Class Notes (922,335)
US (355,963)
UTEP (107)
BE (3)
BE 1101 (3)
All (3)
Reference Guide

Free Body Diagrams - Reference Guides

2 Pages
265 Views
Likes

Department
Basic Engineering
Course Code
BE 1101
Professor
All

This preview shows half of the first page. Sign up to view the full 2 pages of the document.
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
permacharts
permacharts.com

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

Leah — University of Toronto

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto
Saarim — University of Michigan

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan
Jenna — University of Wisconsin

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin
Anne — University of California

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California
Description
permachartsTM F r e eB o d yD ia g ra m s Introduction d’Alembert’s Principle •frces that act upon them; the procedure involves 2 stepsembert’s Principle asserts that inertial and centrifugal effects can be treated like a force •Isolate the object or system (i.e.,detach the rigi•This allows Dynamics problems to be analyzed using the principles of Statics •Replace all forces,either real or virtual (see For• Translational inertia acts in the direction opposite to the direction of the acceleration; its magnitude is the quantity ma •off-axis (angled force) vectors into their XY componentsti2nal inertia acts perpendicular to the curvilinear path (i.e.,radially outward) that an object is traveling; its magnitude is mv / Basic Situations & Free Body Diagrams 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) FREE WEIGHT WEIGHT ON FRICTIONLESS SURFACE •W is a force; therefore,it is a vector •n is the reaction of the floor acting on the stationary weight •This force is due to gravitational interaction between the Earth and the body,which always acts towards the center of the Note: Mass is not a force; it is a property of matter and related to weight by W = mg WEIGHT ON FRICTIONLESS SURFACE WITH HORIZONTAL FORCWEIGHT ON REAL SURFACE WITH ANGLED FORCE • Since the mass is being pushed on a frictionless floor,the only resistance to the acceleration is the inertia (ma) o the mass; it opposes the acceleration • If Px (not shown) matches Rf,then there will be no inertial force (in accordance with Newton’s Second Law) m o • Cables always pull along their line of action at the point of attachmentong their line of action at the point of attachment . s t r a h c a ROLLER CONTACT FRICTIONLESS CONTACT • Roller contacts cannot resist a force parallel to the surface of contact cannot resist a force parallem to the surface of contact •Therefore,any force at this contact must be perpendicular (normal) to the surfacentact must be perpendirular (normal) to the surface e p ROUGH CONTACT OR PIN JOINT WELDED, BOLTED (RIGID) CONNECTION •A swivel or pin joint can resist any linear push or pullhe swivel joint is replaced by a welded,bolted or rigid connection,then the joint can be represented by R (as for the • In two dimensions (2-D),this can be represented by a resultant force with components Rf and Rn orRx and Rymoment) permacharts TM Force Types •There are 2 categories of forces in mechanical analysis (see Force & Vector Representations) B ODY FORCES SURFACE FORCES • Body forces are also known as action-at-a-distance forces • Surface forces are also known as contact forces •They include gravitational,electrical,magnetic,and inertial force•These forces arise from contact between the rigid body and anything it contacts (e.g.,the floor,a cable,a plate to which it is attached with a bolt or pin joint) Note: In Statics and Dynamics,problems are usually limited to grav• Surface forces may be concentrated or distributed inertial forces • Concentrated surface forces can act in compression or tension • Inertial forces are reactions resulting from an acceleration • Compressive forces are represented by conventional arrows that terminate at the point of contact • Translational and rotational inertial forces (identified by d’AlNote:When body forces are concentrated tensile forces,they are represented by conventional arrows that originate at the point of contact expressed by ma and mv (centrifugal force) • Distributed surface forces are usually compressive; therefore,they act perpendicular (normal) to the surface • Body forces are represented by arrows that originate at the cent• However,they can also act tangential to the surface (e.g.,friction) (cg) of the object (rigid body) being analyzed •The arrow points in the direction of the force’s action • Tangential distributed forces are represented by a double-headed arrow indicating that they act along a line Examples: Weight vectors,due to gr
More Less
Unlock Document


Only half of the first page are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit