If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Mechanics (Essentials) - Class 11th>Unit 6

Lesson 2: Visualizing forces - 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 $a=0$.
$\begin{array}{rl}& \\ & \end{array}$
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.

To check your understanding and work toward mastering these concepts, check out our free body diagrams exercise.

## Want to join the conversation?

• In the problem with the block of cheese sliding up an incline, I understand Fg, Ff, and Fn, But it seems like there should be a force causing the uphill slide. Even if the block isn't accelerating, it is overcoming the acceleration of mgsinΘ as well as Ff, isn't it?
It seems like that would require force. Maybe I'm wrong.
• The force up the incline might no longer be acting on the cheese. If you look at a thrown ball in mid air your throwing force is no longer acting on it. It is being carried forward by sheer momentum and the only forces acting on it are gravity and air resistance.

The same is the case with this cheese. Imagine that someone has given it a velocity and then let go (like a curling stone) it will keep moving forward up the incline, but there is no longer any force acting on it to propel it, so given enough time the friction force will make it stop.

Remember that the diagram we look at is a snapshot at a particular time. There might have been a force in the past that is no longer being applied, with only the movement remaining.
• Hey!
Here's what I don't understand: in a system, in which there are two objects, and those objects are stacked (i.e. lie one on top of another) - why would the inferior object's free-body-diagram would include the normal force of the superior object, pointing down, rather than the weight of that very same body? Isn't it always the same? Isn't the normal force suppose to point up, counter-reacting the force exerted by the superior body?
• The normal force doesn't always have to counteract Force due to gravity or weight. Touch a wall, push, Normal force is exerted on your hand (equal mag.).
It arises due to contact, more specifically cuz of the repulsion of atoms between surfaces(you can't touch anything, it's just you feeling the repulsion)
Hence Normal force along with the weight of the above object is exerted on the inferior object.
and, in a free-body dia, forces acting ON a body are expressed to keep things simple.
• If an elevator is accelerating downwards and is coming to a stop, in which direction would the acceleration be pointing?
• The acceleration vector would be pointing upwards since its change in velocity is increasing from a negative value towards zero. Negative velocity would be downward in this case.
• If I put a mug on the table right to the wall, so the mug is on the table and in the same time it touches the wall, will there be a normal force between the mug and the wall?
• Yes. There will be one normal force between the table and the mug (in the vertical direction), and another normal force between the mug and the wall (in the horizontal direction).

Each physical contact between the mug and another object will produce a normal force.
• In a pivoted body, the force that should act upon it will be rotational force. How do I draw o free body diagram for such an object?
• That is a discussion of toqu
• how do you know the direction of force without arrows?
• Think of it intuitively. For example, if a box is being pushed to the right, then the force is to the right.
• Is the double "the" near the end of the second row of Common mistakes and misconceptions (2.) on purpose?
• no, it's a common mistake