Download Notes: Free Body Diagrams

Notes: Free Body Diagrams
Level 1: The Normal Force
In this section, we are going to look at the different types of forces that can act on an object. We are going to
learn the most common ones we see in physics.
Weight
You are already familiar with weight. Recall from the last section that weight (force of gravity) is:
𝐹𝑔 = 𝑚𝑔
Normal Force
A normal force occurs when a surface pushes back on an object. For example, you are sitting in your chair,
pushing down on the chair. The chair is pushing up the exact same amount. That means if your weight is
pressing 500 N down, the chair is pushing up 500 N.
For flat surfaces only, the force of gravity must be equal and opposite to the normal force.
When an object is resting on a flat table, the total forces acting on it sum up to zero. We get a net force of zero
because there are two forces acting on the object- gravity (which pulls the object down) and the normal force,
which pushes back up, and these two forces cancel one another. You will see this written
as FN or sometimes just N (thought I hate this… it is out there).
The forces in this situation are balanced, so the box could be doing one of two thingsmoving at a constant velocity or stilling still. It is not accelerating, unless another
unbalanced force gets involved. An example of a resting object with weight and normal
forces balanced is your book sitting on a table. An example of an object with the force of
gravity and the normal force balanced that is moving at a pretty constant velocity is a
hockey puck gliding across the ice.
Level 2: Other Types of Forces
Force of Friction
Friction is a force that fights motion. If you push a box forward, friction will fight your motion. It tries to stop the
box from moving.
Key Idea
Friction always acts in the opposite direction of motion.
This means that if a ball is rolling forward across a field, friction is pushing backward. If you push a chair to the
left, friction is pushing right. If you slide across the floor in your socks to the right, friction is pushing to the left.
If you push a box across the floor, it seems like there is only one force acting on the box. Actually, there are
four- the force of gravity (weight) pulling down, the normal force of the floor pushing back up, the force you are
applying to the box, and the force of friction. The picture below shows the forces acting on the box.
Imagine kicking a book across the floor. Newton’s 1st Law says the book should go forever, but instead it slows
to a stop. What stopped the book? Friction. Here is a picture of that happening:
The box in this picture is moving to the right, slowing down. The force of gravity and the
normal force are balanced, so they cancel out. That leaves the force of friction as the net
force. It looks like the box should be moving to the right. Actually it is moving to the left
and slowing down. Why is that? Forces don’t just speed objects up-they cause us to
accelerate, which can mean slow down, speed up or change direction. In this case,
the force dragging down the box, slowing it down.
Force to Tension
A force of tension is a force caused by a rope, string or cable pulling on it. You will see this written as F T or
sometimes just T. If there is a rope- there is probably a force of tension.
Air Resistance
This is pretty much friction caused by air. You know, like the stuff that makes your dog look funny when he
sticks his head out the window. If something is moving and there is air- there is air resistance.
Spring Force
The force of a spring acting on an object. We use this for anything stretchy or boing-y. When you go bungee
jumping, you are relying on this force to keep you from crashing into the ground below. If there is a spring
involved, there is probably a spring force.
Force Applied
We can use this for pretty much all the other forces acting on the object that don’t fit into the above categories.
If a hand is pushing on a block, we can say it is an applied force. If you kick a soccer ball, we can say it is the
applied force. You can use this for really any other force, until I tell you otherwise.
Level 3: Drawing Free Body Diagrams
When we are working with forces, we often need to find the net force
acting on an object. To do this, we first start by sketching a picture of the
forces acting on it. We call this picture a free body diagram.
There are a few rules we should follow when drawing a free body
diagram.
1.
2.
3.
4.
Always draw the forces from the center of the object.
The stronger the force is, the longer the arrow is.
The arrow should point in the direction for force is acting
Label the forces acting with letters/symbols
The picture on the right helps you see what this looks like.
Here are a few hints when working with free body diagrams:


The force of gravity always points straight down.
The normal force will always push straight up from a surface. See the examples below. Look carefully
at the last two!


If an object is moving in one direction, friction is acting in the opposite direction.
Think about whether the forces on opposite sides are balanced or not. If they are, the two arrows should
be about the same length. For example, on a flat surface, the force of gravity and the normal force
should have the same length.
Level 4: Using the Free Body Diagram in Calculations
Why do we even waste our time drawing this pictures? Because once we do, it is a lot easier to calculate the net
force acting on an object.
Calculating Force
The equation we use to measure force is:
𝐹𝑛𝑒𝑡 = 𝑚𝑎
where Fnet is the total force acting on an object, m is the mass of the object and a is the acceleration of the
object.
We measure force in Newtons (N).
Newton  kg m/s2
F net (F net) is called a lot of different things: the net force, the total force, or the resultant force. They all pretty
much mean the same thing- add the forces acting on the object together. Sometimes people show this with a
little summation sign, too.
𝐹𝑛𝑒𝑡 = ∑ 𝐹
Don’t let that symbol scare you. It just means that you need to add up all the forces acting on the object. It
basically means Fnet. This is actually used pretty widely in higher level math. It just means “add up”. For
example, let’s say you were given three paychecks this month- one for $100, one for $150, and another for $100.
We could say:
∑ 𝑝𝑎𝑦𝑐ℎ𝑒𝑐𝑘𝑠 = 100 + 150 + 100 = $350
Finding the Net Force
Review
In previous lessons, we learned to add and subtract forces.
We also
Do you
In real
often run into situations that look a little
complicated. It helps to keep the forces
in the x and y directions. Look carefully at
example below to see how to do this.
saw a lot of forces that canceled on another out (see the
examples below. Above them, their net forces are stated.
remember how to find these?
life, we
more
organized
the
5-5
𝑭𝒏𝒆𝒕,𝒙
𝑭𝒏𝒆𝒕,𝒙 = 𝟎𝑵
𝑭𝒏𝒆𝒕,𝒙
𝑭𝒏𝒆𝒕,𝒚
5, left
3-3
𝑭𝒏𝒆𝒕,𝒙 = 𝟓𝑵, 𝒍𝒆𝒇𝒕
𝐹𝑛𝑒𝑡,𝑦 = 𝟎𝑵
𝑭𝒏𝒆𝒕,𝒚
3-3
𝐹𝑛𝑒𝑡,𝑦 = 𝟎𝑵
Finding the Acceleration
Once we know the Fnet in each direction, we can learn a lot about how an object is moving. We do this by using
the equation I already forced you already learned 𝐹𝑛𝑒𝑡 = 𝑚𝑎.
These can actually be pretty fun. They are usually little puzzles. You figure out whatever you can and keep
working at it until you’ve solved the whole thing. They are close cousins of Sudoku puzzles. You should try them
next time you are out on a relaxing date.
Let me model one for you. Let’s say someone gave me the free body diagram below and asked me to find its net
force, mass, and its acceleration. Well, first, I would kick back, put on some slippers, maybe make some
calming tea, and settle into my favorite chair at home for a comfy evening puzzle solving.
Example
Find Fnet, mass and acceleration in the situation below.
First, I would figure out the net force, because that looks pretty easy. There are no forces in the x direction, so I
would have to write:
𝐹𝑛𝑒𝑡,𝑥 = 0
Then I’d total up the forces in the y direction.
𝐹𝑛𝑒𝑡,𝑦 = 40 − 25 = 15 𝑁 𝑢𝑝
Notice I included the direction there. That is necessary.
That was easy enough. Now, they asked me to find the mass. Hmmm… at first this seems impossible because I
don’t have the acceleration. But then I realize they gave me the force of gravity (look up at the free body
diagram). Woot woot! I can use the weight equation for find mass.
𝐹𝑔𝑟𝑎𝑣 = 𝑚𝑔
−25 = 𝑚(−9.8)
𝑚 = 2.6 𝑘𝑔
Alright! Now we are rolling. At this point, I would probably reward myself with a tasty oatmeal cookie. Now, we
are really close. Just a little further…. we have to find the acceleration. To do this, I would use what I learned
above.
𝐹𝑛𝑒𝑡 = 𝑚𝑎
15 = (2.6)𝑎
𝑎 = 5.8 𝑚/𝑠 2
And… done! Now I would congratulate by telling myself that I’m smart and having a celebratory cookie.
Constant Velocity and Acceleration
You should always check the problem for the words “constant velocity” and “at rest”. These words should
reach out and slap you in the face. If you see these words, it means the forces need to be balanced. The net
force will have to add up to zero. If you don’t see these words, you can assume the object is accelerating.
Words
“at rest” or “constant
velocity”
What They Mean
No acceleration
The forces should…
Be balanced
Cancel one another out
Fnet=0
“accelerating” “speeding
up” “slowing down”
Accelerating
Unbalanced
Some of the forces cancel out, but not
all of them
Fnet=ma
Example Problem
A toy car glides along a floor with a constant velocity. Its motor pushes it forward with a force of 20 N. What is
the force of friction acting on it?
Solution
The force of friction acting on the toy car is 20 N. We know this because the car is moving at a constant velocity.
This means it has balanced forces acting on it. The two 25 N force are already balanced. That means the 20 N
force must be canceled out by another 20 N force.
Level 5: Friction
So far, we’ve covered how to solve for how to find the net force, missing forces and the acceleration. In some of
those problems, we even found friction. In many of them, I gave you the force of friction. Where did that
number come from? How can we calculate force? In this section, we explore how to do that.
Types of Force
Static Friction: This is the type of force that fights us when we want to get something to start moving. If I
push against a refrigerator, and I push and push and it just won’t budge, I am fighting static friction. The
harder I push, the more the object pushes back. All the way up until the last second, when it starts to
move then, it is…
Kinetic Friction: Kinetic friction is the type of friction that fights your motion when you are already
moving. This is the type you are used to. If my car is rolling down the highway, friction is trying to slow it
down. When a book slides across a tabletop, friction is what brings it to a stop.
The Coefficient of Friction
The coefficient of friction is a number that tells us how much two surfaces rub against another. If the coefficient
of friction is a small number, there won’t be a lot of friction. If the coefficient of friction is a high number, there
will be a lot of force. Here are some common coefficients of friction:
Notice there is a coefficient of friction for static friction
(in the left column) and one for kinetic friction (in the
right column). These are not always the same.
Some object are very smooth and won’t rub against
one another very much. They have a small coefficient
of friction (such as Teflon and steel, whose µK = 0.04).
Sometimes two surfaces really rub against one another
and cause a lot of friction (like steel on steel, µ K = 0.57)
Notice there aren’t any units on the coefficient of
friction. This is kind of nice- we actually don’t have any.
It’s one of the few values in physics that doesn’t have a
unit.
If the object is at rest, you will use 𝜇𝑠 , the coefficient of
static friction. If the object is moving, you will use 𝜇𝑘 , the coefficient of kinetic friction.
Calculating Friction
We’ve cover this equation in the past, so it might be familiar to you:
𝐹𝑓𝑟 = 𝜇𝐹𝑁
𝐹𝑓𝑟  force of friction (Newtons)
𝜇  coefficient of friction. Like that symbol? It is called mu. Ask me and I’ll show you a stupid way to
remember it. This guy has no units.
𝐹𝑁  normal force (Newtons)
Let’s practice an easy calculation.
Example Problem
A rubber tire with a normal force of 100 N is moving across dry concrete. a) What is the coefficent of friction
between the two surfaces? b) What is the force of friction on the tire? Use the chart above to help you.
Solution
a) Looking at the chart, I see rubber and dry concrete is listed. Which one should I choose? Well, the tire is
moving, so I need to choose the coefficient of kinetic friction. The chart tells me 𝜇𝑘 ,= 0.8
b)
𝐹𝑓𝑟 = 𝜇𝐹𝑁
𝐹𝑓𝑟 = (0.8)(100)
𝐹𝑓𝑟 = 80 𝑁
Example Problem
A sled made of waxed wood has a mass of 10 kg. A girl (mass=25 kg) sliding to a stop on wet snow. How much
friction is acting on her? Use the coefficient chart to help you out.
Solution
Draw a free body diagram of the situation.
We don’t actually know the value of any of these forces yet, so we will have to calculate them. We have the
masses, so finding the force of gravity should be pretty easy.
𝐹𝑔 = 𝑚𝑔
We have use the mass of the kid and the sled together.
𝐹𝑔 = (35)(9.8)
𝐹𝑔 = 𝑚𝑔
𝐹𝑔 = 343 𝑁
I added this to my free body diagram (right). If that is the force of gravity,
what is our normal force? It should have the same magnitude, but the
normal force pushes up, not down.
Now, all we need to find is the force of friction. At first, it looks hopeless.
Then, we remember the friction equation.
𝐹𝑓𝑟 = 𝜇𝐹𝑁
We already know the normal force (343 N). We use the chart to look up the
coefficient of kinetic friction between wood and snow. 𝜇𝑘 ,= 0.1
𝐹𝑓𝑟 = (0.1)(343)
𝐹𝑓𝑟 = 34.4 𝑁