Chapter 7: Forces

7.1 Introduction to Forces: Push and Pull

Forces are an essential concept in physics. A force can cause an object to move, stop, speed up, slow down, or change direction. They do this via a “push” or “pull” action. Forces are typically measured in Newtons

There are different methods of categorizing forces. One way is to differentiate between contact and non-contact forces. Contact forces involve physical contact between two objects, such as friction, tension, and the normal force. Non-contact forces act at a distance without any physical contact, such as the gravitational force, electric force, and magnetic force.

That being said, the various methods of categorizing forces (e.g. push vs. pull, contact vs. non-contact, etc.) are not fundamental. These methods can be useful conceptually, but there isn’t necessarily any tangible benefit in grouping forces into different categories like this. The real benefit comes in understanding how to determine whether or not something is a force in the first place. Whether it a “push” force or a “pull” force will not affect the actual physics at play.

7.2 Types of Forces

While categorizing forces is not terribly useful, knowing the different types of forces is. The reason why this is important is because some forces have equations associated with them. Knowing these equations can simplify our problem solving process immensely.

• Tension is a force that is transmitted through a string, rope, or cable when it is pulled taut. It is a contact force that is applied in a direction parallel to the length of the string, rope, or cable. We denote the tension force generally as either or
• The normal force is the force that is perpendicular to a surface and which prevents an object from falling through it. It occurs when an object is placed on a surface, and the surface pushes back against the object with an equal and opposite force. The word normal is synonymous with perpendicular as the force is directed perpendicular to the surface upon which the object is placed. The normal force is denoted as either or
• The force due to gravity attracts two objects with mass toward each other. On Earth, we calculate the force due to gravity as:

with and the direction always pointing straight down (toward the center of the Earth). Sometimes this is referred to as the weight of an object such that we write . Thus, it is common to denote the force due to gravity as either or

• The spring force is yet another example. It is calculated by the formula:

.

The spring force is often called a restoring force as it tries to restore a spring (or any elastic material) to its equilibrium position. This in indicated by the presence of the negative sign, though this may not be obvious at first. The use of references the unit vector in the x direction. Unit vectors have a magnitude of 1, so it does not change the magnitude of the spring force. Instead it helps us keep track of the direction that the force is pointing in. We know that forces are vectors and must, therefore, have both magnitude and direction. The spring force is no different.

• Air resistance is the force that opposes the motion of an object through the air. It is a type of frictional force that acts in the opposite direction to the object’s motion. For now, we will ignore friction and air resistance. As we will see, these forces are negligible in a surprising number of situations. Air resistance is often denoted in physics 1 courses as Note that here is generally lower case by convention.
• Friction is the force that opposes the motion of two surfaces that are in contact. It occurs whenever two surfaces are in contact with each other and are moving relative to each other, or when one surface is moving and the other is stationary. The force of friction depends on the type of surface and the force pressing the two surfaces together. We will discuss friction in much greater detail in Chapter 13. For now, know that there are two types of friction: static and kinetic Note that these both follow the same convention as air resistance with being lower case.
• Applied forces are ones which do not necessarily fall under one of the previous categories but are caused by something acting on the system. For example, you might push a box across the floor. This would be an applied force because you are causing the force in this situation. Applied forces are generally denoted by However, any label could potentially be appropriate. If someone named Alice is pushing the box across the floor, you could just as properly label the force as

7.3 Forces as Vectors

As we have seen, forces are vectors and thus have both magnitude and direction. The direction of the force is given by the direction of the vector, and the magnitude is given by the length of the vector. To solve problems involving forces, it is important to break down the forces into their vector components, which are the forces acting in the x and y directions.

Chapter Summary

In this chapter, we introduced the concept of forces, essential entities in physics that can cause an object to move, stop, speed up, slow down, or change direction through a “push” or “pull”. They can be categorized into contact and non-contact categories; however, the categorization is not as essential as understanding the nature of the force itself.

We discussed in detail various types of forces: tension, normal, gravitational, spring, air resistance, friction, and applied forces. Each type of force has unique properties and some have corresponding equations that simplify problem-solving. There are many other types of forces beyond the ones mentioned here. However, those are better discussed in later physics courses.

Enroll on Canvas

This course uses Canvas for homework assignments, quizzes, and exams. These assignments are open to everyone. Anyone is allowed to enroll in the Canvas course. In fact, this is highly encouraged as it will help you track your progress as you go through the course. Graded feedback will help you get an idea for what your grade would actually be in a Physics 1 college course. Use this link to enroll in the Canvas course.

Knowledge Check

Answer the quiz questions below.

Continue to Chapter 8: Force Diagrams (Free-Body Diagrams)

Back to Chapter 6: Constant Acceleration

Are you enjoying this content? Read more from our Physics 1 course here!

Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content!