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Free body diagrams

A free body diagram shows all forces acting on an object.

We show forces as arrows.

Each arrow shows the relative magnitude (strength) and direction of a force. So each arrow is a vector.

Keep it simple. Don’t draw the object itself. Just draw a small box, or a big dot (●)

Example 1: A hockey player hits a puck.

At the moment she hits the puck, there are FOUR forces on the puck at the same time:

free body diagram hockey puck

Don’t draw the hockey player: Just draw the puck as a box – and one arrow for each force on it.

F applied = force of stick hitting the puck
F friction = force of friction between puck and the ice.
F gravity = force from Earth’s gravity, which is pulling the puck down.
F normal = The normal force (support force)

Does there have to be a Fnormal? Well, gravity pulls the puck down, so it’d continue to move down – unless something stops it: The atoms of the floor repel the puck.

Example 2. Falling acorn. Don’t consider air resistance.

free body down

Example 3. Falling acorn. Do consider air resistance.

free body falling

Example 4. Flying squirrel leaps from a tree branch. Consider air resistance.

(In pink we can see the flying squirrel’s direction of motion. This is not a force. We’re only showing this here so we can understand why the force of air resistance is pointing where it does.)

Flying squirrel free body

Now you try: In pencil, on a separate sheet of paper, draw free-body diagrams. Use this tutorial The Physics Classroom » Physics Tutorial » Newton’s Laws » Drawing Free-Body Diagrams

Example 5: Karate

Let’s examine an Olympic karate (空手) athlete – “Karate will make its first appearance as an Olympic sport at the 2020 Summer Olympics in Tokyo, Japan. It will feature two events, Kumite and Kata.” (Wikipedia.) The athlete on the left delivers a strike to the athlete on the right.

One of our students has color coded the forces on each athlete, individually.
(This illustration is not fully in the form of a free-body diagram. It’s an attempt to show the forces on a more realistic depiction.)

Karate free body diagram

Example 6: Honors free-body diagram – Basketball

Aatish Bhatia writes “There are four forces on a basketball as it flies through the air. You’ve got gravity, pulling the ball down to the Earth, the buoyant force, that’s pushing the ball up, the drag force due to the air that the ball smashes into, opposing the ball’s motion and slowing down. And finally, there’s a fourth more subtle force, known as the Magnus force, which comes into play whenever the ball is spinning.”

Magnus force on basketball

From “Galileo Got Game”, Aatish Bhatia, Wired, 4/15.

“In 1852, Magnus wondered why cannonballs would often deflect in their path when shot out of a cannon. He realized that as the cannonball spins while flying through the air, it experiences uneven friction (or drag) with the air. This creates an unbalanced force on the cannonball, causing it to deflect sideways. (Newton, being Newton, had already worked this out about 180 years earlier, after watching Cambridge tennis players curve their shots.) Here’s a nice video explainer on the Magnus effect, by Derek Muller of Veritasium.”

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a mathematical model describing change in motion (the acceleration) of objects when acted on by a net force.

HS-PS2-10 (MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

College Board Standards for College Success: Science

PS-PE.1.2.2 Analyze force diagrams to determine if they accurately represent different real-world situations.
PS-PE.1.2.3 Determine, given a force diagram and the initial motion of an object, the change in motion of an object, and explain why the change occurs.

PS-PE.1.2.4 Given real-world situations involving contact, gravitational, magnetic or electric charge forces and an identified object of interest:

PS-PE.1.2.4a Identify the objects involved in the interaction, and identify the pattern of motion (no motion, moving with a constant speed, speeding up, slowing down or changing [reversing] direction of motion) for each object.
PS-PE.1.2.4b Make a claim about the types of interactions involved in the various situations. Justification is based on the defining characteristics of each type of interaction.
PS-PE.1.2.4c Represent the forces acting on the object of interest by drawing a force diagram.
PS-PE.1.2.4d Explain the observed motion of the object. Justification is based on the forces acting on the object.

P-PE.1.2.1 Analyze force diagrams to determine if they accurately represent different situations involving multiple contact, gravitational and/or electrical interactions. When appropriate, determine the one-dimensional vector sum of all the forces (net force), and interpret the meaning of the vector sum of all the forces (net force).

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)

1. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.

1.4 Interpret and apply Newton’s three laws of motion.
1.5 Use a free-body force diagram to show forces acting on a system consisting of a pair of interacting objects. For a diagram with only co-linear forces, determine the net force acting on a system and between the objects.

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