- 124 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' ENGI 1313 Mechanics I ' - ardara

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### 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

- Cartesian force vectors

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

- In this course for analysis of all pulley systems
- Fixed Pulley
- Class 1
- Fixed axle

- Used to change direction of the pull force
- Mechanical advantage of 1

- Class 1

Pulley Systems (cont.)

- Moveable Pulley
- Class 2
- Floating axle

- Used to multiply forces
- Mechanical advantage of 2

- Class 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 ?

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

Classification of Textbook Problems

Hibbeler (2007)

References

- http://en.wikipedia.org
- Hibbeler (2007)
- http://wps.prenhall.com/esm_hibbeler_engmech_1

Download Presentation

Connecting to Server..