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# ENGI 1313 Mechanics I - PowerPoint PPT Presentation

ENGI 1313 Mechanics I. Lecture 12:3D Particle Equilibrium. Chapter 3 Objectives. to introduce the concept of the free-body diagram for a particle. to show how to solve particle equilibrium problems using the equations of equilibrium. Lecture 12 Objectives.

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ENGI 1313 Mechanics I

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## ENGI 1313 Mechanics I

Lecture 12:3D Particle Equilibrium

### Chapter 3 Objectives

• to introduce the concept of the free-body diagram for a particle.

• to show how to solve particle equilibrium problems using the equations of equilibrium

### Lecture 12 Objectives

• to examine and apply Chapter 3 objectives in 3D space

### Note on Tutorial Problem Set #3

• Revised Problem Set

• Problem 6 with spring deleted

• Problem added on Dot Product

### Example 12-01

• A plate with a mass of 150 kg is supported by three cables and is in equilibrium. Find the tension force in each cable.

### Example 12-01 (cont.)

• What is known?

• Plate mass

• Coordinate geometry

• What is needed?

• Convert mass to weight (force)

• Determine cable forces

• Cartesian force vectors

• Magnitude, direction and sense

### Example 12-01 (cont.)

• Draw FBD at A

• Define Cartesian Force Vectors

FA = W= 150 kg (9.806 m/s2) = 1471 N

A

FAC

FAB

FAD

### Example 12-01 (cont.)

• Combine Like Terms

• x, y and z directions

FA = W= 150 kg (9.806 m/s2) = 1471 N

A

FAC

FAB

FAD

### Example 12-01 (cont.)

• Multiply Fx by 1.5 and add to Fy

FA = W= 150 kg (9.806 m/s2) = 1471 N

A

FAC

FAB

FAD

### Example 12-01 (cont.)

• Multiply Fx by 3 and add to Fz

FA = W= 150 kg (9.806 m/s2) = 1471 N

A

FAC

FAB

FAD

### Pulley Systems

• Assumptions

• In this course for analysis of all pulley systems

• Weightless

• Zero friction

• Tension cables

• Fixed Pulley

• Class 1

• Fixed axle

• Used to change direction of the pull force

• Mechanical advantage of 1

### Pulley Systems (cont.)

• Moveable Pulley

• Class 2

• Floating axle

• Used to multiply forces

• Mechanical advantage of 2

### Pulley Systems (cont.)

• Compound Pulley

• Combination of fixed and moveablepulley system

### Example 12-02

D

C

• The "scale" consists of a known weight W which is suspended at A from a cord of total length L. Determine the weight w at B if A is at a distance y for equilibrium. Neglect the sizes and weights of the pulleys.

### Example 12-02 (cont.)

D

C

• Examine Pulley System

• Known weight, W1

• Find weight w2at B for equilibrium position y

W1

W1

W1

w2 = ?

FBD = W1

FBC = W1

B

w2

### Example 12-02 (cont.)

D

C

• Draw FDB at Point B

W1

W1

W1

w2 = ?

How to determine ?

d/2

h

(L-y)/2

### Example 12-02 (cont.)

D

C

• Determine 

• Total cable length, L

• Triangle geometry

• Neglect pulley size and weight

W1

w2

### Example 12-03

• The joint of a space frame is subjected to four member forces. Member OA lies in the x–y plane and member OB lies in the y–z plane. Determine the forces acting in each of the members required for equilibrium of the joint.

### Example 12-03 (cont.)

• Draw 3D FBD at Point O

• Define position and unitvectors for F1

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Draw 3D FBD at Point O

• Define position and unitvectors for F2

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Draw 3D FBD at Point O

• Define position and unitvectors for F3 and F4

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Unit and Force Vectors

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Fx Equilibrium

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Fz Equilibrium

z

F1

O

F3

45

y

40

F2

x

F4

### Example 12-03 (cont.)

• Fy Equilibrium

z

F1

O

F3

45

y

40

F2

x

F4

Hibbeler (2007)

### References

• http://en.wikipedia.org

• Hibbeler (2007)

• http://wps.prenhall.com/esm_hibbeler_engmech_1