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Chapter 2: Problem 2

What is weight? Under what circumstances might something be weightless?

Short Answer

Expert verified
Answer: Weight is the force exerted by gravity on an object, calculated using the formula W = m * g, where W is weight, m is the mass of the object, and g is the acceleration due to gravity. Weightlessness occurs when an object does not experience any force due to gravity or when the forces acting on it are balanced, resulting in a net force of zero. This can happen in outer space, during freefall, or when an object is in a state of equilibrium, such as being submerged in a liquid with buoyancy canceling out gravitational pull.

Step by step solution

01

Definition of Weight

Weight is the force exerted by gravity on an object. Mathematically, it can be represented as the product of an object's mass and the acceleration due to gravity. The formula to calculate weight is: W = m * g, where W represents weight, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s虏 on Earth).
02

Concept of Weightlessness

Weightlessness occurs when an object does not experience any force due to gravity or when the forces acting on it are balanced. In other words, an object is weightless when the net force acting on it is zero.
03

Circumstances for Weightlessness

There are several situations where an object might be considered weightless: 1. In outer space: As an object moves further away from a planet or star, the gravitational force acting on it decreases. In the vacuum of space, far from any celestial bodies, the gravitational force is extremely weak, and an object will appear to be weightless. 2. In freefall: When an object is in freefall, it is this gravitational force that causes it to accelerate towards the Earth. However, since the object and everything within it are moving together, it will seem weightless. Examples of this include astronauts in orbit and skydivers in freefall before opening their parachutes. 3. In a state of equilibrium: When the upward force acting on an object (such as the buoyant force in water) is equal to the downward force due to gravity, the object is in equilibrium and will appear weightless. This can be seen in objects submerged in liquids where their buoyancy cancels out the gravitational pull.

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Key Concepts

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

Weight in Physics
Understanding the concept of weight in physics is crucial for those investigating various aspects of force and motion. Weight is often misrepresented as being synonymous with mass; however, they are distinct properties. Weight is the force that gravity exerts on an object's mass. It is not a fixed characteristic of an object like mass, but rather it depends on the acceleration due to gravity, which can vary from one celestial body to another.

The formula for calculating weight (\( W = m \times g \) where \( W \) represents weight, \( m \) is the mass of the object, and \( g \) is the local acceleration due to gravity) is a fundamental expression in physics. For example, an object's weight on Earth will differ from that on the Moon due to the Moon's lower acceleration due to gravity. However, the mass remains unchanged, emphasizing that weight is a force, and mass is the amount of matter in an object.
Acceleration Due to Gravity
Acceleration due to gravity, denoted by \( g \) is a critical value in physics, representing the rate at which an object speeds up when falling freely under the influence of gravity alone. On Earth, this value is approximately \( 9.8 \text{m/s}^2 \) and is a key factor in calculations involving gravitational force.

This acceleration is the result of the Earth's gravitational pull, and it is constant near the Earth's surface. Importantly, the acceleration due to gravity is considered a 'local' value, meaning that it may differ on other planets or celestial bodies. It is also essential in the context of orbits and spaceflight, as it affects the trajectory and speed of satellites and spacecraft.
Gravitational Force
Gravitational force is the attraction that exists between any two objects with mass. According to Newton's law of universal gravitation, this force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between their centers.

In formula terms, gravitational force is given by \( F = G \frac{m_1 \times m_2}{r^2} \) where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between their centers. The phenomenon of gravity is what gives us weight and keeps planets in orbit around stars, and moons in orbit around planets.
Freefall
Freefall occurs when the only force acting on an object is gravity. In this state, any object, regardless of its mass, will accelerate at the same rate toward the Earth, assuming air resistance is negligible. This ideated scenario is well-illustrated by astronauts in space when they orbit the Earth.

While in freefall, objects or individuals do not experience their own weight, leading to the sensation of weightlessness. For example, skydivers before deploying their parachutes are in freefall, as are astronauts aboard the International Space Station, which is constantly freefalling towards the Earth but also moving sideways fast enough to keep missing it, thus remaining in orbit.
Equilibrium State
An equilibrium state in physics is defined as a condition where the net force acting on an object is zero. When an object is in equilibrium, it either remains at rest or moves with a constant velocity. This concept is an essential part of understanding weightlessness, as an object in equilibrium under the right conditions can appear to be without weight.

For instance, objects submerged in a fluid experience an upward buoyant force that can counteract the downward pull of gravity. When these forces are perfectly balanced, the object neither sinks nor floats, creating an equilibrium state and thus creating the effect of being weightless within the fluid. This principle is integral to various disciplines, including engineering and fluid dynamics.

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