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Article Four of the United States Constitution
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Article Four of the United States Constitution
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Article Four of the United States Constitution outlines the relationship between each state and the others, and the several States and the federal government.
Contents
[hide]
1 Section 1: Full faith and credit
2 Section 2: Rights of state citizens; rights of extradition
2.1 Clause 1: Privileges and Immunities
2.2 Clause 2: Extradition of fugitives
2.3 Clause 3: Fugitive Slave Clause
3 Section 3: New states and federal property
3.1 Clause 1: New states
3.2 Clause 2: Property Clause
4 Section 4: Obligations of the United States
4.1 Clause 1: Republican government
4.2 Clause 2: Protection from invasion and domestic violence
5 See also
6 Notes and references
7 Further reading
8 External links
Section 1: Full faith and credit[edit]
Main article: Full Faith and Credit Clause
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
The first section requires states to extend "full faith and credit" to the public acts, records and court proceedings of other states. Congress may regulate the manner in which proof of such acts, records or proceedings may be admitted.
In Mills v. Duryee, 1t1 U.S. (7 Cranch) 481 (1813), the United States Supreme Court ruled that the merits of a case, as settled by courts of one state, must be recognized by the courts of other states; state courts may not reopen cases which have been conclusively decided by the courts of another state. Later, Chief Justice John Marshall suggested that the judgment of one state court must be recognized by other states' courts as final. However, in McElmoyle v. Cohen, 38 U.S. (13 Pet.) 312 (1839), the court heard a case where one party obtained a judgment in South Carolina and sought to enforce it in Georgia, which had a statute of limitations that barred actions on judgments after a certain amount of time had passed since the judgment was entered. The court upheld Georgia's refusal to enforce the South Carolina judgment. The court found that out-of-state judgments are subject to the procedural law of the states where they are enforced, notwithstanding any priority accorded in the states in which they are issued.
Section 2: Rights of state citizens; rights of extradition[edit]
Clause 1: Privileges and Immunities[edit]
Main article: Privileges and Immunities Clause
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
Clause One of Section 2 requires interstate protection of "privileges and immunities". The seeming ambiguity of the clause has given rise to a number of different interpretations. Some contend that the clause requires Congress to treat all citizens equally. Others suggest that citizens of states carry the rights accorded by their home states while traveling in other states.
Neither of these theories has been endorsed by the Supreme Court, which has held that the clause means that a state may not discriminate against citizens of other states in favor of its own citizens. In Corfield v. Coryell, 6 F. Cas. 546 (C.C.E.D. Pa. 1823), the federal circuit court held that privileges and immunities in respect of which discrimination is barred include
protection by the Government; the enjoyment of life and liberty ... the right of a citizen of one State to pass through, or to reside in any other State, for purposes of trade, agriculture, professional pursuits, or otherwise; to claim the benefits of the writ of habeas corpus; to institute and maintain actions of any kind in the courts of the State; to take, hold and dispose of property, either real or personal; and an exemption from higher taxes or impositions than are paid by the other citizens of the State.
Most other benefits were held not to be protected privileges and immunities. In Corfield the circuit court sustained a New Jersey law giving state residents the exclusive right to gather clams and oysters.
Clause 2: Extradition of fugitives[edit]
Main article: Extradition Clause
A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.
Clause Two requires that fugitives from justice may be extradited on the demand of executive authority of the state from which they flee. The Supreme Court has held that it is not compulsory for the fugitive to have fled after an indictment was issued, but only that the fugitive fled after having committed the crime. The Constitution provides for the extradition of fugitives who have committed "treason, felony or other crime." That phrase incorporates all acts prohibited by the laws of a state, including misdemeanors and small, or petty, offenses.
In Kentucky v. Dennison, 65 U.S. 66 (1860), the Supreme Court held that the federal courts may not compel state governors to surrender fugitives through the issue of writs of mandamus. The Dennison decision was overruled by Puerto Rico v. Branstad, 483 U.S. 219 (1987); now, the federal courts may require the extradition of fugitives.[1] Alleged fugitives generally may not challenge extradition proceedings.
The motives of the governor demanding the extradition may not be questioned. The accused cannot defend himself against the charges in the extraditing state; the fugitive must do so in the state receiving him. However, the accused may prevent extradition by offering clear evidence that he was not in the state he allegedly fled from at the time of the crime.[2] There is no constitutional requirement that extradited fugitives be tried only for the crimes named in the extradition proceedings.
Fugitives brought to states by means other than extradition may be tried, even though the means of the conveyance was unlawful; the Supreme Court so ruled in Mahon v. Justice, 127 U.S. 700 (1888). In Mahon a body of armed men from Kentucky forcibly took, without a warrant, a man in West Virginia to bring him back to Kentucky for formal arrest and trial.
Clause 3: Fugitive Slave Clause[edit]
Main article: Fugitive Slave Clause
No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due.
Pierce Butler and Charles Pinckney, both from South Carolina, submitted this clause to the Constitutional Convention. James Wilson of Pennsylvania objected, stating it would require that state governments enforce slavery at taxpayers' expense. Butler withdrew the clause. However, on the next day the clause was quietly reinstated and adopted by the Convention without objection. This clause was added to the clause that provided extradition for fugitives from justice.[3]
When first adopted, this clause applied to fugitive slaves and required that they be extradited upon the claims of their masters, but it provided no means for doing so. The Fugitive Slave Act of 1793 created the mechanism for recovering a fugitive slave, overruled any state laws giving sanctuary, made it a federal crime to assist an escaped slave, and allowed slave-catchers into every U.S. state and territory. As free states sought to undermine the federal law, the even more severe Fugitive Slave Act of 1850 was enacted.
In 1864, during the Civil War, an effort to repeal this clause of the Constitution failed.[4] This clause was rendered mostly moot when the Thirteenth Amendment abolished slavery.
Section 3: New states and federal property[edit]
Clause 1: New states[edit]
Main article: Admission to the Union
See also: List of U.S. states by date of admission to the Union
New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
The First Clause of Section Three, also known as the Admissions Clause,[5] grants to Congress the authority to admit new states into the Union. Since the establishment of the United States in 1776, the number of states has expanded from the original 13 to 50. It also forbids the creation of new states from parts of existing states without the consent of the affected states and Congress. This latter provision was designed to give Eastern states that still had claims to Western lands (e.g., Virginia and North Carolina) to have a veto over whether their western counties (which eventually became Kentucky and Tennessee) could become states.[6] It would later be applied with regard to the formation of Maine (from Massachusetts) and West Virginia (from Virginia).[7]
At the 1787 Constitutional Convention, a proposal to include the phrase, "new States shall be admitted on the same terms with the original States", was defeated. It was feared that the political power of future new western states would eventually overwhelm that of the established eastern states. Once the new Constitution went into effect, however, Congress admitted Vermont and Kentucky on equal terms and thereafter formalized the condition in its acts of admission for subsequent states, declaring that the new state enters "on an equal footing with the original States in all respects whatever." Thus the Congress, utilizing the discretion allowed by the framers, adopted a policy of equal status for all newly admitted states.[6] With the growth of states' rights advocacy during the antebellum period, the Supreme Court asserted, in Lessee of Pollard v. Hagan (1845), that the Constitution mandated admission of new states on the basis of equality.[8]
Congressional restrictions on the equality of states, even when those limitations have been found in the acts of admission, have been held void by the Supreme Court. For instance the Supreme Court struck down a provision which limited the jurisdiction of the state of Alabama over navigable waters within the state. The Court held,
Alabama is, therefore, entitled to the sovereignty and jurisdiction over all the territory within her limits ... to maintain any other doctrine, is to deny that Alabama has been admitted into the union on an equal footing with the original states ... to Alabama belong the navigable waters and soils under them.
The doctrine, however, can also be applied to the detriment of states, as occurred with Texas. Before admission to the Union, Texas, as an independent nation, controlled water within three miles of the coast, the normal limit for nations. Under the equal footing doctrine, however, Texas was found not to have control over the three-mile belt after admission into the Union, because the original states did not at the time of joining the union control such waters. Instead, by entering the Union, Texas was found to have surrendered control over the water and the soil under it to Congress. Under the Submerged Lands Act of 1953, Congress returned maritime territory to some states, but not to others; the Act was sustained by the Supreme Court.
The constitution is silent on the question of whether or not a state may unilaterally leave, or secede from, the Union. However, the Supreme Court, in Texas v. White (1869), held that a state cannot unilaterally do so.[9]
When, therefore, Texas became one of the United States, she entered into an indissoluble relation. All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.[10]
Clause 2: Property Clause[edit]
The Congress shall have power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.[11]
This clause, commonly known as the Property or Territorial Clause, grants Congress the constitutional authority for the management and control of all territories or other property owned by United States. Additionally, the clause also proclaims that nothing contained within the Constitution may be interpreted to harm (prejudice) any claim of the United States, or of any particular State. The exact scope of this clause has long been a matter of debate.
The federal government owns about twenty-eight percent of the land in the United States.[12] These holdings include national parks, national forests, recreation areas, wildlife refuges, vast tracts of range and public lands managed by the Bureau of Land Management, reservations held in trust for Native American tribes, military bases, and ordinary federal buildings and installations. Although federal property can be found in every state, the largest concentrations are in the west, where, for example, the federal government owns over eighty percent of the land within Nevada.[13]
Pursuant to a parallel clause in Article One, Section Eight, the Supreme Court has held that states may not tax such federal property. In another case, Kleppe v. New Mexico, the Court ruled that the federal Wild Horse and Burro Act was a constitutional exercise of congressional power under the Property Clause – at least insofar as it was applied to a finding of trespass. The case prohibited the entering upon the public lands of the United States and removing wild burros under the New Mexico Estray Law.[14]
A major issue early in the 20th century was whether the whole Constitution applied to the territories called insular areas by Congress. In a series of opinions by the Supreme Court of the United States, referred to as the Insular Cases, the Court ruled that territories belonged to, but were not part of the United States. Therefore, under the Territorial clause Congress had the power to determine which parts of the Constitution applied to the territories. These rulings have helped shape public opinion among Puerto Ricans during the ongoing debate over the commonwealth's political status.
Section 4: Obligations of the United States[edit]
Clause 1: Republican government[edit]
The United States shall guarantee to every State in this Union a Republican Form of Government, [...]
This clause, sometimes referred to as the Guarantee Clause, has long been at the fore-front of the debate about the rights of citizens vis-à-vis the government. The Guarantee Clause mandates that all U.S. states must be grounded in republican principles such as the consent of the governed.[15] By ensuring that all states must have the same basic republican philosophy, the Guarantee Clause is one of several portions of the Constitution which mandates symmetric federalism between the states.
The Constitution does not explain what exactly constitutes a republican form of government. There are, however, several places within it where the principles behind the concept are articulated. Article Seven, the last and shortest of the Constitution's original articles, stipulated that the Constitution, before it could become established as the "Law of the Land", must obtain the consent of the people by being ratified by popular conventions within the several states. Additionally, as it required the ratification of only nine states in order to become established, rather than the unanimous consent required by the Articles of Confederation, the Constitution was more republican, as it protected the majority from effectively being ruled or held captive by the minority.[16]
The Federalist Papers also give us some insight as to the intent of the Founders. A republican form of government is distinguished from a direct democracy, which the Founding Fathers had no intentions of entering. As James Madison wrote in Federalist No. 10, "Hence it is that such democracies have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security or the rights of property; and have in general been as short in their lives as they have been violent in their deaths."
A political crisis in 1840s Rhode Island, the Dorr Rebellion, forced the Supreme Court to rule on the meaning of this clause. At the time, the Rhode Island constitution was the old royal charter established in the 17th century. By the 1840s, only 40% of the state's free white males were enfranchised. An attempt to hold a popular convention to write a new constitution was declared insurrection by the charter government, and the convention leaders were arrested. One of them brought suit in federal court, arguing that Rhode Island's government was not "republican" in character, and that his arrest (along with all of the government's other acts) was invalid. In Luther v. Borden, 48 U.S. 1 (1849), the Court held that the determination of whether a state government is a legitimate republican form as guaranteed by the Constitution is a political question to be resolved by the Congress. In effect, the court held the clause to be non-justiciable.
The Luther v. Borden ruling left the responsibility to establish guidelines for the republican nature of state governments in the hands of the Congress. This power became an important part of Reconstruction after the American Civil War. The Radical Republican majority used this clause as the basis for taking control of the ex-Confederate states and for promoting civil rights for freedmen, plus the limiting of political and voting rights for ex-Confederates, abolishing the ex-Confederate state governments, setting guidelines for the readmission of the rebellious states into the Union.
While the Supreme Court's holding in Luther v. Borden still holds today, the Court, by looking to the Equal Protection Clause of the Fourteenth Amendment (adopted 19 years after Luther v. Borden was decided), has developed new criteria for determining which questions are political in nature and which are justiciable.
Clause 2: Protection from invasion and domestic violence[edit]
[...] and [the United States] shall protect each of them [the States] against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
Section Four requires the United States to protect each state from invasion, and, upon the application of the state legislature (or executive, if the legislature cannot be convened), from domestic violence. This provision was invoked by Woodrow Wilson during the 1914 Colorado coal strike.[17]
See also[edit]
Devolution
List of states and territories of the United States
Notes and references[edit]
Jump up ^ 483 U.S. 219 (1987) ("Kentucky v. Dennison is the product of another time. The conception of the relation between the States and the Federal Government there announced is fundamentally incompatible with more than a century of constitutional development.")
Jump up ^ Hyatt v. People ex rel. Corkran, 188 U.S. 691 (1903) ("We are of opinion that, as the relator showed…he was not within the state of Tennessee at the times stated in the indictments found in the Tennessee court, nor at any time when the acts were, if ever, committed, he was not a fugitive from justice within the meaning of the Federal statute upon that subject…")
Jump up ^ Paul Finkelman, Slavery and the founders: race and liberty in the age of Jefferson, pg 82, 2nd Edition, 2001.
Jump up ^ The vote in the House was 69 for repeal and 38 against, which was short of the two-to-one vote required to amend the Constitution. See the Congressional Globe, 38th Cong., 1st Sess., 1325 (1864)
Jump up ^ Biber, Eric; Colby, Thomas B. "Common Interpretation: The Admissions Clause". National Constitution Center. Retrieved 30 January 2017.
^ Jump up to: a b Forte, David F. "Essays on Article IV: New States Clause". The Heritage Guide to the Constitution. The Heritage Foundation.
Jump up ^ Michael P. Riccards, "Lincoln and the Political Question: The Creation of the State of West Virginia" Presidential Studies Quarterly, Vol. 27, 1997 online edition
Jump up ^ "Doctrine of the Equality of States". Justia.com.
Jump up ^ "Texas v. White 74 U.S. 700 (1868)". Justia.com.
Jump up ^ Texas v. White, 74 U.S. 700 (1868) at Cornell University Law School Supreme Court collection.
Jump up ^ "Archived copy". Archived from the original (PDF) on June 15, 2010. Retrieved 2014-01-07.
Jump up ^ Vincent, Carol Hardy; et al. "Federal Land Ownership: Overview and Data" (PDF). Federation of American Scientists. Congressional Research Service. Retrieved 10 April 2017. CS1 maint: Explicit use of et al. (link)
Jump up ^ Merrill, Thomas W. "Essays on Article IV:Property Clause". The Heritage Guide to the Constitution. The Heritage Foundation.
Jump up ^ 426 U.S. 529 (1976); 96 S.Ct. 2285; 49 L.Ed.2d 34
Jump up ^ Ernest B. Abbott; Otto J. Hetzel (2010). Homeland Security and Emergency Management: A Legal Guide for State and Local Governments. American Bar Association. p. 52.
Jump up ^ Kesler, Charles R. "Essays on Article VII: Ratification Clause". The Heritage Guide to the Constitution. The Heritage Foundation. Retrieved May 9, 2014.
Jump up ^ Wilson, Woodrow (1979). Link, Arthur, ed. The Papers of Woodrow Wilson. 29. Princeton, NJ: Princeton University Press. pp. 525–528. ISBN 9780691046594.
Further reading[edit]
Adam H. Kurland, The Guarantee Clause as a Basis for Federal Prosecutions of State and Local Officials, 62 S. Cal. L. Rev. 369 (1989).
External links[edit]
Kilman, Johnny and George Costello (Eds). (2000). The Constitution of the United States of America: Analysis and Interpretation.
CRS Annotated Constitution: Article 4
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Free body diagram
From Wikipedia, the free encyclopedia
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Block on a ramp and corresponding free body diagram of the block.
In physics and engineering, a free body diagram (force diagram,[1] or FBD) is a graphical illustration used to visualize the applied forces, movements, and resulting reactions on a body in a given condition. They depict a body or connected bodies with all of the applied forces and moments, as well as reactions, that act on that/those body(ies). The body may consist of multiple internal members, for example, a truss, or be a compact body such as a beam. A series of free bodies and other diagrams may be necessary to solve complex problems.
Contents
[hide]
1 Purpose
2 Features
2.1 Modeling the body
2.1.1 Example: A body in free fall
2.2 What is included
2.3 Exclusions
3 Analysis
3.1 Angled forces
4 Example: A block on an inclined plane
5 See also
6 References
7 Notes
Purpose[edit]
Free body diagrams are used to visualize the forces and moments applied to a body and calculate the resulting reactions, in many types of mechanics problems. Most free body diagrams are used both to determine the loading of individual structural components as well as calculating internal forces within the structure in almost all engineering disciplines from Biomechanics to Structural.[2][3] In the educational environment, learning to draw a free body diagram is an important step in understanding certain topics in physics, such as statics, dynamics and other forms of classical mechanics.
Features[edit]
A free body diagram is not meant to be a scaled drawing. It is a diagram that is modified as the problem is solved. There is an art and flexibility to the process. The iconography of a free body diagram, not only how it is drawn but also how it is interpreted, depends upon how a body is modeled.[4]
Free body diagrams consist of:
A simplified version of the body (often a dot or a box)
Forces shown as straight arrows pointing in the direction they act on the body
Moments shown as curved arrows pointing in the direction they act on the body
A coordinate system
Frequently reaction to applied forces are shown with hash marks through the stem of the arrow
The number of forces and moments shown in a free body diagram depends on the specific problem and the assumptions made; common assumptions are neglecting air resistance, friction and assuming rigid bodies. In statics all forces and moments must balance to zero; the physical interpretation of this is that if the forces and moments do not sum to zero the body is accelerating and the principles of statics do not apply. In dynamics the resultant forces and moments can be non-zero.
Free body diagrams may not represent an entire physical body. Using what is known as a "cut" only portions of a body are selected for modeling. This technique exposes internal forces, making them external, therefore allowing analysis. This technique is often used several times, iteratively to peel back forces acting on a physical body. For example, a gymnast performing the iron cross: analyzing the ropes and the person lets you know the total force (body weight, neglecting rope weight, breezes, buoyancy, electrostatics, relativity, rotation of the earth, etc..). Then cut the person out and only show one rope. You get force direction. Then only look at the person, now you can get hand forces. Now only look at the arm to get the shoulder forces and moments, and on and on until the component you intend to analyze is exposed.
Modeling the body[edit]
A body may be modeled in three ways:
a particle. This model may be used when any rotational effects are zero or have no interest even though the body itself may be extended. The body may be represented by a small symbolic blob and the diagram reduces to a set of concurrent arrows. A force on a particle is a bound vector.
rigid extended. Stresses and strains are of no interest but turning effects are. A force arrow should lie along the line of force, but where along the line is irrelevant. A force on an extended rigid body is a sliding vector.
non-rigid extended. The point of application of a force becomes crucial and has to be indicated on the diagram. A force on a non-rigid body is a bound vector. Some use the tail of the arrow to indicate the point of application. Others use the tip.
Example: A body in free fall[edit]
Figure 2: An empty rigid bucket in free fall in a uniform gravitational field with the force arrow at the center of gravity.
Consider a body in free fall in a uniform gravitational field. The body may be
a particle. It is enough to show a single vertically downward pointing arrow attached to a blob.
rigid extended. A single arrow suffices to represent the weight W even though gravitational attraction acts on every particle of the body.
non-rigid extended. In non-rigid analysis, it would be an error to associate a single point of application with the gravitational force.
What is included[edit]
An FBD represents the body of interest and the external forces on it.
The body: This is usually sketched in a schematic way depending on the body - particle/extended, rigid/non-rigid - and on what questions are to be answered. Thus if rotation of the body and torque is in consideration, an indication of size and shape of the body is needed. For example, the brake dive of a motorcycle cannot be found from a single point, and a sketch with finite dimensions is required.
The external forces: These are indicated by labelled arrows. In a fully solved problem, a force arrow is capable of indicating
the direction and the line of action[notes 1]
the magnitude
the point of application.
a reaction as opposed to an applied load if a hash is present through the arrow
Typically, however, a provisional free body sketch is drawn before all these things are known. After all, the whole point of the diagram is to help to determine magnitude, direction, and point of application of the external loads! Thus when a force arrow is originally drawn its length may not be meant to indicate the unknown magnitude. Its line may not correspond to the exact line of action. Even its direction may turn out to be wrong. Very often the original direction of the arrow may be directly opposite to the true direction. External forces known to be small that are known to have negligible effect on the result of the analysis, are sometimes omitted, but only after careful consideration or after other analysis proving it (e.g. buoyancy forces of the air in the analysis of a chair, or atmospheric pressure on the analysis of a frying pan).
The external; forces acting on the object include friction, gravity, normal force, drag, tension, or a human force due to pushing or pulling. When in a non-inertial reference frame (see coordinate system, below), fictitious forces, such as centrifugal pseudoforce are appropriate.
A coordinate system is sometimes included, and is chosen according to convenience (or advantage). Savvy selection of coordinate frame may make defining the vectors simpler when writing the equations of motion. The x direction might be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an x component, and the normal force only has a y component. The force of gravity will still have components in both the x and y direction: mgsin(θ) in the x and mgcos(θ) in the y, where θ is the angle between the ramp and the horizontal.
Exclusions[edit]
There are some things that a free body diagram explicitly excludes. Although other sketches that include these things may be helpful in visualizing a problem, a proper free body diagram should not show:
Bodies other than the free body.
Constraints.
(The body is not free from constraints; the constraints have just been replaced by the forces and moments that they exert on the body.)
Forces exerted by the free body.
(A diagram showing the forces exerted both on and by a body is likely to be confusing since all the forces will cancel out. By Newton's 3rd law if body A exerts a force on body B then B exerts an equal and opposite force on A. This should not be confused with the equal and opposite forces that are necessary to hold a body in equilibrium.)
Internal forces.
(For example, if an entire truss is being analyzed, the forces between the individual truss members are not included.)
Velocity or acceleration vectors.
Analysis[edit]
A free body diagram is analyzed by summing all of the forces, often accomplished by summing the forces in each of the axis directions. When the net force is zero, the body must be at rest or must be moving at a constant velocity (constant speed and direction), by Newton's first law. If the net force is not zero, then the body is accelerating in that direction according to Newton's second law.
Angled forces[edit]
Angled force (F) broken down into horizontal (Fx) and vertical (Fy) components
Determining the sum of the forces is straightforward if all they are aligned with the coordinate frame's axes, but it is somewhat more complex if some forces are not aligned. It is often convenient to analyze the components of the forces, in which case the symbols ΣFx and ΣFy are used instead of ΣF. Forces that point at an angle to the diagram's coordinate axis can be broken down into two parts (or three, for three dimensional problems)—each part being directed along one of the axes—horizontally (Fx) and vertically (Fy).
Example: A block on an inclined plane[edit]
A simple free body diagram, shown above, of a block on a ramp illustrates this.
All external supports and structures have been replaced by the forces they generate. These include:
mg: the product of the mass of the block and the constant of gravitation acceleration: its weight.
N: the normal force of the ramp.
Ff: the friction force of the ramp.
The force vectors show direction and point of application and are labeled with their magnitude.
It contains a coordinate system that can be used when describing the vectors.
Some care is needed in interpreting the diagram.
The normal force has been shown to act at the midpoint of the base, but if the block is in static equilibrium its true location is directly below the center of mass, where the weight acts, because that is necessary to compensate for the moment of the friction.
Unlike the weight and normal force, which are expected to act at the tip of the arrow, the friction force is a sliding vector and thus the point of application is not relevant, and the friction acts all along the whole base.
See also[edit]
Wikimedia Commons has media related to Free body diagrams.
Wikimedia Commons has media related to Vector force diagrams.
Classical Mechanics
Force field analysis – applications of force diagram in social science
Shear and moment diagrams
Kinematic diagram
References[edit]
Jump up ^ "Force Diagrams (Free-body Diagrams)". Western Kentucky University. Retrieved 2011-03-17.
Jump up ^ Ruina, Andy; Pratap, Rudra (2002). Introduction to Statics and Dynamics (PDF). Oxford University Press. pp. 79–105. Retrieved 2006-08-04.
Jump up ^ Hibbeler, R.C. (2007). Engineering Mechanics: Statics & Dynamics (11th ed.). Pearson Prentice Hall. pp. 83–86. ISBN 0-13-221509-8.
Jump up ^ Puri, Avinash (1996). "The Art of Free-body Diagrams". Physics Education. 31 (3): 155. Bibcode:1996PhyEd..31..155P. doi:10.1088/0031-9120/31/3/015.
Notes[edit]
Jump up ^ The line of action is important where moment matters
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