# Applied Mechanics

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Applied Mechanics: the white soul www.hct-f.com

Force is a vector quantity, thus has both magnitude and direction. Thus we need to use vector addition to work out the total force on an object Force is measured in units of Newtons (N) ( magnitude ) ( direction ) N mkgs2 ( F=m.a ) 1- external force ( ) 2- internal force ( ( = response or reaction ))

( ) magnitude direction= 30 degrees A & B points of application line of action 3 ( 3 characteristics ) - magnitude - direction - points of application

A is a pull point: B is a push point

:Types of forces 1- Distributed force ( 2- concentrated force ( point force

:force systems line of actions ( 1- concurrent ) line of actions ( 2- coplanar ) ) line of actions ( 3- parallel line of actions ( parallel coplanar )

1- graphical method 2- analytical method ) 4 ( 1- law of sine and cosine triangle law ) ( R

1 2- resolution to Fx & Fy () Fy ( + ) Fx ) ) F ) tan^-1 ( Fy/Fx

law of sine and cosine

========================================== resolution

laws of sine and cosine resultant

r a&b r cosine r sin sin a&r r 2 =sin1 sin b/b=sin r/r a ( + ) ar ( ( )

A= 900N B= 600N 51= b 53= a N 999 N 996 N 999 ( N ( R 999 N 996 53 51 99 = 53 +51 + 99= 941 R cosine sine ( ) 51

( ) resolution method

y cosine x sine * - -

resolution method

4 Fx cosine Fy sin 71=P=90 N, @p 54=82+71 =Q=75 N,@q ) ( 07 =S=60N, @s ) ( T=80N, @t=40 xx Fx ( 07Fx= 90 cos17+75cos45-80cos40-60cos ) Fx= 57.295 N 07Fy= 90sin17+75sin45+80sin40+60sin 151.781 =Fy ) Fy + Fx ( F

427.591 ( tan^-1 ( Fy/Fx @ 879.27

Objectives of the second unit:

- ( 1 ) Define a force it is the action exerted from a body on another Describe the characteristics

1- magnitude 2- direction 3- points of appliion

- Identify the different types of force systems 1) concurrent it is the system in which all the line of actions join together in one point line of actions 2) coplanar it is the system in which all the line of actions lie on one plane surface line of actions beam 3) parallel it is the system in which all the line of actions parallel to each other line of actions Define resultant it is a single force which will produce same effect on the body as the original system of forces - Determine the resultant of two vectors using the parallelogram method and the laws of sine and cosine parallelogram R

R

- resolve the resultant to its x and y components x component cos y component sin - Determine the resultant of concurrent using resolution method Ry Rx

- Determine the equilibrant of concurrent forces 981

1- Define rigid bodies bodies which won't affect if you apply a force and pull the load and there will be no change in the shape 2- what is known by size of the force Magnitude: the amount or the size of the force

3- True or false - All parallel force systems are coplanar force system also True - we have two laws in the graphical method False - triangle method - parallelogram method - polygon method - the only proper way of finding the Resultant in a sketch with 3 forces is resolution method False there are two methods Analytical: resolution method Graphical: polygon method

) N/10N/15N ( 5 resolution/ laws of sine and cosine/ and the graphical method

21

1r= 150 n 68.63 2r= 408.37 n 439.63 318.2411 7.931 -2.94

4r= 10973.65 n -822.5 77.471

Objectives of the third lesson: Lesson 3 : Equilibrium of Rigid Bodies

Objectives State the conditions for the equilibrium of a rigid body. Draw the free-body-diagram (FBD) of a rigid body. Solve equilibrium problems using the condition for the equilibrium of a rigid body. Free Body Diagram A diagram of a body separated from a system showing all the forces acting to it. ( ) ( tension and weight ) ( Normal and weight )

roller or ball just produces one force

hinge produces 2 forces- horizontal and vertical forces

Fixed produces 3 forces - horizontal - vertical - and moment resolution method ( T )

solve for the horzintal components

) ( 0=02 TB cos 25-TA cos solve for the vertical components ) ( 022 =02 TB sin 25+TA sin TA TB 52 TB= TA cos 20 cos : )022 =02 TA cos 20 cos 25) sin 25+TA sin TB TA

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