# Unit 2.3 | Drawing FBD (Force Diagrams) Quickly and Accurately

###### Jason Kuma

Writer | Coach | Builder | Fremont, CA

###### Article Content
This will be a quick and fun lesson. You will learn how to draw FBDs or force diagrams. An FBD is incredibly important tool to solving hard force problems, as you will see in the next lesson. Before moving on to the next lesson Make sure to use all the resources below to master drawing FBDs.

This course article contains videos that can only be accessed once enrolled in the

### Unit 2 Breakdown

You are on Lesson 3 of 8:

#### In this lesson you will learn:

• What are force body diagrams (FBD)
• Steps to draw an FBD
• Direction of net force and acceleration
• Practice drawing FBDs of complex situations
• Common Misconceptions

### What are FBDs?

FBD is short for “Force Body Diagram.”

It is a drawing, like the one below, showing all forces acting ON a object.

We use FBDs to visualize and simplify complex problems.

While this may seem simple, there’s a lot of important rules and concepts to apply on FBDs.

The best way to learn is to read the steps below, then do a lot of practice.

### Steps for Drawing FBDs

As we go through the steps, keep the following example situation in mind. We will refer back to this and see how the rules apply: A box being pushed to the right at a constant speed across the floor.

1. Draw a DOT to represent an object.
• For the situation above you would draw a small dot to represent the box.
2. Identify, then draw all forces acting on the object according to the force rules (cover in 2.2)
• In this case, there is a very clear pushing force. On your dot, you would draw an arrow to the right and label it Fpush or Fapplied.
3. Check for hidden forces.
• In this case the box is moving at constant speed. This means that there should be zero acceleration and zero net force. So another force is needed to cancel out Fpush. This would be the force of friction (f) acting equal but opposite to Fpush.

Let’s try some harder problems together. Be sure to read the important rules first.

#### 5 Important Rules

1. Generally all objects will have a weight force. Weight ALWAYS points straight down.
2. The direction of the net force is the direction of your acceleration
3. Constant speed means 0 acceleration and thus 0 net force
4. Kinetic friction always acts OPPOSITE to the object’s direction of motion.
5. Normal force is drawn perpendicular (90°) to the surface.

### PS – FDBs

Below are some common situations you will encounter. Try drawing an FBD for these 8 problems. Then watch the short video for the explanations for each.

1. A basket is suspended by a rope from the ceiling.
2. A rightward force is applied to a book to accelerate it across a rough desk.
3. A car applies its brakes to slow down.
4. A skydiver descends with constant velocity.
5. A box rests on a sloped incline.
6. An elevator is traveling up and slowing down
7. Five seconds after you kick a soccer ball in the air (air resistance is negligible)
8. Two cables suspend a heavy neon sign at 45° angles

How many did you get right? If you got 7 or more right, you are ready to move on to the next lesson.

If you need more practice, here are some FBD worksheets: [Enroll For Material Access].

### Lesson 2.3 Recap

In this lesson we covered how to quickly and accurately draw an FBD.

You got to apply your knowledge to challenging practice questions then watched me solve them.

### Lesson 2.4 Preview

In the next lesson we will use FBDs to to derive equations and solve interesting, real world problems. This is generally what most students find hard in Physics. But we will break it down and make it super easy to understand.

###### Jason Kuma

Writer | Coach | Builder | Fremont, CA

## Units in AP Physics 1

Unit 1 – Linear Kinematics

Unit 2 – Linear Forces

Unit 3 – Circular Motion

Unit 4 – Energy

Unit 5 – Momentum

Unit 6 – Torque

Unit 7 – Oscillations

Unit 8 – Fluids

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KinematicsForces
\Delta x = v_i t + \frac{1}{2} at^2F = ma
v = v_i + atF_g = \frac{G m_1m_2}{r^2}
a = \frac{\Delta v}{\Delta t}f = \mu N
R = \frac{v_i^2 \sin(2\theta)}{g}
Circular MotionEnergy
F_c = \frac{mv^2}{r}KE = \frac{1}{2} mv^2
a_c = \frac{v^2}{r}PE = mgh
KE_i + PE_i = KE_f + PE_f
MomentumTorque and Rotations
p = m v\tau = r \cdot F \cdot \sin(\theta)
J = \Delta pI = \sum mr^2
p_i = p_fL = I \cdot \omega
Simple Harmonic Motion
F = -k x
T = 2\pi \sqrt{\frac{l}{g}}
T = 2\pi \sqrt{\frac{m}{k}}
ConstantDescription
gAcceleration due to gravity, typically 9.8 , \text{m/s}^2 on Earth’s surface
GUniversal Gravitational Constant, 6.674 \times 10^{-11} , \text{N} \cdot \text{m}^2/\text{kg}^2
\mu_k and \mu_sCoefficients of kinetic (\mu_k) and static (\mu_s) friction, dimensionless. Static friction (\mu_s) is usually greater than kinetic friction (\mu_k) as it resists the start of motion.
kSpring constant, in \text{N/m}
M_E = 5.972 \times 10^{24} , \text{kg} Mass of the Earth
M_M = 7.348 \times 10^{22} , \text{kg} Mass of the Moon
M_M = 1.989 \times 10^{30} , \text{kg} Mass of the Sun
VariableSI Unit
s (Displacement)\text{meters (m)}
v (Velocity)\text{meters per second (m/s)}
a (Acceleration)\text{meters per second squared (m/s}^2\text{)}
t (Time)\text{seconds (s)}
m (Mass)\text{kilograms (kg)}
VariableDerived SI Unit
F (Force)\text{newtons (N)}
E, PE, KE (Energy, Potential Energy, Kinetic Energy)\text{joules (J)}
P (Power)\text{watts (W)}
p (Momentum)\text{kilogram meters per second (kgm/s)}
\tau (Torque)\text{newton meters (Nm)}
I (Moment of Inertia)\text{kilogram meter squared (kgm}^2\text{)}
f (Frequency)\text{hertz (Hz)}

General Metric Conversion Chart

Example of using unit analysis: Convert 5 kilometers to millimeters.

1. Start with the given measurement: \text{5 km}

2. Use the conversion factors for kilometers to meters and meters to millimeters: \text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}}

3. Perform the multiplication: \text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}} = 5 \times 10^3 \times 10^3 \, \text{mm}

4. Simplify to get the final answer: \boxed{5 \times 10^6 \, \text{mm}}

Prefix

Symbol

Power of Ten

Equivalent

Pico-

p

10^{-12}

Nano-

n

10^{-9}

Micro-

µ

10^{-6}

Milli-

m

10^{-3}

Centi-

c

10^{-2}

Deci-

d

10^{-1}

(Base unit)

10^{0}

Deca- or Deka-

da

10^{1}

Hecto-

h

10^{2}

Kilo-

k

10^{3}

Mega-

M

10^{6}

Giga-

G

10^{9}

Tera-

T

10^{12}

1. Some answers may be slightly off by 1% depending on rounding, etc.
2. Answers will use different values of gravity. Some answers use 9.81 m/s2, and other 10 m/s2 for calculations.
3. Variables are sometimes written differently from class to class. For example, sometime initial velocity v_i is written as u ; sometimes \Delta x is written as s .
4. Bookmark questions that you can’t solve so you can come back to them later.
5. Always get help if you can’t figure out a problem. The sooner you can get it cleared up the better chances of you not getting it wrong on a test!

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