Construction Free-Body Diagramsfor Planar Bodies

StevenVukazichSanJoseStateUniversity

• Choose the free body to isolate;• Draw a Free Body Diagram (FBD) of the body;– Isolate the body from all of its surroundings,– Magnitudes and directions of all known and unknown

forces acting on the body should be included and clearly indicated,

– Indicate dimensions on the FBD,• Write the equations of equilibrium and solve the

equations for the unknown quantities.

General procedure for the Analysis of Planar Bodies in Static Equilibrium

• Choose the free body to isolate;• Isolate the body from all of its surroundings;• Magnitudes and directions of all known and

unknown forces acting on the body should be included and clearly indicated;

• Dimensions should be indicated on the FBD.Most errors in mechanics problems

result from a mistake in the FBD

General procedure for the constructionof Free Body Diagrams

Consider the two-dimensional system

A B

C

D

E

15°50° 25°

150 lb

The system consists of alight, flexible, and inextensible rope connecting:• A 150 lb weight to a ring at C;• The ring at C to the right hand

wall at D; • The ring at C to the left hand

wall at point A running over a frictionless pulley at B.

Any part of the system may be isolated and many free-body diagrams can be drawn

A B

C

D

E

15°50°

25°

150 lb

Consider imaginary cuts at sections 1 – 61

23

45

6

Concept of Tension

A B

C

D

E

15°50°

25°

150 lb

Free-Body diagram of bodyisolated by cuts 2 and 6

1

23

45

6

2

6

TCD

TCDFor equilibrium, the segment of rope must be pulled by forces that are equal, opposite, and along the line of the rope

The tension force in the rope (TCD) is an unknown force and the direction of the force (25°) is known

25°

Effect of the Weight of a Body

A B

C

D

E

15°50°

150 lb

Free-Body diagram of bodyisolated by cut 3

1

23

45

6

150 lb

The weight of the body can be expressed as a resultant force acting at its center of gravity

Both the tension force in the rope (150 lb) and the direction of the force (vertical) are known

3

150 lb

25°

G

Tension Force in Ropes over Pulleys

A B

C

D

E

15°50°

150 lb

Free-Body diagram of bodyisolated by cuts 1, 4, and 5

1

23

45

6

For an ideal pulley, TAB = TBCThe reactive force at the pulley axle consists of an unknown force and direction

4

5

50°1

TBC

TAB = TBC

15°

FB 𝜃

The tension force in the rope (TBC) is unknown and the magnitude (FB) and direction (𝜃)of the pulley axle reaction force are unknown

25°

Free-Body Diagram of Ring at C

A B

C

D

E

15°50°

150 lb

Free-Body diagram of bodyisolated by cuts 1, 2, and 3

1

23

45

6

2

50° 1

TBC

One rope tension (150 lb) is known. Two rope tension forces (TBC and TCD) are unknown. All three rope directions are known

3

25°

TCD

150 lb

25°

Free Body Diagram Notes

250°

1

TBC

3

25°

TCD

150 lb

4

5

50°1

TBC

TBC

15°

FB 𝜃

25°

2

6 TCD

TCD

150 lb3

150 lb

Equal and Opposite forces

1 unknown0 equilibrium equations3 unknowns

2 equilibrium equations 2 unknowns

2 equilibrium equations