Statics

Prof. Martha Selby
02-24-2013

Prepared by: Walter Bennette

Mechanics

The study of forces acting on bodies.

3 Branches of Mechanics:

  • Statics
  • Dynamics
  • Strength of Materials

Video showing all three

Statics 

The study of rigid bodies that are in equilibrium

Force

A "push" or "pull" exerted by one body on another, such as:

  - a person pushing on a wall  

  - gravity pulling on a person

Force: example

Force: example

Scalar/Vector

Scalar

A quantity possessing only a magnitude
 - mass, length, time

Vector

A quantity that has both a magnitude and a direction
  - velocity, force

Force

Force is a vector quantity, therefore a force is completely described by:

  1. magnitude
  2. direction
  3. point of application

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Force

What is a Newton (N)?

A Newton is the force required to give a mass of 1 kg. an acceleration of 1 m/sec/sec.

What is a pound (lbf)?

Another measurement of force (1 lbf = 4.44822 N)

Vectors

Types of vectors used in statics:

  • Coplanar vectors lie in the same plane

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Vectors

Types of vectors used in statics:

  • Concurrent vectors have lines of action that pass through the same point.

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Vectors

Types of vectors used in statics:

  • Colinear vectors act along the same line of action.

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Vector Addition

The parallelogram law

Resolution of forces into components

The net effect of a number of forces on one point can be the same as the effect of one force

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Finding Resultant Forces

Turn multiple forces to one:

  1. Resolve each force into X & Y components

  2. Add all X components
    \( Rx=Fx_1+Fx_2+Fx_3+... \)

  3. Add all Y components
    \( Ry=Fy_1+Fy_2+Fy_3+... \)

  4. Find the resultant force, \( \vec R \)
    \( R= \left (Rx^2 + Ry^2 \right )^{\frac{1}{2}} \)
    \( \alpha = tan^{-1} \left (\frac{R_y}{R_x} \right ) \)












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A Moment

The tendency of a force to cause rotation about a point.

\( Moment = ( force's \ magnitude) * \) \( (perpendicular \ distance \ from \ force's \ line \ of \ action \ to \ the \ point) \)

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\( M_B = 10.0 \ N \ (1.5 \ m) = 15 \ Nm, \ direction \ is \ clockwise \)
\( M_A = 10.0 \ N \ (2.0 \ m) = 15 \ Nm, \ direction \ is \ counter \ clockwise \)

A Moment

In Class Problems

For 12.2 and 12.3 find the \( x \) and \( y \) components of the force F. The angle \( \theta \), is measured positive counterclockwise from the positive x-axis. Include a sketch of the force F and its components.

# F \( \theta \)
12.2 \( 3.7(10)^3 \) N \( 105^{\ \circ} \)
12.3 \( 5.1(10)^2 \) lbf \( -220^{\ \circ} \)

In Class Problems

For 12.5 find the resultant of the two concurrent forces F, which makes an angle \( \theta \) with respect to the positive x-axis, and G which makes an angle \( \phi \) with respect to the positive x-axis. Show a sketch of F and G and the resultant.

# F \( \theta \) G \( \phi \)
12.5 \( 8.6(10)^2 \) N \( 35^{\ \circ} \) \( 5.7(10)^2 \) N \( 120^{\ \circ} \)

In Class Problems

For problem 12.20, the force F goes through the origin of the xy-coordinate system and makes an angle \( \theta \ \) with the horizontal, as shown in the figure. Points A and B are at the coordinates indicated on the figure in units of feet. Calculate the moment of F about points A and B, assigning positive values to counterclockwise moments.

# F \( \theta \)
12.20 \( 7450 \) lbf \( 330^{\ \circ} \)