In today’s post, we will be discussing forces:
What are forces? A force is the action of one body against another. When we apply a force to an object, that object will usually move in the direction we apply that force. (Example: You push a shopping cart with the applied force of your hand. The cart moves in the direction you push it).
Newton’s Laws of Motion
Before we discuss equations to find forces, we need to discuss Newton’s 3 Laws of Motion – 3 of the most important laws in physics! These 3 Laws are discussed in the video below at 0:28.
Fundamental Dimensions
What are fundamental dimensions? Almost every unit we use in Physics I can be broken down into three main units:
a) Mass, M
b) Length, L
c) Time, T
For example, if we look at a Newton (Newtons are used to measure force), the units are kilogram * meter / second^2. Kilograms are units of mass, meters are units of length, and seconds are units of time! So a Newton is a combination of the three basic dimensions, and is a unit of mass * length / time^2. This is at 5:28 in the video.
Different Types of Forces and Free Body Diagrams
There are many different types of forces at play on everyday objects. Force is measured in units of Newtons. Each force has certain characteristics, which are the following:
a) Each force either usually acts in the x-direction, y-direction, or both.
b) Each force can have its own equation to calculate the magnitude if you are given other information in a word problem.
c) Each force comes into play only in certain situations.
d) Each force has its own subscript to identify the type of force. Force is denoted with a big F, and a little subscript indicates the type of force it is (eg. Fg means Force of Gravity).
e) Each force can be either a Contact Force (forces that cause movement when you touch them) or a Body force/Action at a Distance force (forces that cause movement on an object without directly touching it)
Free Body Diagrams (FBDs) are simplified diagrams using arrows to show all the different forces at play on an object, and the directions which those forces act in. Drawing FBDs is discussed at 15:02 in the attached video above.
We can set up Newton’s second law, Sum of Forces = mass * acceleration, once we have our FBD’s, in order to sum the forces in each direction and solve for their magnitude (that part is not covered in this post though). The different forces that usually come up in FBDs are the following:
a) Force of gravity – this is the only body/action at a distance force! The rest of the forces that follow are contact forces.
Denoted by: Fg or W (for weight)
Direction: Almost always directly down, in the y-axis! On inclined surfaces, this might change.
Used when: ALWAYS! Gravity is ALWAYS acting on every object that is on Earth.
Equation: W = Fg = mass (in kilograms) * gravitational acceleration constant (9.8 meters/second^2).
b) Normal Force.
Denoted by: Fn.
Direction: Perpendicular to the surface the object rests on, usually in the direction opposite to gravity, which is up in the y-axis. On inclined surfaces, this might change.
Used when: Anytime your object is resting on a surface.
Equation: No specific equation
c) Tension Force.
Denoted by: Ft.
Direction: In the direction your object is being pulled by the rope/pulley/string. Can usually be in either x, y, or both directions.
Used when: Anytime your object is being pulled by a rope/pulley/string
Equation: No specific equation
d) Friction Force.
Denoted by: Ff. Can be specifically Ffk, Ffs, or Ffs max.
Direction: Opposite to the direction that the object is moving in, usually in the x-direction.
Used when: Ffk (force of kinetic friction) is when your object is moving. Ffs (force of static friction) is when your object is not moving. Ffs max (maximum force of static friction) is the maximum amount of force that needs to be applied in order to get the object to move, right before static friction becomes kinetic friction.
Equation: All these types of frictional forces have the same equation, Ff = Fn (normal force) * U. U can be U with different subscripts like Uk, Us, or Us max. The U is called “mew” and is actually a greek letter that denotes the coefficient of friction. (See image below)
e) Buoyant Force.
Denoted by: Fb
Direction: Perpendicular to surface that your object is resting on (usually opposite to Fg, and points up in the y-axis).
Used when: Anytime your object is resting on water. This is analogous to the normal force, which is when your object rests on any surface. But Fb is used only when you’re on water.
Equation: No specific equation
f) Applied Force.
Denoted by: Fa
Direction: Can be in the x, y, or both directions.
Used when: Anytime your object is being physically pushed or pulled from something that is not a rope/pulley/string (otherwise it would be Force of Tension)
Equation: No specific equation
g) Drag Force.
Denoted by: Fd.
Direction: Usually points directly upward in the y-axis. This force is air resistance that slows you down when you are in free fall, so it is like friction but in the air.
Used when: Anytime an object is in free fall through the air.
Equation: No specific equation.
h) Spring Force.
Denoted by: Fs.
Direction: This can be in the x or y direction, but usually not both.
Used when: Your object is attached to a spring. Usually this will be a whole unit on its own and won’t appear in the early stages of forces and FBDs.
Equation: Hooke’s Law states that the Spring Force Fs = k * x. k is the spring constant, which is a constant that’s different for every spring. Spring constant is measured in Newtons/meter, N/m. x is the displacement of the spring, and it can be a positive or negative number depending whether the spring was stretched or compressed. x is measured in meters, m.
