Free-BodyDiagrams

PHYSICSSEMESTER ONE

NANSLO Physics Core Units and Laboratory Experimentsby the North American Network of Science Labs Online,a collaboration between WICHE, CCCS, and BCcampus

is licensed under a Creative Commons Attribution 3.0 Unported License;

based on a work at rwsl.nic.bc.ca.Funded by a grant from EDUCAUSE through the Next 

Generation Learning Challenges.

Introduction• Physical objects can be subjected to

several different forces at one time

• Force magnitudes and directions vary

• Forces can be related to each other

• Finding unknown forces may be complicated

Creative Commons Attribution 3.0 Unported License

Free-Body Diagrams

• Free-body diagrams (FBDs) are sketches showing the relative magnitude and direction of all forces acting on an object

• They help us see the relationships between the forces

• They assist in organizing our solutions.

Creative Commons Attribution 3.0 Unported License

Creating a FBD

Case:Find the net force on a 1.0 kg object (rock, animal, crate, computer …) on a horizontal surface with an applied force of 5.0 N to the right, and a coefficient of kinetic friction of 0.20.

Creative Commons Attribution 3.0 Unported License

Creating a FBD

1. Represent the object with a square.

2. Add and label an arrow with the approximate magnitude and direction of one force acting on the object.

3. Repeat step 2 for all forces. 4. Choose a convenient set of

axes.

Fg

nFFk

FBD showing the forces on the object.

y

x

Creative Commons Attribution 3.0 Unported License

Other Notes on FBDs

• It is usually easiest to set one axis in the expected direction of motion.

• FBDs only show all forces on a single object. If you need to consider forces on two objects, draw two FBDs.

• Assume that all forces apply to the same point. Otherwise, the question is a torque and rotational equilibrium problem.

Creative Commons Attribution 3.0 Unported License

Back to Case: Define Terms

m = 1.0 kg, F = 5.0 N i, μk = 0.20, ΣF =?• We can assume that the acceleration

due to gravity is g = 9.8 m/s2 (this doesn’t need to be stated).

• You can often define most variables within the FBD itself.

Creative Commons Attribution 3.0 Unported License

Net Force• We are looking the net force

ΣF = FN + Fg + F + Ff

• Express the forces in components

ΣFxi + ΣFy j= FN j – Fg j + F i – Ff i

ΣFx= F – Ff

ΣFy = FN – Fg

Creative Commons Attribution 3.0 Unported License

Using the FBD• There is no motion in the y-direction so,

according to Newton’s First Law, the normal force must balance force of gravity.

ΣFy = FN – Fg = 0

21.0 9.8

9.8

N g

ms

F F

mg

kg

N

Creative Commons Attribution 3.0

Unported License

Using the FBD

The magnitudes of the normal force and friction are related by the equation

Evaluating,

f k NF F

N

NFf

0.2

8.920.0

Creative Commons Attribution 3.0 Unported License

Using the FBD

Using the definitions of the directions, we can write the forces as vectors.

Fg = -9.8 N j, FN = 9.8 N j, F = 5.0 N i

and Ff = -2.0 N i

The net force on the object is then

Fnet = n + Fg + F + Ff = 3.0 N i

The net force is 3.0 N to the right.

Creative Commons Attribution 3.0 Unported License

Sample FBDs

• A book at rest on a table top.

• A satellite orbiting earth.

Fg

FN

Fg

Creative Commons Attribution 3.0 Unported License

More Sample FBDs

• An apple suspended from a branch.

• A crate being pushed up a ramp. Fg

T

FAFf

FN

Fg coordinates x

y

Creative Commons Attribution 3.0 Unported License

Summary• Free-Body Diagrams are useful tools in

organizing the relationships between the forces on a single object. – The object in a FBD is represented by a box.– The forces are represented by arrows with

appropriate directions and relative magnitudes.

• A suitable coordinate system can be selected to simplify calculations.

• Unknown forces can be found using Newton’s Laws of Motion and other physics relationships.

Creative Commons Attribution 3.0 Unported License