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Reference Guide

Permachart - Marketing Reference Guide: Fictitious Force, Body Force, Centrifugal Force

2 pages194 viewsFall 2015

Department
Basic Engineering
Course Code
BE 1101
Professor
All
Chapter
Permachart

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Free Body Diagrams are used to solve problems which are concerned with the equilibrium of rigid bodies and the
forces that act upon them; the procedure involves 2 steps
Isolate the object or system (i.e., detach the rigid body from the ground) and sketch it carefully in outline form
Replace all forces, either real or virtual (see Force Types), with vector representations
After replacing the forces, define the axes orientation (i.e., select the most convenient angle) and then resolve all
off-axis (angled force)vectors into their XY components
Wis a force; therefore, it is a vector
This force is due to gravitational interaction between the Earth and the body, which always acts towards the center of the
Earth (i.e., straight down)
Note: Mass is not a force; it is a property of matter and related to weight by W=mg
Note: In each situation, the diagram on the left is indicated by the heading of the section (e.g., WEIGHT ON FRICTIONLESS SURFACE); the diagram on the right is the corresponding Free Body Diagram (see Force & Vector Representations)
• Since the mass is being pushed on a frictionless floor, the only resistance to the acceleration is the inertia (ma)
of the mass; it opposes the acceleration
• Cables always pull along their line of action at the point of attachment
• Roller contacts cannot resist a force parallel to the surface of contact
Therefore, any force at this contact must be perpendicular (normal) to the surface
A swivel or pin joint can resist any linear push or pull
• In two dimensions (2-D), this can be represented by a resultant force with components Rf and Rn or Rx and Ry
Rn is the reaction of the floor acting on the stationary weight
In this case, Rn =Wor Action = Reaction (Newtons Third Law)
The rough floor gives rise to frictional resistance
• If Px (not shown) matches Rf, then there will be no inertial force (in accordance with Newton’s Second Law)
• Cables always pull along their line of action at the point of attachment
• Frictionless contacts cannot resist a force parallel to the surface of contact
Therefore, any force at this contact must be perpendicular (normal) to the surface
• If the swivel joint is replaced by a welded, bolted or rigid connection, then the joint can be represented by R(as for the
swivel or pin joint) and it can also resist a torque (or moment)
D’Alemberts Principle asserts that inertial and centrifugal effects can be treated like a force
This technique is also known as dynamic equilibrium
This allows Dynamics problems to be analyzed using the principles of Statics
Translational inertia acts in the direction opposite to the direction of the acceleration; its magnitude is the quantity ma
Rotational inertia acts perpendicular to the curvilinear path (i.e., radially outward) that an object is traveling;
its magnitude is mv 2/
r
Introduction d’Alembert’s Principle
Basic Situations & Free Body Diagrams
FREE WEIGHT
WEIGHT ON FRICTIONLESS SURFACE WITH HORIZONTAL FORCE
TAUT CABLE
ROLLER CONTACT
ROUGH CONTACT OR PIN JOINT
WEIGHT ON FRICTIONLESS SURFACE
WEIGHT ON REAL SURFACE WITH ANGLED FORCE
SAGGING CABLE
FRICTIONLESS CONTACT
WELDED, BOLTED (RIGID) CONNECTION
Free Body Diagrams
TM
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