Unit 2.2 | Common Linear Forces in Physics
- 11 minutes
- 4 formulas
- 20 questions
- 3 videos
Forces exist all around us.
There are forces like weight and friction, and strong nuclear forces.
We will learn about some commonly used linear force in AP Physics and first year Physics. Later we will use these forces to solve real world problems!
This course article contains videos that can only be accessed once enrolled in the Learn AP Physics from Scratch Course.
Unit 2 Breakdown
In this lesson you will learn:
- What are linear forces and why they are important
- How we use forces in Physics
- Seven common linear forces and their equations
The Importance of Forces
Force is the most important concept to learn in Physics.
In fact, the rest of Physics is just learning about different types of forces and how they work.
Think about planets. From this we study gravitational forces.
Now zoom down to the microscopic level. From this we study the forces that hold atoms together. We call this the “strong force” because it is one of the strongest forces to exist!
What is a force?
Simply put, a force is a push or pull.
And it doesn’t have to be a physical push or pull. Magnets, for example, can push and pull without needing to touch.
A force has a direction and a magnitude. Thus it’s a vector quantity.
Reflect back to Newton’s second law: F = ma. This equation tells us that forces cause acceleration.
In this Unit we ONLY cover linear forces — forces that act in a straight line.
Pushing a Box
Think about pushing a box from rest.
As long as your pushing force, is greater than the frictional force, the box will speed up. In other words, you are accelerating the box.
All forces are responsible for accelerating objects.
Units
Newtons (N) is the standard unit for force.
Example: 100 N of pulling force.
Let’s derive the unit of force using Newton’s 2nd Law:
F = m x a → F = [kg] x [m/s2].
*Replace variables on the right side of the arrow with standard units .
So the unit, “Newton,” is a simple way of writing kg·m/s2.
Forces to Know
In order to excel in Physics, you MUST memorize a few basic forces and their formulas.
Forces can be anything! It doesn’t only have the forces given below. There’s no right or wrong way to write these as long as you know what the label means.
For example. Let’s say you want to describe an engine pushing a car. We can “make up” a label called Fengine.
The forces given below are the most common ones you’ll come across in problems.
- Applied forces (FA or A)
- Weight (mg or W or Fw)
- Tension (T or FT)
- Normal force (N or FN)
- Static Friction (fs)
- Kinetic Friction (fk)
- Spring Force (Fspring)
Now let’s cover each force in depth.
Applied Forces
Generally written as FA.
An applied force is a general force. There are no strict rules or equations for it.
Usually an applied force is responsible for pushing or pulling something.
For example. A car speeds up (accelerates). This means there is a force being applied. We can call this force Fengine, we can call it FA, or any other label that describes it best.
Weight
Let me state three commonly misunderstood facts:
- Weight is a force.
- Mass and weight are NOT the same
- Gravity’s pull (your weight) is a force, but g is NOT a force.
Let’s start with g, the acceleration due to gravity.
Acceleration due to Gravity (g)
[katex] g = 9.81 \, m/s^2[/katex]
Look at the units carefully. The units of g are [katex]m/s^2[/katex], which is a unit of acceleration.
Thus, g is an acceleration NOT a force. The force of gravity on you is your weight.
Mass
Mass is what an object is made up of. Your mass is the same everywhere in the universe.
The only way you can lose mass is if you trim your hair, go on a diet, etc.
We measure mass in kilograms (kg). For example: A person that has a mass of 70 kg.
Helpful tip: a scale doesn’t measure your mass. It measures the normal force pushing up on you (your apparent weight), then divides by g to show kg.
The force of Weight
Weight is a force that we get when we multiply mass by acceleration due to gravity.
[katex]\text{Weight} = mg[/katex]
This comes from [katex]F = ma[/katex]. We use the acceleration due to gravity ([katex]g[/katex]) in place of a general acceleration ([katex]a[/katex]).
Weight can also be written as [katex]F_W[/katex], [katex]W[/katex], or [katex]F_g[/katex].
And since [katex]g[/katex] is a vector that always points down, your weight is also a vector that will always point directly down.
All objects, on earth, will have weight.
For example: Suppose I have a mass of 50 kg. My weight will be: 50 kg × 9.81 m/s2 = 490.5 Newtons.
Weight depends on gravity. The less the gravity, the less we will weigh. Astronauts in orbit still have gravity pulling on them; they only feel weightless because they are in free fall.
Tension
Tension forces can be anything involved with ropes, strings, or cables. Here’s a few examples in which you will find tension:
- Elevators
- Hanging signs
- Pulling objects with a cord
- Hanging objects
- Yo-yos
- Guitar or stringed instruments
If your problem involves any of the above, then you will likely be dealing with a tension force.
There is no set equation for tension. You will have to derive it based on each problem. We will cover this in the next lessons.
You can write tension as [katex]T[/katex], [katex]F_T[/katex] or [katex]F_{Tension}[/katex].
Normal Force
This is the force exerted by ANY surface, perpendicular (90°) to that surface.
All surfaces, floors, tables, will exert a normal force.
There is even a normal force acting on you right now! If you are sitting, the normal force is coming from your seat, pushing up equal and opposite to your weight. They balance because you aren’t accelerating, not because of Newton’s third law (weight’s third-law partner is your pull on Earth).
Like tension and applied forces, there is NO set equation for Normal force. You will have to derive an equation for normal forces for every problem.
Misconception on Normal Forces
A lot of students think that normal forces are opposite to weight.
This is not always true. Instead, normal forces are always perpendicular to the surface.
Here’s an example that demonstrates this: Look at the box on the ramp below. While weight points straight down, notice how the normal force doesn’t point opposite to weight. Rather it points perpendicular to the surface.
Friction
There are two types of friction ([katex]f[/katex]) — static friction and kinetic friction.
While they have two different meanings they share the same equation:
[katex] f = \mu N [/katex]
Where N is the normal force, and µ (pronounced ‘mew’) is the coefficient of friction.
The coefficient of friction tells you how rough a surface is.
For example a µ = .1 would be very slippery, like ice. And a µ of .8 would be very rough, like a highway.
Static vs Kinetic Friction
To summarize, static friction holds an object in place, while kinetic friction resists motions once the object is already in motion.
Both use the same formula for friction, but the coefficient for static friction is generally greater than kinetic friction (for the same surface). We write it like this:
[katex] \mu_sN > \mu_kN [/katex]
Friction as you push harder
Spring Force
The spring force comes from Hooke’s Law. It states that the force exerted on a spring is directly proportional to how much you stretch or compress it. Here’s the equation
[katex] F_{spring} = kx [/katex]
Where k is the spring constant and x is the distance compressed/stretched
Anything involving a spring will have a spring force.
Lesson 2.2 Recap
You learned the seven most common linear forces in Physics, their equations, which problems to apply it to, and some misconceptions.
Furthermore, you learned about the significant difference between mass and weight.
Naming forces turned out to be ambiguous, but simple. For example weight can be written as [katex]F_W[/katex], [katex]W[/katex] or [katex]mg[/katex].
Finally, you now understand the difference between static and kinetic friction.
Later, in Lesson 2.4, you will use these forces to derive custom equations.
Lesson 2.3 Preview
In the next lesson we will use our knowledge of forces to create simple force diagrams called FBDs. Drawing FBDs quickly and accurately will assist us in solving complex problems with ease!
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This article was written by Jason