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Chapter 1: Problem 73

Bring out the differences between the mass and the weight of a body.

Short Answer

Expert verified
Answer: Mass and weight are different in the following ways: Mass is a scalar quantity representing the amount of matter in an object, while weight is a vector quantity representing the gravitational force acting on the object. Mass remains constant regardless of an object's location, while weight varies depending on location. Mass is measured in kilograms (kg), while weight is measured in newtons (N). They are related through the formula W = mg, where W is the weight, m is the mass, and g is the gravitational acceleration.

Step by step solution

01

Define Mass

Mass is the amount of matter present in a body. It is a scalar quantity and remains constant for the body, regardless of its location in the universe. The unit of mass is the kilogram (kg).
02

Define Weight

Weight is the force exerted by gravity on a body. It is a vector quantity, meaning it has both magnitude and direction. The weight of an object can vary depending on its location, such as on Earth, the Moon, or in space. The unit of weight is the newton (N).
03

Explain the Relationship Between Mass and Weight

The weight of an object is calculated using the formula: W = mg, where W represents the weight of the object, m represents its mass, and g represents the gravitational acceleration (approximately 9.81 m/s虏 on Earth's surface).
04

Explain the Unit of Measurement for Mass and Weight

The units for mass and weight are different. Mass is measured in kilograms (kg) while weight is measured in newtons (N).
05

Provide an Example

Let's consider an object with a mass of 10 kg. To calculate the weight of this object on Earth, use the formula W = mg: W = (10 kg) * (9.81 m/s虏) = 98.1 N The mass of the object is 10 kg and its weight on Earth is 98.1 N.
06

Summarize the Differences

To summarize, mass and weight differ in various ways: 1. Mass is a scalar quantity, while weight is a vector quantity. 2. Mass is the amount of matter in an object and remains constant regardless of its location, whereas weight is the gravitational force acting on an object, and it varies depending on the object's location. 3. Mass is measured in kilograms (kg), while weight is measured in newtons (N). 4. The relationship between mass and weight is given by the formula W = mg, where W is the weight, m is the mass, and g is the gravitational acceleration.

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Key Concepts

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

Mass
Mass refers to the amount of matter in a body. Think of it as the "stuff" that composes an object. Unlike some physical properties, mass does not change even if you move an object from one place to another. So, whether you're on Earth, the Moon, or floating in space, your mass stays the same.
  • Mass is a scalar quantity, meaning it only has magnitude and no direction.
  • It's measured using the unit kilograms (kg).
  • It's intrinsic to the object and doesn't change with location.
Mass helps us understand how much matter an object contains, making it essential in understanding other physical properties like density and energy.
Weight
Weight is a bit trickier than mass because it changes based on where you are. Weight is the force exerted by gravity on an object. Because it involves force, weight is a vector quantity, which means it has both magnitude (how much) and direction (where to). The direction is always towards the center of whatever celestial body you're on.
  • Weight is calculated using the formula: \( W = mg \), where \( W \) is weight, \( m \) is mass, and \( g \) is gravitational acceleration.
  • It's measured in newtons (N), which are the same units used for all forces.
  • The weight of an object changes depending on its location in the universe and the gravitational pull there.
So while your mass remains constant, your weight can change if you move to the Moon, which has less gravity than Earth.
Gravitational Force
Gravitational force is a fundamental force of nature that acts between any two objects with mass. It's this force that gives rise to an object's weight. This force pulls objects towards each other and is why we stay grounded on Earth rather than floating away.
  • It depends on two things: the masses of the objects involved, and the distance between them.
  • The formula to calculate gravitational force is given by Newton's law of universal gravitation: \( F = \frac{Gm_1m_2}{r^2} \), where \( F \) is the force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between them.
  • This force decreases with distance but never truly disappears unless one of the masses is zero.
Understanding gravitational force helps comprehend why objects have weight and how celestial bodies like planets and moons interact.
Scalar and Vector Quantities
Understanding the difference between scalar and vector quantities is crucial for grasping concepts like mass and weight. Scalars are quantities only described by their magnitude. For example, time and mass are scalars; you don't need a direction to define them.
  • Scalars have only magnitude.
  • Examples include time, temperature, and as noted, mass.
Vectors, however, require both magnitude and direction for their description. They tell you not just "how much" but also "in what direction." For instance, forces, including weight, are vectors.
  • Vectors have both magnitude and direction.
  • Examples include velocity, acceleration, and forces such as weight.
Recognizing these differences helps in solving problems across physics by clearly understanding what type of quantity you are dealing with.

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