Chapter 1: Problem 14
Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?
Short Answer
Expert verified
Mass measures matter and is constant, while weight measures gravitational force and varies. Weight on the Moon is one-sixth of Earth's because the Moon's gravity is weaker.
Step by step solution
01
Define Mass
Mass is a measure of the amount of matter in an object. It is usually measured in kilograms (kg) and is a scalar quantity, which means it has magnitude but no direction. Mass is a constant property and does not change based on location.
02
Define Weight
Weight is the force exerted on an object due to gravity. It is measured in newtons (N) and is a vector quantity, meaning it has both magnitude and direction. Weight can be calculated using the formula: \(weight = mass \times gravitational\text{ acceleration} (g)\).
03
Compare Mass and Weight
Mass and weight are different because mass is a measure of matter, whereas weight is a measure of the force of gravity acting on that matter. Mass remains constant regardless of location, while weight varies depending on the gravitational pull at different locations.
04
Gravitational Acceleration on Earth
On Earth, the gravitational acceleration is approximately \(9.8 \text{ m/s}^2\). This means if an object has a mass of 1 kg, its weight on Earth is \(1 \text{ kg} \times 9.8 \text{ m/s}^2 = 9.8 \text{ N}\).
05
Gravitational Acceleration on the Moon
The Moon's gravitational acceleration is approximately \(1.63 \text{ m/s}^2\). This is about one-sixth of Earth’s gravitational acceleration.
06
Calculate Weight on the Moon
Since the Moon's gravity is about one-sixth of Earth's, an object will weigh one-sixth as much on the Moon. For example, if an object weighs \(60 \text{ N}\) on Earth, it will weigh \(\frac{60}{6} = 10 \text{ N}\) on the Moon.
07
Summary of Differences
Mass is constant and unaffected by location, whereas weight depends on the local gravitational field. Weight on the Moon is one-sixth that on Earth because the Moon's gravitational pull is weaker.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass
Mass is the measurement of the amount of matter in an object. Matter consists of all the atoms and molecules in the object. This quantity is typically measured in kilograms (kg).
Mass doesn't change regardless of where the object is located.
So, if you have a mass of 70 kg on Earth, you will still have a mass of 70 kg on the Moon or anywhere else in the universe.
Mass is a scalar quantity, which means it simply has a magnitude and no direction. If you were to imagine mass as a property, think of it as the 'stuff' an object is made of. No matter where you go, this 'stuff' doesn't change.
Mass doesn't change regardless of where the object is located.
So, if you have a mass of 70 kg on Earth, you will still have a mass of 70 kg on the Moon or anywhere else in the universe.
Mass is a scalar quantity, which means it simply has a magnitude and no direction. If you were to imagine mass as a property, think of it as the 'stuff' an object is made of. No matter where you go, this 'stuff' doesn't change.
Weight
Weight is the force that gravity exerts on an object. Unlike mass, weight can change based on where you are, because the force of gravity changes in different locations. Weight is measured in newtons (N).
To calculate weight, you use the formula:
\[\text{weight} = \text{mass} \times \text{gravitational acceleration} (g)\]
An important distinction is that weight is a vector quantity. This means it has both magnitude and direction. The direction is always pointing towards the center of the planet or moon that creates the gravitational pull.
If you weigh 60 N on Earth, you would weigh much less on the Moon due to the Moon's weaker gravitational force.
To calculate weight, you use the formula:
\[\text{weight} = \text{mass} \times \text{gravitational acceleration} (g)\]
An important distinction is that weight is a vector quantity. This means it has both magnitude and direction. The direction is always pointing towards the center of the planet or moon that creates the gravitational pull.
If you weigh 60 N on Earth, you would weigh much less on the Moon due to the Moon's weaker gravitational force.
Gravitational Acceleration
Gravitational acceleration, denoted as 'g', is the acceleration of an object due to the force of gravity. On Earth, this value is approximately \[9.8 \text{ m/s}^2\], but it changes based on the celestial body.
For instance, on the Moon, the gravitational acceleration is about \[1.63 \text{ m/s}^2\]
When calculating weight, it's crucial to use the gravitational acceleration of the location in question. That is why your weight differs between Earth and the Moon.
If you have a mass of 1 kg, on Earth your weight would be \[1 \text{ kg} \times 9.8 \text{ m/s}^2 = 9.8 \text{ N}\]
Whereas on the Moon, your weight would be \[1 \text{ kg} \times 1.63 \text{ m/s}^2 = 1.63 \text{ N}\].
For instance, on the Moon, the gravitational acceleration is about \[1.63 \text{ m/s}^2\]
When calculating weight, it's crucial to use the gravitational acceleration of the location in question. That is why your weight differs between Earth and the Moon.
If you have a mass of 1 kg, on Earth your weight would be \[1 \text{ kg} \times 9.8 \text{ m/s}^2 = 9.8 \text{ N}\]
Whereas on the Moon, your weight would be \[1 \text{ kg} \times 1.63 \text{ m/s}^2 = 1.63 \text{ N}\].
Scalar Quantity
A scalar quantity is any physical measurement that has magnitude but no direction. Mass is a perfect example of this.
Other examples include temperature, speed, and energy.
When you state the mass of an object, you don't have to specify a direction.
It's enough to say something weighs 10 kg, without stating any direction. Scalars make calculations simpler, as you only deal with their numerical values without considering their orientation in space.
Other examples include temperature, speed, and energy.
When you state the mass of an object, you don't have to specify a direction.
It's enough to say something weighs 10 kg, without stating any direction. Scalars make calculations simpler, as you only deal with their numerical values without considering their orientation in space.
Vector Quantity
A vector quantity has both magnitude and direction. Weight falls into this category.
Other examples of vector quantities include velocity, force, and displacement.
Vectors are typically represented by arrows to indicate their direction and magnitude.
For instance, the weight of an object not only has a value (magnitude), but it also points toward the center of the gravitational source (Earth, Moon, etc.). This directional component makes vectors more complex compared to scalars, as one has to account for both how much and which way.
Other examples of vector quantities include velocity, force, and displacement.
Vectors are typically represented by arrows to indicate their direction and magnitude.
For instance, the weight of an object not only has a value (magnitude), but it also points toward the center of the gravitational source (Earth, Moon, etc.). This directional component makes vectors more complex compared to scalars, as one has to account for both how much and which way.
