
  • Weight is felt when normal force is present.
  • In an orbiting satellite, the normal force is missing, causing weightlessness.
Perceiving weightlessness is due to the lack of this counteracting normal force while in free fall inside the satellite.

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Most popular questions from this chapter

Which of the following are correct? (1) An astronaut going from the earth to the Moon will experience weightlessness once. (2) When a thin uniform spherical shell gradually shrinks maintaining its shape, the gravitational potential at its centre decreases. (3) In the case of a spherical shell, the plot of \(V\) versus \(r\) is continuous. (4) In the case of a spherical shell, the plot of gravitational field intensity \(I\) versus \(r\) is continuous.

An artificial satellite of the earth is launched in circular orbit in the equatorial plane of the earth and the satellite is moving from west to east. With respect to a person on the equator, the satellite is completing one round trip in \(24 \mathrm{~h}\). Mass of the earth is \(M=6 \times 10^{24} \mathrm{~kg} .\) For this situation, the orbital radius of the satellite is (1) \(2.66 \times 10^{4} \mathrm{~km}\) (2) \(6400 \mathrm{~km}\) (3) \(36,000 \mathrm{~km}\) (4) \(29,600 \mathrm{~km}\)

A ring of radius \(R=4 \mathrm{~m}\) made of a highly dense material has a mass \(m_{1}=5.4 \times 10^{9} \mathrm{~kg}\) distributed uniformly over its circumference. A highly dense particle of mass \(m_{2}=6 \times 10^{8} \mathrm{~kg}\) is placed on the axis of the ring at a distance \(3 \mathrm{~m}\) from the center of the ring. Find the speed of the particle (in \(\mathrm{cm} / \mathrm{s}\) ), when the particle is at the center of the ring. Except mutual gravitational interaction of the two, neglect all other forces.

Suppose the gravitational force varies inversely as the nh power of the distance. Then, the time period of a planet in \(a\) circular orbit of radius \(R\) around the Sun will be proportional to (1) \(R^{n}\) (2) \(R^{(n+1)}{2}\) (3) \(R^{\frac{(n-1)}{2}}\) (4) \(R^{-n}\)

The earth (mass \(=10^{24} \mathrm{~kg}\) ) revolves round the Sun with an angular velocity \(2 \times 10^{-7} \mathrm{rad} \mathrm{s}^{-1}\) in a circular orbit of radius \(1.5 \times 10^{8} \mathrm{~km}\). Find the force exerted by the Sun on the earth \(\left(\mathrm{in} \times 10^{21} \mathrm{~N}\right)\)

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