addition of system of coplanar forces, em

UNIVERSITY OF NAMIBIAFACULTY OF ENGINEERING AND INFORMATION TECHNOLOGY

Engineering Mechanics I: Statics

Tutorial sessionADDITION OF A SYSTEM OF COPLANAR FORCES

Date: 10/08/2010By Ithete yaHango

1. Determine the x and y components of F1 and F2 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.

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 theresultant force.

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

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

Engineering Mechanics ITutorial Session

Topics:

• Cartesian Vectors• Addition and subtraction of Cartesian Vectors

Date: 17/08/201

7. Given the forces as F1= (60 i – 50j + 40k) N and F2 = (– 40 i – 85j + 30k) N.

(a) Sketch each force on an x, y, z reference.

(b) Determine the magnitude and coordinate direction angles of the resultant force.

8. Two forces act on the hook shown in below. Specify the magnitude of F2 and its coordinate direction angles of F2 that the resultant force FR acts along the positive y axis and has a magnitude of 800 N.

Home work

1. Revise the topic you have done so far.2. Do example 2.10 on page 493. Do exercise 2-58 and 2- 59 on page 514. Read with understanding: • Position vectors• Force vector directed along a line

Engineering Mechanics ITutorial 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.

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.

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

Home work

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

Engineering Mechanics ITutorial Session

Topic:

• Equilibrium of a Particle: Three – Dimensional Force Systems

Date: 31/08/201

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.

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.

Home Work1. Revise the examples in chapter 32. Revise the examples in chapters 1 – 23. Do problems 3.7, 3.12, 3.17 and 3.45

(Hibbeler 11th Edition)4. Revise Chapters 1 – 3.

Engineering Mechanics ITutorial 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 Babout 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

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

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.

Engineering Mechanics ITutorial Session

Topic: Cont.

Force system resultants• Moment of a force about a point• Cross product

Date: 23/09/2010

4. The boom has length L, weight Wb, 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, Wb = 800 Na = 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) Na=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 momentof 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 ITutorial Session

Topic:

Force system resultants• Moment of a force along an axis• Moment of a couple

Date: 05/10/2010

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

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.

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

4. Determine the couple moment acting on the pipe shown below. Segment AB is directed 300 below the x-y plane.