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lesson 1: ​ ​ Types of Forces

Newton's laws of motion and forces:.

But did Newton have this in mind?!?

What is a  Force ?

Two types of  force diagrams :, everyday forces :.

Sample Problems : Draw Force Diagrams

Calculating net forces :, sample problems : using fbd s to determine net force.

the four fundamental forces :

Teacher Notes : Egg Spin Experiment for Next class

Quizlet: lesson 1.

Learning Objectives

By the end of this section, you will be able to:

• Distinguish between kinematics and dynamics
• Understand the definition of force
• Identify simple free-body diagrams
• Define the SI unit of force, the newton
• Describe force as a vector

The study of motion is called kinematics , but kinematics only describes the way objects move—their velocity and their acceleration. Dynamics is the study of how forces affect the motion of objects and systems. It considers the causes of motion of objects and systems of interest, where a system is anything being analyzed. The foundation of dynamics are the laws of motion stated by Isaac Newton (1642–1727). These laws provide an example of the breadth and simplicity of principles under which nature functions. They are also universal laws in that they apply to situations on Earth and in space.

Newton’s laws of motion were just one part of the monumental work that has made him legendary ( Figure 5.2 ). The development of Newton’s laws marks the transition from the Renaissance to the modern era. Not until the advent of modern physics was it discovered that Newton’s laws produce a good description of motion only when the objects are moving at speeds much less than the speed of light and when those objects are larger than the size of most molecules (about 10 −9 10 −9 m in diameter). These constraints define the realm of Newtonian mechanics. At the beginning of the twentieth century, Albert Einstein (1879–1955) developed the theory of relativity and, along with many other scientists, quantum mechanics. Quantum mechanics does not have the constraints present in Newtonian physics. All of the situations we consider in this chapter, and all those preceding the introduction of relativity in Relativity , are in the realm of Newtonian physics.

Working Definition of Force

Dynamics is the study of the forces that cause objects and systems to move. To understand this, we need a working definition of force. An intuitive definition of force —that is, a push or a pull—is a good place to start. We know that a push or a pull has both magnitude and direction (therefore, it is a vector quantity), so we can define force as the push or pull on an object with a specific magnitude and direction. Force can be represented by vectors or expressed as a multiple of a standard force.

The push or pull on an object can vary considerably in either magnitude or direction. For example, a cannon exerts a strong force on a cannonball that is launched into the air. In contrast, Earth exerts only a tiny downward pull on a flea. Our everyday experiences also give us a good idea of how multiple forces add. If two people push in different directions on a third person, as illustrated in Figure 5.3 , we might expect the total force to be in the direction shown. Since force is a vector, it adds just like other vectors. Forces, like other vectors, are represented by arrows and can be added using the familiar head-to-tail method or trigonometric methods. These ideas were developed in Vectors .

Figure 5.3 (b) is our first example of a free-body diagram , which is a sketch showing all external forces acting on an object or system. The object or system is represented by a single isolated point (or free body), and only those forces acting on it that originate outside of the object or system—that is, external force s —are shown. (These forces are the only ones shown because only external forces acting on the free body affect its motion. We can ignore any internal forces within the body.) The forces are represented by vectors extending outward from the free body.

Free-body diagrams are useful in analyzing forces acting on an object or system, and are employed extensively in the study and application of Newton’s laws of motion. You will see them throughout this text and in all your studies of physics. The following steps briefly explain how a free-body diagram is created; we examine this strategy in more detail in Drawing Free-Body Diagrams .

Problem-Solving Strategy

Drawing free-body diagrams.

• Draw the object under consideration. If you are treating the object as a particle, represent the object as a point. Place this point at the origin of an xy -coordinate system.
• Include all forces that act on the object, representing these forces as vectors. However, do not include the net force on the object or the forces that the object exerts on its environment.
• Resolve all force vectors into x - and y -components.
• Draw a separate free-body diagram for each object in the problem.

We illustrate this strategy with two examples of free-body diagrams ( Figure 5.4 ). The terms used in this figure are explained in more detail later in the chapter.

The steps given here are sufficient to guide you in this important problem-solving strategy. The final section of this chapter explains in more detail how to draw free-body diagrams when working with the ideas presented in this chapter.

Development of the Force Concept

A quantitative definition of force can be based on some standard force, just as distance is measured in units relative to a standard length. One possibility is to stretch a spring a certain fixed distance ( Figure 5.5 ) and use the force it exerts to pull itself back to its relaxed shape—called a restoring force —as a standard. The magnitude of all other forces can be considered as multiples of this standard unit of force. Many other possibilities exist for standard forces. Some alternative definitions of force will be given later in this chapter.

Let’s analyze force more deeply. Suppose a physics student sits at a table, working diligently on his homework ( Figure 5.6 ). What external forces act on him? Can we determine the origin of these forces?

In most situations, forces are grouped into two categories: contact forces and field forces . As you might guess, contact forces are due to direct physical contact between objects. For example, the student in Figure 5.6 experiences the contact forces C → C → , F → F → , and T → T → , which are exerted by the chair on his posterior, the floor on his feet, and the table on his forearms, respectively. Field forces, however, act without the necessity of physical contact between objects. They depend on the presence of a “field” in the region of space surrounding the body under consideration. Since the student is in Earth’s gravitational field, he feels a gravitational force w → w → ; in other words, he has weight.

You can think of a field as a property of space that is detectable by the forces it exerts. Scientists think there are only four fundamental force fields in nature. These are the gravitational, electromagnetic, strong nuclear, and weak fields (we consider these four forces in nature later in this text). As noted for w → w → in Figure 5.6 , the gravitational field is responsible for the weight of a body. The forces of the electromagnetic field include those of static electricity and magnetism; they are also responsible for the attraction among atoms in bulk matter. Both the strong nuclear and the weak force fields are effective only over distances roughly equal to a length of scale no larger than an atomic nucleus ( 10 −15 m 10 −15 m ). Their range is so small that neither field has influence in the macroscopic world of Newtonian mechanics.

Contact forces are fundamentally electromagnetic. While the elbow of the student in Figure 5.6 is in contact with the tabletop, the atomic charges in his skin interact electromagnetically with the charges in the surface of the table. The net (total) result is the force T → T → . Similarly, when adhesive tape sticks to a piece of paper, the atoms of the tape are intermingled with those of the paper to cause a net electromagnetic force between the two objects. However, in the context of Newtonian mechanics, the electromagnetic origin of contact forces is not an important concern.

Vector Notation for Force

As previously discussed, force is a vector; it has both magnitude and direction. The SI unit of force is called the newton (abbreviated N), and 1 N is the force needed to accelerate an object with a mass of 1 kg at a rate of 1 m/s 2 1 m/s 2 : 1 N = 1 kg · m/s 2 . 1 N = 1 kg · m/s 2 . An easy way to remember the size of a newton is to imagine holding a small apple; it has a weight of about 1 N.

We can thus describe a two-dimensional force in the form F → = a i ^ + b j ^ F → = a i ^ + b j ^ (the unit vectors i ^ and j ^ i ^ and j ^ indicate the direction of these forces along the x -axis and the y -axis, respectively) and a three-dimensional force in the form F → = a i ^ + b j ^ + c k ^ . F → = a i ^ + b j ^ + c k ^ . In Figure 5.3 , let’s suppose that ice skater 1, on the left side of the figure, pushes horizontally with a force of 30.0 N to the right; we represent this as F → 1 = 30.0 i ^ N . F → 1 = 30.0 i ^ N . Similarly, if ice skater 2 pushes with a force of 40.0 N in the positive vertical direction shown, we would write F → 2 = 40.0 j ^ N . F → 2 = 40.0 j ^ N . The resultant of the two forces causes a mass to accelerate—in this case, the third ice skater. This resultant is called the net external force F → net F → net and is found by taking the vector sum of all external forces acting on an object or system (thus, we can also represent net external force as ∑ F → ∑ F → ):

This equation can be extended to any number of forces.

In this example, we have F → net = ∑ F → = F → 1 + F → 2 = 30.0 i ^ + 40.0 j ^ N F → net = ∑ F → = F → 1 + F → 2 = 30.0 i ^ + 40.0 j ^ N . The hypotenuse of the triangle shown in Figure 5.3 is the resultant force, or net force. It is a vector. To find its magnitude (the size of the vector, without regard to direction), we use the rule given in Vectors , taking the square root of the sum of the squares of the components:

The direction is given by

measured from the positive x -axis, as shown in the free-body diagram in Figure 5.3 (b).

Let’s suppose the ice skaters now push the third ice skater with F → 1 = 3.0 i ^ + 8.0 j ^ N F → 1 = 3.0 i ^ + 8.0 j ^ N and F → 2 = 5.0 i ^ + 4.0 j ^ N F → 2 = 5.0 i ^ + 4.0 j ^ N . What is the resultant of these two forces? We must recognize that force is a vector; therefore, we must add using the rules for vector addition:

Check Your Understanding 5.1

Find the magnitude and direction of the net force in the ice skater example just given.

Interactive

Engage the Phet simulation below to learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.

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Force Lesson – An Introduction To Forces

This 3-DAY, 63 slide Force lesson package / Forces Mini Unit begins with an Overview of Force which requires students to collaboratively think about the topic and create a definition. The Four Fundamental Forces are discussed as well as the Forces all around us. It then gets more specific and talks about Normal, Friction and Tension forces as well as the difference between a Contact and an Action at a distance force. Ways of Measuring force as well as System and Free-Body Diagrams, Finding Fnet and Force vectors finish the lesson.

There are many opportunities for students to test their knowledge through “Check Your Understanding” slides with the teacher version containing the answers (these are generally problem-based questions like they would see on a test or quiz). I encourage collaboration and there are also many instances where the students are asked to think critically in small groups. There are 5 videos embedded in the PowerPoint. Simply start the slideshow and click the image and it will open in your browser. The PowerPoint contains diagrams, examples and explanations. It includes the lesson (student and teacher versions of the PowerPoint) and a student lesson handout as a word document which follows the PowerPoint.

Included in the lesson package is:

– The teacher version of the PowerPoint – The student version of the PowerPoint – 5 videos embedded into the PowerPoint – Many opportunities for students to check their understanding – Critical thinking questions to encourage collaboration and inquiry – Student lesson handout

In order, the lesson covers: – Force Overview – What is a Force? – The Four Fundamental Forces – Forces all around us – Normal, Friction and Tension force – Contact vs. Action at a distance force – Measuring force – System and Free-Body Diagrams – Finding Fnet – Force vectors

The student version of the PowerPoint contains multiple blanks that need to be filled in throughout the lesson. These blanks are conveniently underlined and bolded on the teacher copy. I have found this to be the most effective means of keeping my students engaged and active without having them write everything out. This also leaves more time for discussion and activities.

Within my complete Forces Unit you can find the following lesson packages: Lesson 1 – Forces Introduction Lesson 2 – Newton’s 3 Laws of Motion Lesson 3 – Friction Lesson 4 – Universal Gravitation Lesson 5 – Ramps, Pulley’s and Forces

The entire Forces Unit can be purchased at a 32% discount BY CLICKING HERE

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Types of Forces

Forces that act on objects such as friction, gravity, tension, spring force..

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Types of Forces: Explanation, Review, and Examples

• The Albert Team
• Last Updated On: February 16, 2023

Now that you’ve mastered the basics of kinematics, it’s time to get into what causes different movements to occur – forces. A force in physics is generally described as a push or pull that can cause something to accelerate (which includes causing it to stop). There are a few different types of forces and by the end of this article, you should be able to identify each one and start looking for them in the real world. 

What We Review

Describing Forces

A force is a push that can cause something to accelerate. This can be a literal push, for example, pushing on a large piece of furniture to move it around a room. It could be less literal, like pushing the gas pedal in a car. You don’t push on the car itself, but the engine starts working harder to move the car forward. This is a far less literal “push” but it is still a force causing the car to speed up. This “push” can be even less intuitive as forces can also act at a distance. For example, two magnets can attract or repel each other without touching. We’ll learn about these different types of forces soon, but first, let’s establish some language for talking about forces.

Is Force a Vector?

We talked about vectors and scalars back when we first began learning about kinematics and these ideas still apply. Think about when you push a piece of furniture around – maybe having to move your bed out from the wall when you change your sheets. 

You don’t just push on it randomly and hope it will go in the direction you need it to. To move the bed, you push on it in the direction you want it to move. You also probably know how hard you’ll need to push your bed in order to move it. That means you have both a direction and a magnitude, which will be true of all types of forces. So, the answer to the question of Is force a vector? is yes . In fact, sometimes you may have your physics teacher refer specifically to force vectors, meaning a vector describing a force. To draw these vectors yourself, you’d want to make something like the diagram below. 

This is a free body diagram and they’ll come in handy very often. For now, though, you just need to know that it’s how we visualize a vector relative to an object. We’ve written an “F” next to the arrow to show that the vector is specifically a force vector.

What are the Units of Force?

You’ll start to find that after a certain point in physics, most units are named after scientists. For example, the units used to describe force are Newtons (signified with an N). The unit Newtons is named after Sir Isaac Newton – a famous physicist who was one of the first to truly work with and understand forces. When he first published his research, it was absolutely groundbreaking. Today, a few centuries later, we still rely on Newton’s Laws to explain most of what we know about physics. We don’t need to go too far into his laws here, but there is one that helps to explain what Newtons actually are.

Newton’s Laws tell us that force is equal to mass times acceleration. If you’ll recall from previous work, the units for mass are \text{kg} and those for acceleration are \text{ m/s}^2 . If force is the product of these two values, then Newtons must be the product of their units and, in fact, that’s true. One Newton is equivalent to one \text{ kg m/s}^2 . While writing out Newtons alone isn’t too confusing, if you start adding in even more units it can get out of hand quite quickly. So, scientists decided to simplify things and honor Newton for all of his groundbreaking research in the process by creating the Newton.

Types of Forces

You can split the types of forces you encounter in physics into two categories – those that need to touch an object (contact forces) and those that can affect an object from a distance (field forces). We’ll discuss both in-depth and give several common examples of each type. It is possible that you’ll encounter more if you continue to study physics through college and make a career out of it, but for the average high school physics course, this article will be sufficient.

Types of Contact Forces

Contact forces are probably the most obvious ones. These are forces where an object needs to be in direct contact with another (actually touching it) in order to experience a force. The table below lists common types of contact forces:

Types of Forces at a Distance

A more abstract idea is that of a force at a distance. In terms of calculations, field forces work similarly to contact forces, but understanding them takes a little more imagination. Instead of being in direct contact with something, these forces create an area around an object (the field) that can affect other objects around it. These fields technically extend infinitely around the object creating them, but they grow weaker at greater distances and become completely negligible at a given point. The table below lists the most common types of field forces you’re likely to encounter. Depending on the class, you may also encounter some nuclear forces, but we won’t cover those here.

Mass and Weight

The type of force you are most likely to interact with and study is gravity. This is true in everyday life as well as in your physics course – that means it’s really important to understand. In most everyday conversations, people talk about gravity as a thing really big objects have and it doesn’t get much more nuanced than that. In order to properly answer the question What is the force of gravity? we need to go a little bit deeper. Gravity is the field force created by the presence of mass. Any object with mass – from the tiniest of elementary particles to the largest of galaxies – can create a gravitational field. That includes the Earth and the Sun and you and whatever device you’re using to read this article. 

The idea of mass is another place where common language tends to get us confused in the world of physics. We generally think of mass as similar to the word “massive” – something that is very large. We also tend to use it somewhat interchangeably with weight, but in physics, these two concepts are very different. To really understand how we talk about gravity, we’ll need to define weight and how it differs from mass. First, let’s talk about how gravity and weight are related.

How are Gravity and Weight Related?

When you think of weight, you probably think of the number you’d see on a scale at the doctor’s office. While that is correct, there’s a bit more to it from a physics perspective. The number that shows up on the scale is a measurement of how strongly the Earth’s gravitational field is pulling on you. So, your weight would change depending on what gravitational field you were in. For example, if you weigh 120\text{ lbs} on Earth, you’ll only weigh about 20\text{ lbs} on the moon because it has a weaker gravitational field. In addition, if Jupiter has a surface for you to stand on, you would weigh about 300\text{ lbs} .

Your weight is not an inherent property of you. It is a way to measure the strength of the gravitational field that you’re in. All objects create gravitational fields, but we usually only talk about weight when looking at objects like planets, moons, stars, and other celestial bodies large enough to stand on. This is because the weight of a hat on your head generated by the strength of your gravitational field is negligible in comparison to the weight of that hat generated by the strength of the Earth’s gravitational field. But, this leaves the question: If gravity determines weight, what determines gravity? 

What is the Difference Between Mass and Weight?

While weight is determined by the strength of the gravitation field you’re in, the mass of an object doesn’t change. Mass is an inherent property determined by how many elementary particles – electrons, protons, neutrons, etc. – something contains. These elementary particles contain the fundamental properties to shape the universe into the series of gravitational fields that dictate how we live. Adding up the mass of each individual particle in an object will give you the object’s total mass. Then, you can determine the strength of the object’s gravitational field. Newton’s Law of Universal Gravitation explains in more detail how to find the force of gravity between two masses. Right now, it’s important to know that mass is an inherent value of an object (meaning it won’t change depending on environmental conditions), and weight is determined by the strength of the gravitational field an object happens to be in. 

You may have noticed that mass creates the gravitational field and that weight is determined by the strength of a gravitational field. That is one way in which these two properties are tightly linked. Weight is a measure of gravitational field strength, but a gravitational field can only apply a force to an object with mass. So, weight can also be used to measure an object’s mass if the gravitational field strength is already known.

In conclusion, forces shape every aspect of the world we live in from how we walk, to the way we talk, to how we can live on a giant rock orbiting a ball of plasma. We only talked in-depth about gravity here, but as you continue your physics journey you’ll learn about all of the other types of forces mentioned above. If you take your studies far enough you may even learn about some that weren’t mentioned at all. Physics is built on figuring out how the universe acts with itself, and learning about the types of force and how we work with them is a major step in truly understanding the way our universe works.

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Aristotle famously represented a force as anything that causes an object to undergo “unnatural motion”. Sir Isaac Newton was one of the first scientists to study gravity and force. Any kind of force is just a push or a pull. It can be described as a push or pull on an object.

What is Force?

Push or pull of an object is considered a force. Push and pull come from the objects interacting with one another. Terms like stretch and squeeze can also be used to denote force. In Physics, force is defined as:

The push or pull on an object with mass causes it to change its velocity.

Force is an external agent capable of changing a body’s state of rest or motion. It has a magnitude and a direction. The direction towards which the force is applied is known as the direction of the force, and the application of force is the point where force is applied.

The Force can be measured using a spring balance. The SI unit of force is Newton(N).

What are the Effects of Force?

In physics, motion is defined as the change in position with respect to time. In simpler words, motion refers to the movement of a body. Typically, motion can either be described as:

• Change in speed
• Change in direction

The Force has different effects, and here are some of them.

• Force can make a body that is at rest to move.
• It can stop a moving body or slow it down.
• It can accelerate the speed of a moving body.
• It can also change the direction of a moving body along with its shape and size.

Force Videos

Force and its types.

Force – Push And Pull

Centripetal And Centrifugal Force

Tension Force

You may also want to check out these topics given below!

• Force: Push And Pull Action
• Types of Forces
• Centripetal and Centrifugal Force
• Pseudo Force
• Balanced Forc

Formula for Force

The quantity of force is expressed by the vector product of mass (m) and acceleration (a). The equation or the formula for force can mathematically be expressed in the form of:

• a = acceleration

It is articulated in Newton (N) or Kgm/s 2 .

Acceleration a is given by

• v = velocity
• t = time taken

So Force can be articulated as:

Inertia formula is termed as p = mv which can also be articulated as Momentum.

Therefore, Force can be articulated as the rate of change of momentum.

F = p/t = dp/dt

Force formulas are beneficial in finding out the force, mass, acceleration, momentum, velocity in any given problem.

Unit of Force

• In the centimeter gram second system of unit (CGS unit) force is expressed in dyne.
• In the standard international system of unit (SI unit) it is expressed in Newton (N) .

Types of Force

Force is a physical cause that can change an object’s state of motion or dimensions. There are two types of forces based on their applications:

Contact Force

Non-contact force.

Forces that act on a body either directly or through a medium are called contact forces.

Examples of contact forces are:

• Muscular Force
• Mechanical Force
• Frictional Force

We can use the muscular force of animals like bullocks, horses, and camels to get the activities done. The frictional force is another type of contact force, which acts between a pair of a surface in contact and tends to oppose the motion of one surface over the other.

Forces that act through spaces without making direct contact with the body are called non-contact forces.

Examples of non-contact forces are:

• Gravitational Force
• Electrostatic Force
• Magnetic Force

The force exerted by a magnet on other magnets is called magnetic force. Magnetic force and electrostatic force act on an object from a distance. That’s the reason they are non-contact forces. The strength of gravity is an attractive force that is exerted by the Earth on objects, which makes them fall to the land. The weight of a body is the force that is pulled by the earth towards the centre.

Solved Examples

Q.1) How much net force is required to accelerate a 1000 kg car at 4.00 m/s 2 ?

• a = 4.00 m/s 2
• m = 1000 kg

Therefore, 

Q.2) Aimee has a toy car mass of 2 kg. How much force should she apply to the car so that it should travel with the acceleration of 8 m/s 2 ?

• m (Mass of toy car) = 2 Kg,
• a (Acceleration) = 8m/s2,

F is Force to be applied by Aimmee = m × a

= 2 Kg × 8 m/s2 = 16 Kgm/s2  = 16 N.

Q.3) A hammer having a mass of 1 kg going with a speed of 6 m/s hits a wall and comes to rest in 0.1 sec. Compute the obstacle force that makes the hammer stop.

• Mass of Hammer, m = 1 kg
• Initial Velocity, u = 6 m/s
• Final Velocity, v = 0 m/s
• Time Taken, t = 0.1 s

The acceleration is: a = (v – u)/t

Thus, the retarding Force, F = ma = 1 × 60 = 60 N

What is the Line of Action of a Force?

The line along which a force acts on an object is called the force’s line of action . The point where the force is acting on an object is called the point of application of the force . The force which opposes the relative motion between the surfaces of two objects in contact and acts along the surfaces is called the force of friction.

Galileo experimentally proved that objects that are in motion move with constant speed when there is no force acting on it. He could note that when a sphere rolls down an inclined plane, its speed increases because of the gravitational pull acting on it.

When all the forces acting on an object are balanced, the net force acting is zero. But, if all the forces acting on a body result in an unbalanced force, then the unbalanced force can accelerate the body, which means that a net force acting on a body can either change the magnitude of its velocity or change the direction of its velocity. For example, when many forces act on a body, and the body is found to be at rest, we can conclude that the net force acting on the body is zero.

Frequently Asked Questions – FAQs

Which is the weakest force in nature.

Gravity is the weakest force as its coupling constant is small in value.

Which force is strongest?

The strongest force is the strong nuclear force which is 100 times stronger than the electromagnetic force.

What are some types of forces?

Basically, there are two types of forces:

• Non-contact forces
• Contact forces

What are some examples of force?

Some examples of force are:

• Gravitational force
• Electric force
• Magnetic force
• Nuclear force
• Frictional force

Which force causes a charged balloon to attract another balloon?

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what are all the different types of force

contact and non contact force

cohesive and adhesive, surface tension, magnetic, gravitational force, tension force, frictional force, centripetal force, centrifugal force, electrostatics, upthrust, electrical force and nuclear force

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1.4: Forces

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A force is any influence that causes a body to accelerate. Forces on a body can also cause stress in that body, which can result in the body deforming or breaking. Though forces can come from a variety of sources, there are three distinguishing features to every force. These features are the magnitude of the force, the direction of the force, and the point of application of the force. Forces are often represented as vectors (as in the diagram to the right) and each of these features can be determined from a vector representation of the forces on the body.

The magnitude of a force is the degree to which the force will accelerate the body it is acting on; it is represented by a scalar (a single number). The magnitude can also be thought of as the strength of the force. When forces are represented as vectors, the magnitude of the force is usually explicitly labeled. The length of the vector also often corresponds to the relative magnitude of the vector, with longer vectors indicating larger magnitudes.

The magnitude of force is measured in units of mass times length over time squared. In metric units the most common unit is the Newton (N), where one Newton is one kilogram times one meter over one second squared. This means that a force of one Newton would cause a one-kilogram object to accelerate at a rate of one meter per second squared. In English units, the most common unit is the pound (lb), where one pound is equal to one slug times a foot over a second squared. This means that a one-pound force would cause an object with a mass of one slug to accelerate at a rate of one foot per second squared.

\[ Force \, = \, \frac{(mass)(distance)}{(time)^2} \]

\[ 1 \, \text{Newton} \, (N) \, = \, \frac{(kg)(m)}{s^2} \]

\[ 1 \, \text{pound} \, (lb) \, = \, \frac{(slug)(ft)}{s^2} \]

In addition to having magnitudes, forces also have directions. As we said before, a force is any influence that causes a body to accelerate. Since acceleration has a specific direction, force also has a specific direction that matches this acceleration. The direction of the force is indicated in diagrams by the direction of the vector representing the force.

Direction has no units, but it is usually given by reporting angles between the vector representing the force and coordinate axes, or by reporting the X, Y, and Z components of the vector. Often times vectors that have the same direction as one of the coordinate axes will not have any angles or components listed. If this is true, it is usually safe to assume that the direction does match the direction of one of the coordinate axes.

Point of Application:

The point, or points, at which a force is applied to a body is important for understanding how the body will react. For particles, there is only a single point for the forces to act on, but for rigid bodies there are an infinite number of possible points of application. Some points of application will lead to the body undergoing simple linear acceleration; some will exert a moment on the body which will cause the body to undergo rotational acceleration as well as linear acceleration.

Depending on the nature of the point of application of a force, there are three general types of forces. These are point forces , surface forces , and body forces . Below is a diagram of a box being pulled by a rope across a frictionless surface. The box has three forces acting on it. The first is the force from the rope. This is a force applied to a single point on the box, and is therefore modeled as point force. Point forces are represented by a single vector. Second is the normal force from the ground that is supporting the box. Because this force is applied evenly to the bottom surface of the box, it is best modeled as a surface force. Surface forces are indicated by a number of vectors drawn side by side with a profile line to indicate the magnitude of the force at any point. The last force is the gravitational force pulling the box downward. Because this force is applied evenly to the entire volume of the box, it is best modeled as a body force. Body forces are sometimes shown as a field of vectors as shown, though they are often not drawn out at all because they end up cluttering the free body diagram.

We will also sometimes talk about distributed forces . A distributed force is simply another name for either a surface or a body force.

The exact point or surface that the force is acting on can be drawn as either the head or the tail of the force vector in the free body diagram. Because of the principle of transmissibility , both options are known to represent the same physical system.

Types of Force ( Edexcel A Level Maths: Mechanics )

Revision note.

Types of Force

What is a force.

• A force is a vector quantity, it has both magnitude and direction
• A force is a push or a pull on an object
• A force is measured in Newtons
• In A level mathematical models, forces act at a single point called a particle which occupies a single point in space

What types of force are used in mechanics?

• Weight is the effect of mass and gravity, it always acts downwards
• Tension is a pulling force, it always acts away from an object
• Thrust is a pushing force, it always acts towards an object
• Friction is a resistive force, it acts to oppose the motion of an object
• Every surface will produce a reaction force , it will always act perpendicular to the surface

Mass, Gravity and Weight

• Mass is a scalar quantity, measured in kilograms , kg
• Mass is universal, it does not change based on location
• g is the acceleration due to gravity, measured in m s -2
• On Earth, g is approximately 9.8 m s -2 , although its exact value varies with location
• g is different elsewhere in the universe
• Weight is a vector quantity
• Weight varies with location
• Weight always acts vertically downwards towards the ground

Worked example

The diagram below shows a car towing a trailer by a light inextensible string.

Forces D , R , F    and T  N act on the car and caravan as shown.

Write a brief description of which each force represents.

• Braking – suggests thrust
• Air resistance – suggests a resistive force
• It will help you understand the problem
• Add more things to the diagram as you progress through the question
• You may not even need all the forces from your diagram
• You should always round your answers to three significant figures, however if using g = 9.8 m s -2 within a calculation, use two significant figures.

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Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

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We Would Like to Suggest ...

Apply the method described in the paragraph above to construct free-body diagrams for the various situations described below. Answers are shown and explained at the bottom of this page.

• A book is at rest on a tabletop. Diagram the forces acting on the book. See answer.  
• A gymnast holding onto a bar, is suspended motionless in mid-air. The bar is supported by two ropes that attach to the ceiling. Diagram the forces acting on the combination of gymnast and bar. See answer.  
• An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling. See answer.  
• A flying squirrel is gliding (no wing flaps ) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel. See answer.  
• A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. See answer.  
• A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. See answer.  
• A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack. See answer.  
• A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver. See answer.  
• A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Neglect air resistance. Diagram the forces acting upon the sled. See answer.  
• A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. Diagram the forces acting upon the football as it rises upward towards its peak. See answer.  
• A car is coasting to the right and slowing down. Neglect air resistance. Diagram the forces acting upon the car. See answer.

Answers to the above exercise are shown here. If you have difficulty drawing free-body diagrams, then you ought to be concerned. Continue to review the the list of forces and their description and this page in order to gain a comfort with constructing free-body diagrams.

1. A book is at rest on a tabletop. A free-body diagram for this situation looks like this:

Return to Questions

Return to Info on Free-body diagrams

Return to on-line Force Description List

2. A gymnast holding onto a bar, is suspended motionless in mid-air. The bar is supported by two ropes that attach to the ceiling. Diagram the forces acting on the combination of gymnast and bar. A free-body diagram for this situation looks like this:

3. An egg is free-falling from a nest in a tree. Neglect air resistance. A free-body diagram for this situation looks like this:

4. A flying squirrel is gliding (no wing flaps ) from a tree to the ground at constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:

5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:

6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:

7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. A free-body diagram for this situation looks like this:

8. A skydiver is descending with a constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:

9. A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Neglect air resistance. A free-body diagram for this situation looks like this:

10. A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. A free-body diagram for this situation looks like this:

11. A car is coasting to the right and slowing down. Neglect air resistance. A free-body diagram for this situation looks like this:

Return to on-line Force Description List