STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING

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STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING. Today’s Objectives : Students will be able to: a) Identify what is mechanics / statics. b) Work with two types of units. c) Round the final answer appropriately. d) Apply problem solving strategies. In-Class activities :

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STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING

Today’s Objectives:

Students will be able to:

a) Identify what is mechanics / statics.

b) Work with two types of units.

c) Round the final answer appropriately.

d) Apply problem solving strategies.

• In-Class activities:
• What is mechanics
• System of units
• Numerical calculations
• Sample concept quiz
• Problem solving strategy
• Sample attention quiz

1. The subject of mechanics deals with what happens to a body when ______ is / are applied to it.

A) magnetic field B) heat C) forces

D) neutrons E) lasers

2. ________________ still remains the basis of most of today’s engineering sciences.

A) Newtonian Mechanics B) Relativistic Mechanics

C) Euclidean Mechanics C) Greek Mechanics

WHAT IS MECHANICS??
• Study of what happens to a “thing” (the technical name is “body”) when FORCES are applied to it.
• Either the body or the forces could be large or small.
SYSTEMS OF UNITS (Section 1.3)
• Four fundamental physical quantities.
• Length, mass, time, force.
• One equation relates them, F = m * a
• We use this equation to develop systems of units
• Units are arbitrary names we give to the physical quantities.
UNIT SYSTEMS
• Define 3 of the units and call them the base units.
• Derive the 4th unit (called the derived unit) using F = m * a.
• We will work with one unit system in static’s: SI.

RULES FOR USING SI SYMBOLS (Section 1.4)

• No Plurals (e.g., m = 5 kg not kgs )
• Separate Units with a • (e.g., meter second = m • s )
• Most symbols are in lowercase ( some exception are N,
• Pa, M and G)
• Exponential powers apply to units , e.g., cm2 = cm • cm
• Other rules are given in your textbook
NUMERICAL CALCULATIONS (Section 1.5)
• Must have dimensional “homogeneity.” Dimensions have to be the same on both sides of the equal sign, (e.g. distance = speed  time.)
• Use an appropriate number of significant figures (3 for
• answer, at least 4 for intermediate calculations). Why?
• Be consistent when rounding off.
• - greater than 5, round up (3528  3530)
• - smaller than 5, round down (0.03521  0.0352)
• - equal to 5, see your textbook.

SAMPLE CONCEPT QUIZ

1. Evaluate the situation, in which mass(kg), force (N), and length(m) are the base units and recommend a solution.

A) A new system of units will have to be formulated

B) Only the unit of time have to be changed from second to

something else

C) No changes are required.

D) The above situation is not feasible

SAMPLE CONCEPT QUIZ (continued)

2. Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations.

A) Historically slide rules could not handle more than three significant figures.

B)Three significant figures gives better than one-percent accuracy.

C) Telephone systems designed by engineers have area codes consisting of three figures.

D) Most of the original data used in engineering calculations do not have accuracy better than one percent

PROBLEM SOLVING STRATEGY: IPE, A 3 Step Approach

1. Interpret:Read carefully and determine what is given and what is to be found/ delivered. Ask, if not clear. If necessary, make assumptions and indicate them.

2. Plan: Think about major steps (or a road map) that you will take to solve a given problem. Think of alternative/creative solutions and choose the best one.

3. Execute: Carry out your steps. Use appropriate diagrams and equations. Estimate your answers. Avoid simple calculation mistakes. Reflect on / revise your work.

SAMPLE ATTENTION QUIZ

A) 12345.6 N B) 12.3456 kN C) 12 kN

D) 12.3 kN E) 123 kN

2. In three step IPE approach to problem solving, what does P stand for

A) Position B) Plan C) Problem

D) Practical E) Possible

Today’s Objective:

Students will be able to :

a) Resolve a 2-D vector into components

b) Add 2-D vectors using Cartesian vector notations.

• In-Class activities:
• Check homework
• Parallelogram law
• Resolution of a vector using
• Cartesian vector notation (CVN)
• Attention quiz

1. Which one of the following is a scalar quantity?

A) Force B) Position C) Mass D) Velocity

2. For vector addition you have to use ______ law.

A) Newton’s Second

B) the arithmetic

C) Pascal’s

D) the parallelogram

There are four concurrent cable forces acting on the bracket.

How do you determine the resultant force acting on the bracket ?

SCALARS AND VECTORS (Section 2.1)

ScalarsVectors

Examples: mass, volume force, velocity

Characteristics: It has a magnitude It has a magnitude

(positive or negative) and direction

Addition rule: Simple arithmetic Parallelogram law

Special Notation: None Bold font, a line, an

arrow or a “carrot”

VECTOR OPERATIONS(Section 2.2)

Scalar Multiplication

and Division

VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE

Parallelogram Law:

Triangle method (always ‘tip to tail’):

How do you subtract a vector? How can you add more than two concurrent vectors graphically ?

RESOLUTION OF A VECTOR

“Resolution” of a vector is breaking up a vector into components. It is kind of like using the parallelogram law in reverse.

CARTESIAN VECTOR NOTATION (Section 2.4)
• We ‘ resolve’ vectors into components using the x and y axes system
• Each component of the vector is shown as a magnitude and a direction.
• The directions are based on the x and y axes. We use the “unit vectors” i and j to designate the x and y axes.

For example,

F = Fx i + Fy j or F' = F'x i + F'y j

The x and y axes are always perpendicular to each other. Together,they can be directed at any inclination.

• Step 1 is to resolve each force into its components
• Step 3 is to find the magnitude and angle of the resultant vector.
• Step 2 is to add all the x components together and add all the y components together. These two totals become the resultant vector.

EXAMPLE

Given: Three concurrent forces acting on a bracket.

Find: The magnitude and angle of the resultant force.

Plan:

a) Resolve the forces in their x-y components.

b) Add the respective components to get the resultant vector.

c) Find magnitude and angle from the resultant components.

EXAMPLE (continued)

F1 = { 15 sin 40° i + 15 cos 40° j } kN

= { 9.642 i + 11.49 j } kN

F2 = { -(12/13)26 i + (5/13)26 j } kN

= { -24 i + 10 j } kN

F3 = { 36 cos 30° i– 36 sin 30° j } kN

= { 31.18 i– 18 j } kN

y

FR

x

EXAMPLE (continued)

Summing up all the i and j components respectively, we get,

FR = { (9.642 – 24 + 31.18) i + (11.49 + 10 – 18) j } kN

= { 16.82 i + 3.49 j } kN

FR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN

 = tan-1(3.49/16.82) = 11.7°

1. Can you resolve a 2-D vector along two directions, which are not at 90° to each other?

A) Yes, but not uniquely.

B) No.

C) Yes, uniquely.

2. Can you resolve a 2-D vector along three directions (say at 0, 60, and 120°)?

A) Yes, but not uniquely.

B) No.

C) Yes, uniquely.

CONCEPT QUIZ

GROUP PROBLEM SOLVING

Given: Three concurrent forces acting on a bracket

Find: The magnitude and angle of the resultant force.

Plan:

a) Resolve the forces in their x-y components.

b) Add the respective components to get the resultant vector.

c) Find magnitude and angle from the resultant components.

GROUP PROBLEM SOLVING (continued)

F1 = { (4/5) 850 i - (3/5) 850 j } N

= { 680 i - 510 j } N

F2 = { -625 sin(30°) i - 625 cos(30°) j } N

= { -312.5 i - 541.3 j } N

F3 = { -750 sin(45°) i + 750 cos(45°) j } N

{ -530.3 i + 530.3 j } N

y

x

FR

GROUP PROBLEM SOLVING (continued)

Summing up all the i and j components respectively, we get,

FR = { (680 – 312.5 – 530.3) i + (-510 – 541.3 + 530.3) j }N

= { - 162.8 i - 521 j } N

• FR = ((162.8)2 + (521)2)½ = 546 N
• = tan–1(521/162.8) = 72.64° or

From Positive x axis  = 180 + 72.64 = 253 °

y

x

30°

F = 80 N

ATTENTION QUIZ

1. Resolve Falong x and y axes and write it in vector form. F = { ___________ } N

A) 80 cos (30°) i - 80 sin (30°) j

B) 80 sin (30°) i + 80 cos (30°) j

C) 80 sin (30°) i - 80 cos (30°) j

D) 80 cos (30°) i + 80 sin (30°) j

2. Determine the magnitude of the resultant (F1 + F2) force in N when F1 = { 10 i + 20 j } N and F2 = { 20 i + 20 j } N .

A) 30 N B) 40 N C) 50 N

D) 60 N E) 70 N

End of the Lecture

Let Learning Continue