# Engineering Mechanics Tutorials

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### UNIVERSITY OF NAMIBIA FACULTY OF ENGINEERING AND INFORMATION TECHNOLOGY Engineering Mechanics I: Statics:

UNIVERSITY OF NAMIBIA FACULTY OF ENGINEERING AND INFORMATION TECHNOLOGY Engineering Mechanics I: Statics Tutorial session ADDITION OF A SYSTEM OF COPLANAR FORCES Date : 10/08/2010 By Ithete yaHango

### Slide 2:

1. Determine the x and y components of F 1 and F 2 acting on the boom shown below. Express each force as a Cartesian vector .

### 2. The link in figure below is subjected to two forces F1 and F2. Determine the magnitude and direction of the resultant force. :

2. The link in figure below is subjected to two forces F 1 and F 2 . Determine the magnitude and direction of the resultant force.

### 3. The end of the boom 0 in the figure below is subjeted to three concurrent and coplanar forces. Determine the magnitude and direction of the resultant force.:

3. The end of the boom 0 in the figure below is subjeted to three concurrent and coplanar forces. Determine the magnitude and direction of the resultant force.

### Slide 5:

5. Resolve the 30 N force into components along the u and v axes, and determine the magnitude of each of these components .

### Slide 6:

6. The force F = 450 N acts on the frame. Resolve this force into components acting along member AB and AC. and determine the magnitude of each component .

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topics: Cartesian Vectors Addition and subtraction of Cartesian Vectors Date: 17/08/201

### Slide 8:

7. Given the forces as F 1 = (60 i – 50 j + 40 k ) N and F 2 = ( – 40 i – 85 j + 30 k ) N. Sketch each force on an x, y, z reference. Determine the magnitude and coordinate direction angles of the resultant force.

### Slide 9:

8. Two forces act on t he hook shown in below . Specify the magnitude of F 2 and its coordinate direction angles of F 2 that the resultant force F R a cts along the positive y axis and has a magnitude of 800 N.

### Home work:

Home work Revise the topic you have done so far. Do example 2.10 on page 49 Do exercise 2-58 and 2- 59 on page 51 Read with understanding: Position vectors Force vector directed along a line

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topics: Position Vectors Force Vector Directed along a Line Date: 24/08/201

### 1. The Man shown below pulls on the cord with a force of 350 N. Find the coordinates of the end points (A and B) of the cord, hence plot the position vector r. :

1. The Man shown below pulls on the cord with a force of 350 N. Find the coordinates of the end points (A and B) of the cord, hence plot the position vector r.

### Slide 13:

2. Represent the position vector r acting from point A (3m, 5m, 6m) to point B (5m, - 2m, 1m) in Cartesian vector form. Determine its coordinate direction angles and find the distance between points A and B .

### Slide 14:

3. Determine the magnitude and coordinate direction angles of the resultant force.

### Home work:

Home work Please revise until the penultimate topics Read Dot products and its applications Chapter 3

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topic: Equilibrium of a Particle: Three – Dimensional Force Systems Date: 31/08/201

### Slide 17:

1. The joint of a space frame is subjected to four forces. Strut OA lies in the x-y plane and strut OB lies in the y-z plane. Determine the forces acting in each of the three struts required for equilibrium . F = 2kN.

### Slide 18:

2 . The 100 kg crate as shown below is supported by three cords, one of which is connected to a spring. Determine the tension in each cord and the stretch of the spring.

### Slide 19:

Home Work Revise the examples in chapter 3 Revise the examples in chapters 1 – 2 Do problems 3.7, 3.12, 3.17 and 3.45 ( Hibbeler 11 th Edition) Revise Chapters 1 – 3.

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topic: Force system resultants Moment of a force about a point Cross product Date: 21/09/2010

### 1. Determine the magnitude and directional sense of the resultant moment of the forces at A and B about point O. θ1 = 300, θ2 = 45 0, a = 5 m, b = 13 m, c = 3 m, d = 6 m, e = 3 m, f = 6 m, F1 = 40 N, F2 = 60 N:

1. Determine the magnitude and directional sense of the resultant moment of the forces at A and B about point O . θ 1 = 30 0 , θ 2 = 45 0 , a = 5 m, b = 13 m, c = 3 m, d = 6 m, e = 3 m, f = 6 m, F 1 = 40 N, F 2 = 60 N

### 2. Determine the moment of each force about the bolt located at A. FB = 40 N a = 2.5 m α = 20 0 γ = 30 0 FC = 50 N b = 0.75 m β = 25 0:

2. Determine the moment of each force about the bolt located at A . F B = 40 N a = 2.5 m α = 20 0 γ = 30 0 F C = 50 N b = 0.75 m β = 25 0

### 3. The Snorkel Co. produces the articulating boom platform that can support weight W. If the boom is in the position shown, determine the moment of this force about points A, B and C. W = 550N, a = 3 m, b = 16 m, c = 15 m,θ1 = 300, θ2 = 70 0.:

3. The Snorkel Co . produces the articulating boom platform that can support weight W . If the boom is in the position shown, determine the moment of this force about points A , B and C . W = 550N, a = 3 m, b = 16 m, c = 15 m, θ 1 = 30 0 , θ 2 = 70 0 .

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topic: Cont. Force system resultants Moment of a force about a point Cross product Date : 23/09/2010

### Slide 26:

4. The boom has length L, weight W b , and mass center at G. If the maximum moment that can be developed by the motor at A is M, determine the maximum load W, having a mass center at G ', that can be lifted . L = 30 m, W b = 800 N a = 14 m, b = 2 m, θ = 30 0 and M = 20 × 103 N⋅ M.

### 5. Determine the moment of the force at A about point O. Express the result as a Cartesian vector. F =(60i – 30j – 20k) N a=4m, b = 7m, c = 3 m, d = 4 m, e = 6 m and f = 2 m:

5. Determine the moment of the force at A about point O. Express the result as a Cartesian vector. F =(60 i – 30 j – 20 k ) N a =4m, b = 7m, c = 3 m, d = 4 m, e = 6 m and f = 2 m

### 6. The pole supports a traffic light of weight W. Using Cartesian vectors, determine the moment of the weight of the traffic light about the base of the pole at A. W = 22 N, a = 12 m and θ = 30 0:

6. The pole supports a traffic light of weight W . Using Cartesian vectors, determine the moment of the weight of the traffic light about the base of the pole at A . W = 22 N, a = 12 m and θ = 30 0

### Engineering Mechanics I Tutorial Session:

Engineering Mechanics I Tutorial Session Topic: Force system resultants Moment of a force along an axis Moment of a couple Date: 05/10/2010

### Slide 30:

1. Determine the moment of the force F about the Oa axis. Express the result as a Cartesian vector . F={ 50 i – 20 j + 20 k}N, a = 6 m, b = 2 m, c = 1 m, d = 3 m. e = 4 m.

### Slide 31:

2. The hood of the automobile is supported by the strut AB , which exerts a force F on the hood. Determine the moment of this force about the hinged axis y . F = 24 N a = 2 m b = 4 m c = 2 m d = 4 m.

### Slide 32:

3. Determine the magnitude and direction of the couple moment a cting on the gear as shown below.

### Slide 33:

4. Determine the couple moment acting on the pipe shown below. Segment AB is directed 30 0 below the x-y plane. 