In science and engineering , the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition.
127-403: A tripod is a portable three-legged frame or stand, used as a platform for supporting the weight and maintaining the stability of some other object. The three-legged (triangular stance) design provides good stability against gravitational loads as well as horizontal shear forces , and better leverage for resisting tipping over due to lateral forces can be achieved by spreading the legs away from
254-422: A Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong , electromagnetic , weak , and gravitational . High-energy particle physics observations made during
381-472: A lever mechanism – a lever-balance. The standard masses are often referred to, non-technically, as "weights". Since any variations in gravity will act equally on the unknown and the known weights, a lever-balance will indicate the same value at any location on Earth. Therefore, balance "weights" are usually calibrated and marked in mass units, so the lever-balance measures mass by comparing the Earth's attraction on
508-404: A standard value of 9.80665 m/s , which gives the standard weight . The force whose magnitude is equal to mg newtons is also known as the m kilogram weight (which term is abbreviated to kg-wt ) In the operational definition, the weight of an object is the force measured by the operation of weighing it, which is the force it exerts on its support . Since W is the downward force on
635-406: A balance." Operational balances (rather than definitions) had, however, been around much longer. According to Aristotle, weight was the direct cause of the falling motion of an object, the speed of the falling object was supposed to be directly proportionate to the weight of the object. As medieval scholars discovered that in practice the speed of a falling object increased with time, this prompted
762-420: A body is the product of its mass and the acceleration due to gravity. This resolution defines weight as a vector, since force is a vector quantity. However, some textbooks also take weight to be a scalar by defining: The weight W of a body is equal to the magnitude F g of the gravitational force on the body. The gravitational acceleration varies from place to place. Sometimes, it is simply taken to have
889-469: A century on how to define weight for their students. The current situation is that a multiple set of concepts co-exist and find use in their various contexts. Discussion of the concepts of heaviness (weight) and lightness (levity) date back to the ancient Greek philosophers . These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle , weight and levity represented
1016-452: A change to the concept of weight to maintain this cause-effect relationship. Weight was split into a "still weight" or pondus , which remained constant, and the actual gravity or gravitas , which changed as the object fell. The concept of gravitas was eventually replaced by Jean Buridan 's impetus , a precursor to momentum . The rise of the Copernican view of the world led to
1143-464: A constant mass m {\displaystyle m} to then have any predictive content, it must be combined with further information. Moreover, inferring that a force is present because a body is accelerating is only valid in an inertial frame of reference. The question of which aspects of Newton's laws to take as definitions and which to regard as holding physical content has been answered in various ways, which ultimately do not affect how
1270-580: A different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result . If both of these pieces of information are not known for each force, the situation is ambiguous. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate
1397-439: A false weight induced by imperfect measurement conditions, for which he introduced the term apparent weight as compared to the true weight defined by gravity. Although Newtonian physics made a clear distinction between weight and mass, the term weight continued to be commonly used when people meant mass. This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 to officially declare "The word weight denotes
SECTION 10
#17328514376901524-482: A force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion. Some forces are consequences of
1651-474: A force that existed intrinsically between two charges . The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction , was both attractive and repulsive (there was intrinsic polarity ), was independent of the mass of the charged objects, and followed the superposition principle . Coulomb's law unifies all these observations into one succinct statement. Subsequent mathematicians and physicists found
1778-582: A frame of reference if it at rest and not accelerating, whereas a body in dynamic equilibrium is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa. Static equilibrium was understood well before the invention of classical mechanics. Objects that are not accelerating have zero net force acting on them. The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on
1905-459: A key principle of Newtonian physics. In the early 17th century, before Newton's Principia , the term "force" ( Latin : vis ) was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named vis viva (live force) by Leibniz . The modern concept of force corresponds to Newton's vis motrix (accelerating force). Sir Isaac Newton described
2032-431: A level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force ). The situation produces zero net force and hence no acceleration. Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because
2159-481: A quantity of the same nature as a force : the weight of a body is the product of its mass and the acceleration due to gravity", thus distinguishing it from mass for official usage. In the 20th century, the Newtonian concepts of absolute time and space were challenged by relativity. Einstein's equivalence principle put all observers, moving or accelerating, on the same footing. This led to an ambiguity as to what exactly
2286-407: A situation that is commonly referred to as weightlessness . However, being in free fall does not affect the weight according to the gravitational definition. Therefore, the operational definition is sometimes refined by requiring that the object be at rest. However, this raises the issue of defining "at rest" (usually being at rest with respect to the Earth is implied by using standard gravity ). In
2413-421: A stable mount for the weapon when firing. Tripods are generally restricted to heavier weapons where the weight would be an encumbrance. For lighter weapons such as rifles , a bipod is more common. However, in recent times tripod saddles have become popular for precision rifle shooting sports, with the weapon placed in a vise -like rest which is mounted to a tripod head or with the weapon mounted directly to
2540-432: A straight line will see it continuing to do so. According to the first law, motion at constant speed in a straight line does not need a cause. It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time . If
2667-745: A surface up to the limit specified by the coefficient of static friction ( μ s f {\displaystyle \mu _{\mathrm {sf} }} ) multiplied by the normal force ( F N {\displaystyle \mathbf {F} _{\text{N}}} ). In other words, the magnitude of the static friction force satisfies the inequality: 0 ≤ F s f ≤ μ s f F N . {\displaystyle 0\leq \mathbf {F} _{\mathrm {sf} }\leq \mu _{\mathrm {sf} }\mathbf {F} _{\mathrm {N} }.} The kinetic friction force ( F k f {\displaystyle F_{\mathrm {kf} }} )
SECTION 20
#17328514376902794-413: A system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained. Some textbooks use Newton's second law as a definition of force. However, for the equation F = m a {\displaystyle \mathbf {F} =m\mathbf {a} } for
2921-484: A unidirectional force or a force that acts on only one body. In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F 1 , 2 + F 2 , 1 = 0. {\displaystyle \mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but
3048-421: Is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at
3175-487: Is defined as the force necessary to accelerate an object of one-pound mass at 1 ft/s , and is equivalent to about 1/32.2 of a pound- force . The slug is defined as the amount of mass that accelerates at 1 ft/s when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass). The kilogram-force is a non-SI unit of force, defined as the force exerted by a one-kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne
3302-417: Is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of
3429-478: Is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field. Gravitational force and weight thereby became essentially frame-dependent quantities. This prompted the abandonment of the concept as superfluous in the fundamental sciences such as physics and chemistry. Nonetheless, the concept remained important in the teaching of physics. The ambiguities introduced by relativity led, starting in
3556-501: Is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass. The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity does not vary too much on the surface of the Earth. In a uniform gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. For example, object A weighs 10 times as much as object B, so therefore
3683-428: Is often also referred to as the apparent weight. In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter , whereas weight is a force that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass"
3810-544: Is only one-sixth of what the object would have on Earth. So a man of mass 180 pounds weighs only about 30 pounds-force when visiting the Moon. In most modern scientific work, physical quantities are measured in SI units. The SI unit of weight is the same as that of force: the newton (N) – a derived unit which can also be expressed in SI base units as kg⋅m/s (kilograms times metres per second squared). In commercial and everyday use,
3937-481: Is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of m {\displaystyle m} will experience a force: F = m g . {\displaystyle \mathbf {F} =m\mathbf {g} .} For an object in free-fall, this force
Tripod - Misplaced Pages Continue
4064-397: Is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If Δ x {\displaystyle \Delta x}
4191-411: Is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI. The sensation of weight is caused by the force exerted by fluids in the vestibular system , a three-dimensional set of tubes in the inner ear . It is actually the sensation of g-force , regardless of whether this is due to being stationary in the presence of gravity, or, if
4318-515: Is the coefficient of kinetic friction . The coefficient of kinetic friction is normally less than the coefficient of static friction. Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys , which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along
4445-432: Is the mass and v {\displaystyle \mathbf {v} } is the velocity . If Newton's second law is applied to a system of constant mass , m may be moved outside the derivative operator. The equation then becomes F = m d v d t . {\displaystyle \mathbf {F} =m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}.} By substituting
4572-418: Is the newton (N) , and force is often represented by the symbol F . Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion . Types of forces often encountered in classical mechanics include elastic , frictional , contact or "normal" forces , and gravitational . The rotational version of force is torque , which produces changes in
4699-410: Is the displacement, the force exerted by an ideal spring equals: F = − k Δ x , {\displaystyle \mathbf {F} =-k\Delta \mathbf {x} ,} where k {\displaystyle k} is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to
4826-410: Is the distance between the two objects' centers of mass and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointed in the direction away from the center of the first object toward the center of the second object. This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until
4953-468: Is the electromagnetic force, E {\displaystyle \mathbf {E} } is the electric field at the body's location, B {\displaystyle \mathbf {B} } is the magnetic field, and v {\displaystyle \mathbf {v} } is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with
5080-488: Is the force of body 1 on body 2 and F 2 , 1 {\displaystyle \mathbf {F} _{2,1}} that of body 2 on body 1, then F 1 , 2 = − F 2 , 1 . {\displaystyle \mathbf {F} _{1,2}=-\mathbf {F} _{2,1}.} This law is sometimes referred to as the action-reaction law , with F 1 , 2 {\displaystyle \mathbf {F} _{1,2}} called
5207-581: Is the magnitude of the hypothetical test charge. Similarly, the idea of the magnetic field was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge q {\displaystyle q} due to electric and magnetic fields: F = q ( E + v × B ) , {\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),} where F {\displaystyle \mathbf {F} }
Tripod - Misplaced Pages Continue
5334-591: Is the momentum of object 1 and p 2 {\displaystyle \mathbf {p} _{2}} the momentum of object 2, then d p 1 d t + d p 2 d t = F 1 , 2 + F 2 , 1 = 0. {\displaystyle {\frac {\mathrm {d} \mathbf {p} _{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {p} _{2}}{\mathrm {d} t}}=\mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} Using similar arguments, this can be generalized to
5461-438: Is the momentum of the system, and F {\displaystyle \mathbf {F} } is the net ( vector sum ) force. If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time. In common engineering applications
5588-449: Is the velocity of the object and r {\displaystyle r} is the distance to the center of the circular path and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to
5715-437: Is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals: F k f = μ k f F N , {\displaystyle \mathbf {F} _{\mathrm {kf} }=\mu _{\mathrm {kf} }\mathbf {F} _{\mathrm {N} },} where μ k f {\displaystyle \mu _{\mathrm {kf} }}
5842-442: Is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward. Newton's contribution to gravitational theory
5969-464: The Aristotelian theory of motion . He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction . Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by Isaac Beeckman , René Descartes , and Pierre Gassendi , became
6096-526: The ISO International standard ISO 80000-4:2006, describing the basic physical quantities and units in mechanics as a part of the International standard ISO/IEC 80000 , the definition of weight is given as: Definition Remarks The definition is dependent on the chosen frame of reference . When the chosen frame is co-moving with the object in question then this definition precisely agrees with
6223-400: The action and − F 2 , 1 {\displaystyle -\mathbf {F} _{2,1}} the reaction . Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. and thus that there is no such thing as
6350-476: The center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system. Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved in any closed system . In a system of two particles, if p 1 {\displaystyle \mathbf {p} _{1}}
6477-519: The gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Yet others define it as the magnitude of the reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale. Thus, in a state of free fall , the weight would be zero. In this sense of weight, terrestrial objects can be weightless: so if one ignores air resistance , one could say
SECTION 50
#17328514376906604-417: The 1960s, to considerable debate in the teaching community as how to define weight for their students, choosing between a nominal definition of weight as the force due to gravity or an operational definition defined by the act of weighing. Several definitions exist for weight , not all of which are equivalent. The most common definition of weight found in introductory physics textbooks defines weight as
6731-409: The 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines . The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for
6858-425: The 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet , moon , comet , or asteroid . The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed. The electrostatic force was first described in 1784 by Coulomb as
6985-402: The 7th and 8th millennia BC. Sacrificial tripods were found in use in ancient China usually cast in bronze but sometimes appearing in ceramic form. They are often referred to as " dings " and usually have three legs, but in some usages have four legs. The Chinese use sacrificial tripods symbolically in modern times, such as in 2005, when a "National Unity Tripod" made of bronze was presented by
7112-500: The Aristotelean view of physics. The introduction of Newton's laws of motion and the development of Newton's law of universal gravitation led to considerable further development of the concept of weight. Weight became fundamentally separate from mass . Mass was identified as a fundamental property of objects connected to their inertia , while weight became identified with the force of gravity on an object and therefore dependent on
7239-439: The acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law . Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass ( m ⊕ {\displaystyle m_{\oplus }} ) and
7366-412: The actual gravity that would be experienced near the poles. Force A force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force
7493-399: The applied force is opposed by static friction , generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and
7620-430: The applied load. For an object in uniform circular motion , the net force acting on the object equals: F = − m v 2 r r ^ , {\displaystyle \mathbf {F} =-{\frac {mv^{2}}{r}}{\hat {\mathbf {r} }},} where m {\displaystyle m} is the mass of the object, v {\displaystyle v}
7747-502: The atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids , differences in pressure result in forces being directed along the pressure gradients as follows: F V = − ∇ P , {\displaystyle {\frac {\mathbf {F} }{V}}=-\mathbf {\nabla } P,} where V {\displaystyle V}
SECTION 60
#17328514376907874-433: The body by the centre of earth and there is no acceleration in the body, there exists an opposite and equal force by the support on the body. Also it is equal to the force exerted by the body on its support because action and reaction have same numerical value and opposite direction. This can make a considerable difference, depending on the details; for example, an object in free fall exerts little if any force on its support,
8001-417: The central Chinese government to the government of northwest China's Xinjiang Uygur Autonomous Region to mark its fiftieth birthday. It was described as a traditional Chinese sacrificial vessel symbolizing unity. In ancient Greece, tripods were frequently used to support lebes , or cauldrons, sometimes for cooking and other uses such as supporting vases. Tripods are commonly used on machine guns to provide
8128-582: The comparison mass are in virtually the same location, so experiencing the same gravitational field , the effect of varying gravity does not affect the comparison or the resulting measurement. The Earth's gravitational field is not uniform but can vary by as much as 0.5% at different locations on Earth (see Earth's gravity ). These variations alter the relationship between weight and mass, and must be taken into account in high-precision weight measurements that are intended to indirectly measure mass. Spring scales , which measure local weight, must be calibrated at
8255-428: The constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles , such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries
8382-406: The constant forward velocity. Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction . In such a situation,
8509-515: The construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical " test charge " anywhere in space and then using Coulomb's Law to determine the electrostatic force. Thus the electric field anywhere in space is defined as E = F q , {\displaystyle \mathbf {E} ={\mathbf {F} \over {q}},} where q {\displaystyle q}
8636-498: The context of the object. In particular, Newton considered weight to be relative to another object causing the gravitational pull, e.g. the weight of the Earth towards the Sun. Newton considered time and space to be absolute. This allowed him to consider concepts as true position and true velocity. Newton also recognized that weight as measured by the action of weighing was affected by environmental factors such as buoyancy. He considered this
8763-408: The crucial properties that forces are additive vector quantities : they have magnitude and direction. When two forces act on a point particle , the resulting force, the resultant (also called the net force ), can be determined by following the parallelogram rule of vector addition : the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that
8890-417: The definition of acceleration , the algebraic version of Newton's second law is derived: F = m a . {\displaystyle \mathbf {F} =m\mathbf {a} .} Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if F 1 , 2 {\displaystyle \mathbf {F} _{1,2}}
9017-406: The early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light and also provided insight into the forces produced by gravitation and inertia . With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised
9144-428: The elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as
9271-403: The equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment
9398-407: The factory. When the scale is moved to another location on Earth, the force of gravity will be different, causing a slight error. So to be highly accurate and legal for commerce, spring scales must be re-calibrated at the location at which they will be used. A balance on the other hand, compares the weight of an unknown object in one scale pan to the weight of standard masses in the other, using
9525-424: The force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects. The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of
9652-402: The force exerted on a body by gravity. This is often expressed in the formula W = mg , where W is the weight, m the mass of the object, and g gravitational acceleration . In 1901, the 3rd General Conference on Weights and Measures (CGPM) established this as their official definition of weight : The word weight denotes a quantity of the same nature as a force : the weight of
9779-417: The force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever ; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion . Dynamic equilibrium
9906-400: The force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields
10033-401: The fundamental ones. In such situations, idealized models can be used to gain physical insight. For example, each solid object is considered a rigid body . What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo
10160-410: The interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light . This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum . When objects are in contact,
10287-456: The laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes. Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines , but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part, this
10414-567: The legendary apple falling from the tree , on its way to meet the ground near Isaac Newton , was weightless. The unit of measurement for weight is that of force , which in the International System of Units (SI) is the newton . For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, and about one-sixth as much on the Moon . Although weight and mass are scientifically distinct quantities,
10541-404: The load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine. A simple elastic force acts to return a spring to its natural length. An ideal spring
10668-403: The local force of gravity can vary by up to 0.5% at different locations, spring scales will measure slightly different weights for the same object (the same mass) at different locations. To standardize weights, scales are always calibrated to read the weight an object would have at a nominal standard gravity of 9.80665 m/s (approx. 32.174 ft/s ). However, this calibration is done at
10795-464: The location at which the objects will be used to show this standard weight, to be legal for commerce. This table shows the variation of acceleration due to gravity (and hence the variation of weight) at various locations on the Earth's surface. The historical use of "weight" for "mass" also persists in some scientific terminology – for example, the chemical terms "atomic weight", "molecular weight", and "formula weight", can still be found rather than
10922-427: The magnetic field. The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs . These " Maxwell's equations " fully described the sources of the fields as being stationary and moving charges, and
11049-432: The magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to
11176-440: The mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum, F = d p d t = d ( m v ) d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}={\frac {\mathrm {d} \left(m\mathbf {v} \right)}{\mathrm {d} t}},} where m
11303-416: The mass of object A is 10 times greater than that of object B. This means that an object's mass can be measured indirectly by its weight, and so, for everyday purposes, weighing (using a weighing scale ) is an entirely acceptable way of measuring mass. Similarly, a balance measures mass indirectly by comparing the weight of the measured item to that of an object(s) of known mass. Since the measured item and
11430-551: The mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. A modern statement of Newton's second law is a vector equation: F = d p d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},} where p {\displaystyle \mathbf {p} }
11557-438: The motion of all objects using the concepts of inertia and force. In 1687, Newton published his magnum opus, Philosophiæ Naturalis Principia Mathematica . In this work Newton set out three laws of motion that have dominated the way forces are described in physics to this day. The precise ways in which Newton's laws are expressed have evolved in step with new mathematical approaches. Newton's first law of motion states that
11684-644: The natural behavior of an object at rest is to continue being at rest, and the natural behavior of an object moving at constant speed in a straight line is to continue moving at that constant speed along that straight line. The latter follows from the former because of the principle that the laws of physics are the same for all inertial observers , i.e., all observers who do not feel themselves to be in motion. An observer moving in tandem with an object will see it as being at rest. So, its natural behavior will be to remain at rest with respect to that observer, which means that an observer who sees it moving at constant speed in
11811-566: The normal force in action is the impact force on an object crashing into an immobile surface. Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction . The static friction force ( F s f {\displaystyle \mathbf {F} _{\mathrm {sf} }} ) will exactly oppose forces applied to an object parallel to
11938-466: The object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction. Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together
12065-437: The object would weigh at standard gravity, not the actual local force of gravity on the object. If the actual force of gravity on the object is needed, this can be calculated by multiplying the mass measured by the balance by the acceleration due to gravity – either standard gravity (for everyday work) or the precise local gravity (for precision work). Tables of the gravitational acceleration at different locations can be found on
12192-446: The object. A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances . For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that
12319-427: The object. A common example of this is the effect of buoyancy , when an object is immersed in a fluid the displacement of the fluid will cause an upward force on the object, making it appear lighter when weighed on a scale. The apparent weight may be similarly affected by levitation and mechanical suspension. When the gravitational definition of weight is used, the operational weight measured by an accelerating scale
12446-473: The operational definition, the weight of an object at rest on the surface of the Earth is lessened by the effect of the centrifugal force from the Earth's rotation. The operational definition, as usually given, does not explicitly exclude the effects of buoyancy , which reduces the measured weight of an object when it is immersed in a fluid such as air or water. As a result, a floating balloon or an object floating in water might be said to have zero weight. In
12573-455: The operational definition. If the specified frame is the surface of the Earth, the weight according to the ISO and gravitational definitions differ only by the centrifugal effects due to the rotation of the Earth. In many real world situations the act of weighing may produce a result that differs from the ideal value provided by the definition used. This is usually referred to as the apparent weight of
12700-481: The original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on
12827-409: The other two. When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium . Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in static equilibrium with respect to
12954-400: The person is in motion, the result of any other forces acting on the body such as in the case of acceleration or deceleration of a lift, or centrifugal forces when turning sharply. Weight is commonly measured using one of two methods. A spring scale or hydraulic or pneumatic scale measures local weight, the local force of gravity on the object (strictly apparent weight force ). Since
13081-451: The preferred " atomic mass ", etc. In a different gravitational field, for example, on the surface of the Moon , an object can have a significantly different weight than on Earth. The gravity on the surface of the Moon is only about one-sixth as strong as on the surface of the Earth. A one-kilogram mass is still a one-kilogram mass (as mass is an intrinsic property of the object) but the downward force due to gravity, and therefore its weight,
13208-503: The projectile to its target. This explanation requires a continuous medium such as air to sustain the motion. Though Aristotelian physics was criticized as early as the 6th century, its shortcomings would not be corrected until the 17th century work of Galileo Galilei , who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus . Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove
13335-414: The radius ( R ⊕ {\displaystyle R_{\oplus }} ) of the Earth to the gravitational acceleration: g = − G m ⊕ R ⊕ 2 r ^ , {\displaystyle \mathbf {g} =-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},} where
13462-466: The resurgence of the Platonic idea that like objects attract but in the context of heavenly bodies. In the 17th century, Galileo made significant advances in the concept of weight. He proposed a way to measure the difference between the weight of a moving object and an object at rest. Ultimately, he concluded weight was proportionate to the amount of matter of an object, not the speed of motion as supposed by
13589-473: The rotational speed of an object. In an extended body, each part often applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress . In equilibrium these stresses cause no acceleration of the body as the forces balance one another. If these are not in equilibrium they can cause deformation of solid materials, or flow in fluids . In modern physics , which includes relativity and quantum mechanics ,
13716-621: The same laws of motion , his law of gravity had to be universal. Succinctly stated, Newton's law of gravitation states that the force on a spherical object of mass m 1 {\displaystyle m_{1}} due to the gravitational pull of mass m 2 {\displaystyle m_{2}} is F = − G m 1 m 2 r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},} where r {\displaystyle r}
13843-547: The same amount of work . Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids . Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology . In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of
13970-400: The string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on
14097-446: The surface of the Sun, the Earth's moon, each of the planets in the solar system. The "surface" is taken to mean the cloud tops of the giant planets (Jupiter, Saturn, Uranus, and Neptune). For the Sun, the surface is taken to mean the photosphere . The values in the table have not been de-rated for the centrifugal effect of planet rotation (and cloud-top wind speeds for the giant planets) and therefore, generally speaking, are similar to
14224-461: The tendency to restore the natural order of the basic elements: air, earth, fire and water. He ascribed absolute weight to earth and absolute levity to fire. Archimedes saw weight as a quality opposed to buoyancy , with the conflict between the two determining if an object sinks or floats. The first operational definition of weight was given by Euclid , who defined weight as: "the heaviness or lightness of one thing, compared to another, as measured by
14351-406: The term "weight" is usually used to mean mass, and the verb "to weigh" means "to determine the mass of" or "to have a mass of". Used in this sense, the proper SI unit is the kilogram (kg). In United States customary units , the pound can be either a unit of force or a unit of mass. Related units used in some distinct, separate subsystems of units include the poundal and the slug . The poundal
14478-429: The terms are often confused with each other in everyday use (e.g. comparing and converting force weight in pounds to mass in kilograms and vice versa). Further complications in elucidating the various concepts of weight have to do with the theory of relativity according to which gravity is modeled as a consequence of the curvature of spacetime . In the teaching community, a considerable debate has existed for over half
14605-410: The theory is used in practice. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll . Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as " vector quantities ". This means that forces follow
14732-401: The tripod head. The astronomical tripod is a sturdy three-leg stand used to support telescopes or binoculars, though they may also be used to support attached cameras or ancillary equipment. The astronomical tripod is normally fitted with an altazimuth or equatorial mount to assist in tracking celestial bodies. Weight Some standard textbooks define weight as a vector quantity,
14859-413: The unknown object and standard masses in the scale pans. In the absence of a gravitational field, away from planetary bodies (e.g. space), a lever-balance would not work, but on the Moon, for example, it would give the same reading as on Earth. Some balances are marked in weight units, but since the weights are calibrated at the factory for standard gravity, the balance will measure standard weight, i.e. what
14986-487: The vector direction is given by r ^ {\displaystyle {\hat {\mathbf {r} }}} , is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant G {\displaystyle G} is used to describe the relative strength of gravity. This constant has come to be known as the Newtonian constant of gravitation , though its value
15113-412: The velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates
15240-563: The vertical centre. Variations with one, two, and four legs are termed monopod , bipod , and quadripod (similar to a table ). First attested in English in the early 17th century, the word tripod comes via Latin tripodis ( GEN of tripus ), which is the romanization of Greek τρίπους ( tripous ), "three-footed" ( GEN τρίποδος , tripodos ), ultimately from τρι- ( tri- ), "three times" (from τρία , tria , "three") + πούς ( pous ), "foot". The earliest attested form of
15367-405: The web. Gross weight is a term that is generally found in commerce or trade applications, and refers to the total weight of a product and its packaging. Conversely, net weight refers to the weight of the product alone, discounting the weight of its container or packaging; and tare weight is the weight of the packaging alone. The table below shows comparative gravitational accelerations at
15494-586: The word is the Mycenaean Greek 𐀴𐀪𐀠 , ti-ri-po , written in Linear B syllabic script. Many cultures, including the ancient peoples of China and Greece , used tripods as ornaments , trophies , sacrificial altars , cooking vessels or cauldrons, and decorative ceramic pottery. Tripod pottery have been part of the archaeological assemblage in China since the earliest Neolithic cultures of Cishan and Peiligang in
15621-521: Was due to an incomplete understanding of the sometimes non-obvious force of friction and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton . With his mathematical insight, Newton formulated laws of motion that were not improved for over two hundred years. By
15748-521: Was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic . Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame " did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of
15875-436: Was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as g {\displaystyle \mathbf {g} } and has a magnitude of about 9.81 meters per second squared (this measurement
16002-459: Was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion . Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that
16129-499: Was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of G {\displaystyle G} using a torsion balance ; this was widely reported in the press as a measurement of the mass of the Earth since knowing G {\displaystyle G} could allow one to solve for the Earth's mass given the above equation. Newton realized that since all celestial bodies followed
#689310