Mass vs. Weight and the Normal Force

Professor Dave Explains
27 Feb 201704:51
EducationalLearning
32 Likes 10 Comments

TLDRIn this informative video, Professor Dave clarifies the common misconception between mass and weight. He explains that mass, a measure of an object's inertia, is scalar and constant, while weight, a force due to gravity, is vector and varies with location. Using the example of a 100 kg person, he illustrates how weight changes with gravity's strength but mass remains the same. The video also touches on the representation of weight in free body diagrams and introduces the concept of the normal force, emphasizing the relationship between mass, weight, and gravitational fields.

Takeaways
  • πŸ“ Mass and weight are distinct terms; mass is a scalar quantity, while weight is a vector.
  • πŸŒ— Mass measures an object's inertia or the amount of matter it contains, and is constant for an object unless there's a significant change in its composition.
  • πŸ”’ Weight is the force exerted on an object due to gravity and has both magnitude and direction.
  • 🌐 The gravitational force on Earth is approximately 9.8 meters per second squared, which affects the weight of objects.
  • πŸŒ™ On the moon, the gravitational pull is about one-sixth that of Earth, resulting in a person weighing considerably less.
  • πŸš€ In the vacuum of space, far from gravitational fields, objects are essentially weightless due to the lack of gravitational force.
  • πŸ”— The relationship between mass and weight is proportional; objects with more mass will have greater weight.
  • πŸ“ Weight can be calculated using Newton's second law: F = ma (Force equals mass times acceleration).
  • πŸ“š Free body diagrams on Earth must include weight as a force, depicted as a vector pointing towards the Earth's center.
  • πŸ›‘οΈ The normal force is the reaction force exerted by a surface, perpendicular to it, and equals the weight of an object when at rest on a flat surface.
  • πŸ”„ Newton's third law states that for every force, there is an equal and opposite force, which applies to the interaction between weight and normal force.
Q & A
  • What is the primary difference between mass and weight?

    -Mass is a scalar quantity that represents the amount of matter in an object and has only magnitude, while weight is a vector quantity that represents the force exerted on an object due to gravity and has both magnitude and direction.

  • How does mass relate to an object's inertia?

    -Mass is a measure of an object's inertia, which is the property that resists changes in its state of motion. The greater the mass, the greater the inertia.

  • Why do we often use the term 'mass' when we refer to our weight in everyday language?

    -In common parlance, we refer to our weight when we actually mean our mass because weight can be calculated from mass and is proportional to it, but mass is the fundamental property that does not change with location.

  • How does the acceleration due to gravity vary between Earth and the Moon?

    -On Earth, the acceleration due to gravity is approximately 9.8 meters per second squared, while on the Moon, it is about one-sixth of that of Earth due to the Moon's smaller mass.

  • What happens to an object's weight in the vacuum of space far from any massive object?

    -In the vacuum of space, far from any massive object, an object will be essentially weightless because there will be no appreciable acceleration due to gravity.

  • How is weight calculated using Newton's second law?

    -Weight can be calculated using the formula F = ma, where F is the force (weight), m is the mass of the object, and a is the acceleration due to gravity (g).

  • What is the significance of the normal force in the context of an object's weight?

    -The normal force is the force exerted by the surface on which an object rests, and it is equal in magnitude and opposite in direction to the object's weight. It acts perpendicular to the surface and prevents the object from sinking into the surface.

  • How does the presence of a gravitational field affect an object's weight?

    -The presence and strength of a gravitational field affect an object's weight because weight is the force of gravity acting on the object's mass. A stronger gravitational field will result in a greater weight, while in a weaker field or no field, the weight will be less or effectively zero.

  • What is the role of mass in a free body diagram?

    -In a free body diagram, mass is represented by the object's weight, which is a vector pointing straight down towards the center of the Earth (or another massive body). The magnitude of this vector is the product of the mass and the local acceleration due to gravity (g).

  • How does Newton's third law relate to the forces acting on an object at rest?

    -Newton's third law states that for every action, there is an equal and opposite reaction. When an object is at rest, the weight (downward force due to gravity) and the normal force (upward force from the surface) are equal in magnitude and opposite in direction, resulting in no net force and thus no acceleration according to Newton's first law.

  • What are some other forces that can act upon objects besides gravity?

    -Besides gravity, objects can be subject to various forces such as friction, tension, applied forces, magnetic forces, and others, all of which can influence the object's state of motion or rest.

Outlines
00:00
πŸ“š Understanding Mass vs. Weight

This paragraph introduces the fundamental difference between mass and weight, clarifying common misconceptions. It explains that mass is a scalar quantity, representing an object's inertia and the amount of matter it contains, while weight is a vector quantity that includes direction and is the force exerted on an object due to gravity. The relationship between mass and weight is proportional, with mass being constant and weight varying based on gravitational influence. The example of a 100 kg person is used to illustrate how weight changes with gravity's strength, such as on Earth, the Moon, and in space, while mass remains the same. The concept of the normal force is introduced as the opposing force to weight when an object is at rest on a surface.

Mindmap
Support and Resources
Comprehension Check
Space
Moon
Earth
Gravity's Role
Scalar vs. Vector
Engagement
Additional Forces
Understanding Distinction
Force Equilibrium
Normal Force
Weight Representation
Examples
Constant Mass
Proportionality
Differences
Weight
Mass
Professor Dave
Common Misconception
Conclusion and Further Learning
Free Body Diagrams and Forces
Relationship between Mass and Weight
Defining Mass and Weight
Introduction
Understanding the Concepts of Mass and Weight
Alert
Keywords
πŸ’‘Mass
Mass is a scalar quantity that represents the amount of matter in an object. It is a measure of an object's inertia, meaning its resistance to any change in its state of motion. In the video, it is emphasized that mass is constant and does not change regardless of location. For instance, a 100-kilogram person has the same mass on Earth, the Moon, or in space, although their weight varies depending on the gravitational field.
πŸ’‘Weight
Weight is a vector quantity that describes the force exerted on an object due to gravity. It has both magnitude and direction, pointing towards the center of the gravitational field. Weight is dependent on both the mass of the object and the local acceleration due to gravity (g). The video clarifies that while mass is constant, weight can change based on the gravitational field, such as being less on the Moon or effectively zero in the vacuum of space.
πŸ’‘Scalar
A scalar is a type of physical quantity that has magnitude but no direction. In the context of the video, mass is described as a scalar because it only has a size value and does not involve direction. This is in contrast to vectors, which have both magnitude and direction.
πŸ’‘Vector
A vector is a physical quantity that has both magnitude and direction. Unlike scalars, vectors are represented by arrows that indicate the size and direction of the force. In the video, weight is identified as a vector because it not only has magnitude, which is the force's strength, but also a direction, which is towards the center of the gravitational field.
πŸ’‘Inertia
Inertia is the property of an object that resists changes in its state of motion. It is directly related to the mass of an object; the greater the mass, the greater the inertia. In the video, inertia is used to explain why mass is a measure of how much matter is present in an object and how it resists changes in motion.
πŸ’‘Gravitational Field
A gravitational field is the region around a massive object where its gravitational force affects other objects. The strength of the gravitational field determines the acceleration due to gravity (g) and thus the weight of objects within that field. The video explains that the gravitational field affects the weight of objects but not their mass.
πŸ’‘Newton's Second Law
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This law is used to calculate weight, as weight is the force due to gravity. The video uses this law to illustrate the relationship between mass, acceleration due to gravity (g), and weight.
πŸ’‘Acceleration Due to Gravity
Acceleration due to gravity is the rate at which objects accelerate towards the Earth when in free fall, ignoring air resistance. It is approximately 9.8 meters per second squared near the Earth's surface. This value varies slightly depending on the location on Earth and is different on other celestial bodies like the Moon. The video explains that this acceleration affects the weight of objects but not their mass.
πŸ’‘Free Body Diagram
A free body diagram is a graphical representation that shows all the forces acting on an object. It is a tool used in physics to analyze the motion of objects by isolating the object from its surroundings and depicting the forces as vectors. In the video, it is mentioned that weight, being a force, must be included in a free body diagram pointing downwards, while the normal force is depicted as an upward force.
πŸ’‘Normal Force
The normal force is the reaction force exerted by a surface on an object in contact with it. It is always perpendicular to the surface and acts in the opposite direction to the force that the object exerts on the surface. In the video, the normal force is discussed in the context of supporting the weight of an object on a flat surface, where it acts upwards to counteract the object's weight.
πŸ’‘Comprehension Check
A comprehension check is a method used in educational content to ensure that the audience has understood the material presented. It often involves questions or prompts that encourage the audience to reflect on what they have learned. In the video, the professor concludes with a comprehension check to reinforce the understanding of the difference between mass and weight.
Highlights

Mass and weight are often confused but have distinct meanings.

Mass is a scalar quantity, representing the measure of an object's inertia or the amount of matter it contains.

Weight is a vector quantity, which means it has both magnitude and direction, and is a force exerted due to gravity.

Gravity is a force that pulls objects towards Earth, affecting weight but not mass.

Mass and weight are proportional; more mass means more weight.

An object's weight can vary depending on its location, due to differences in gravitational pull.

On Earth, the acceleration due to gravity is 9.8 meters per second squared.

The moon's gravity is about one-sixth that of Earth, resulting in less weight for the same mass.

In the vacuum of space, far from gravitational fields, an object can be essentially weightless.

The mass of an object remains constant regardless of its weight in different gravitational environments.

Weight is calculated using Newton's second law, F = ma.

In free body diagrams, weight is represented as a downward vector towards the center of the Earth.

The normal force is the reaction force exerted by a surface, opposite in direction to the weight.

The greater the mass, the greater the weight and the opposing normal force.

When only the normal force and weight act on an object, they are equal, and the object remains at rest.

Understanding the difference between mass and weight is crucial for studying other forces acting on objects.

Transcripts
00:00

Professor Dave here, let's learn the

00:02

difference between mass and weight.

00:10

Most people are familiar with the terms

00:12

mass and weight, and might assume that

00:15

mass is simply a fancy word for weight.

00:18

In actuality this is not the case, and

00:21

the two terms have rather different

00:23

meanings. To put it simply, mass is a

00:26

scalar and weight is a vector. This means

00:30

that mass has only magnitude, since it is

00:33

a measure of an object's inertia, or

00:35

essentially how much matter is present

00:38

within the object. Weight, on the other hand

00:40

has magnitude but also direction because

00:44

it is a force, specifically the force

00:47

that is exerted on an object by virtue

00:49

of its position in a gravitational field.

00:51

We will learn more about gravity later,

00:54

but for now we can just operate under

00:57

the common understanding that gravity is

00:59

a force that pulls things towards Earth.

01:02

Mass and weight are related in that they

01:06

are proportional and objects with more

01:09

mass will weigh more than objects with

01:11

less mass, but they are not the same

01:14

thing, and when we discuss our weight in

01:17

common parlance we are actually

01:19

referring to our mass. Weight can be

01:24

calculated using Newton's second law or

01:27

F = ma. Take an object like a 100

01:30

kilogram person. This value represents

01:33

the mass of the person, which is more or

01:36

less constant barring any huge changes

01:38

in diet, as it is a measure of the amount

01:41

of matter in the person. But the weight

01:45

of the person will depend on their

01:47

location. On the surface of the earth the

01:50

acceleration due to gravity is 9.8

01:53

meters per second squared, so their

01:55

weight will be 980 Newtons. On the moon

01:59

acceleration due to gravity is about

02:01

one-sixth of that of earth, because the

02:04

moon is much less massive, so the person

02:07

will weigh considerably less as well. In

02:11

vacuum of space far away from any

02:14

massive object, the person will be

02:16

essentially weightless, since there will

02:18

be no appreciable acceleration due to

02:21

gravity. In all of these cases the mass

02:25

of the person does not change, but their

02:28

weight will vary depending on the

02:30

presence and strength of a gravitational

02:33

field. Since weight is a force, we will

02:36

have to include weight in any free body

02:39

diagram representing objects on earth.

02:42

This will be a vector with magnitude

02:44

equal to m times g pointing straight

02:47

down towards the center of the earth

02:49

where g represents the local

02:51

acceleration due to gravity. We learned

02:55

from Newton's third law that any force

02:57

has an equal and opposite force and so

02:59

we will often encounter something called

03:01

the normal force. The normal force is

03:05

exerted by whatever surface the object

03:07

sits on, and it points in the direction

03:09

that is perpendicular to the surface. If

03:13

this is a flat horizontal surface, the

03:15

normal force will be straight up

03:17

opposite in direction to the object's

03:20

weight. The more mass an object contains

03:24

the greater its weight and the greater

03:26

the opposing normal force. If these are

03:29

the only two forces acting on the object

03:31

they will be equal, and the object will

03:34

remain at rest. Now that we understand

03:37

the distinction between mass and weight

03:39

as well as the way that weight will be

03:42

depicted in free body diagrams, we are

03:45

ready to look at other forces that can

03:47

act upon objects. Let's check comprehension.

04:19

Thanks for watching, guys. Subscribe to my

04:22

channel for more tutorials, support me on

04:24

patreon so I can keep making content, and

04:26

as always feel free to email me: