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### Course: AP®︎/College Physics 1>Unit 3

Lesson 1: Introduction to forces and free body diagrams

# Introduction to forces and free body diagrams review

Review the key concepts and skills for forces, including how to draw free body diagrams.

## Key terms

TermMeaning
ForceA push or pull on an object, usually has symbol $F$. Has SI units of Newtons ($\text{N}$) or $\frac{\text{kg m}}{{\text{s}}^{2}}$.
Contact forceA force that requires contact between objects. Examples are tension, normal force, and friction.
Long range forceA force that does not need contact between objects to exist. One example is the gravitational force (weight).
Free body diagramA diagram showing the forces acting on the object. The object is represented by a dot with forces are drawn as arrows pointing away from the dot. Sometimes called force diagrams.

## Types of forces

Force (symbol)Force typeDescription
Weight (${F}_{g}$ or $W$)Long rangeForce from gravity acting on an object with mass. Sometimes called force of gravity. Pulls towards the Earth (down) always.
Tension (${F}_{T}$ or $T$)ContactForce of something pulling on an object. Can be caused by a string, rope, chain, cord, cable, or wire.Pulls along the direction of the rope on the object.
Normal force (${F}_{N}$ or $N$)ContactForce between two objects when they touch. Pushes perpendicularly to the object’s surface.
Friction (${F}_{f}$ or $f$)ContactForce resisting sliding between surfaces. Pushes parallel to the contact surface and in the opposite direction of sliding.

## How to make a free body diagram

1. Start by identifying the contact forces. Let's look for what the object is touching by outlining the object (see Figure 1 below). Draw a dot where something touches the outline; where there is a dot, there must be at least one contact force. Draw the force vectors at the contact points to represent how they push or pull on the object (including correct direction).
2. After we have identified the contact forces, draw a dot to represent the object we are interested in (see Figure 2 below). We only want to find the forces acting on our object and not forces the object exerts on other objects.
3. Draw a coordinate system and label the positive directions. If the object is on an incline, then align the axes with the incline.
4. Draw the contact forces on the dot with an arrow pointing away from the dot. Make sure the arrow lengths are relatively proportional to each other. Label all forces.
5. Draw and label our long range forces. This will usually be weight unless there is electric charge or magnetism involved.
6. Draw and label your acceleration vector off to the side of the dot -- not touching the dot. If there is no acceleration, then write $a=0$.
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Here is an example of a free body diagram for a block of cheese resting on a table (see figure 2 below). Gravity pulls down on the cheese’s mass with weight ($W$) and the table pushes up on the cheese with a normal force ($N$). Since there are no ropes and the cheese is not trying to slide, there is no tension or friction.

## Common mistakes and misconceptions

1. Sometimes people draw the forces of the object acting on other things. We only want to draw the forces pushing or pulling on our object. Only focus on what is happening to the object of interest.
2. Sometimes people forget the directions of the different types of forces. Weight is always down, friction is always parallel to the the contact surface, normal force is always perpendicular to the contact surface, and tension only pulls.