Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass i.e. to accelerate. Force can be described intuitively as a push or a pull. A force has both direction, making it a vector quantity, it is measured in the SI unit of newtons and represented by the symbol F. The original form of 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 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, is inversely proportional to the mass of the object. Concepts related to force include: thrust. In an extended body, each part applies forces on the adjacent parts; such internal mechanical stresses cause no acceleration of that body as the forces balance one another. Pressure, the distribution of many small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate.
Stress causes deformation of solid materials, or flow in fluids. 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 was due to an incomplete understanding of the sometimes non-obvious force of friction, a inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion at a constant velocity. Most of the previous misunderstandings about motion and force were corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved for nearly three hundred years. By the early 20th century, Einstein developed a theory of relativity that predicted the action of forces on objects with increasing momenta near the speed of light, 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 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 and gravitational. High-energy particle physics observations made during 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 the same amount of work. Analysis of the characteristics of forces culminated in the work of Archimedes, 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 of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone, he distinguished between the innate tendency of objects to find their "natural place", which led to "natural motion", unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as 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; the place where the archer moves the projectile was at the start of the flight, while the projectile sailed through the air, no discernible efficient cause acts on it.
Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation demands a continuum like air for change of place in general. Aristotelian physics began facing criticism in medieval science, first by John Philoponus in the 6th century; the shortcomings of Aristotelian physics would not be corrected until the 17th century work of Galileo Galilei, 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 the Aristotelian theory of motion, he showed that the bodies were accelerated by gravity to an extent, independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction. Sir Isaac Newton described the motion of all objects using the concepts of inertia and force, in doing so he found they obey certain conservation laws.
In 1687, Newton published his thesis Philosophiæ Naturalis Principia Mathematica. In this work Newton set out three laws of motion that to this day are t
Centrifugal force
In Newtonian mechanics, the centrifugal force is an inertial force that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis passing through the coordinate system's origin and parallel to the axis of rotation. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis; the concept of centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, centrifugal clutches, in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a rotating coordinate system. The term has sometimes been used for the reactive centrifugal force, a reaction to a centripetal force. Centrifugal force is an outward force apparent in a rotating reference frame, it does not exist. All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or to the Sun.
A reference frame, at rest relative to the "fixed stars" is taken to be an inertial frame. Any system can be analyzed in an inertial frame. However, it is more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, descriptions more intuitive; when this choice is made, fictitious forces, including the centrifugal force, arise. In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially outward force, proportional to their mass, to the distance from the axis of rotation of the frame, to the square of the angular velocity of the frame; this is the centrifugal force. As humans experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force. Motion relative to a rotating frame results in another fictitious force: the Coriolis force. If the rate of rotation of the frame changes, a third fictitious force is required.
These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame. A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, changing direction. If a car is traveling at a constant speed along a straight road a passenger inside is not accelerating and, according to Newton's second law of motion, the net force acting on him is therefore zero. If the car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling him towards the right; this is the fictitious centrifugal force. It is needed within the passenger's local frame of reference to explain his sudden tendency to start accelerating to the right relative to the car—a tendency which he must resist by applying a rightward force to the car in order to remain in a fixed position inside. Since he pushes the seat toward the right, Newton's third law says that the seat pushes him toward the left.
The centrifugal force must be included in the passenger's reference frame: it counteracts the leftward force applied to the passenger by the seat, explains why this otherwise unbalanced force does not cause him to accelerate. However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced, thus the "centrifugal force" he feels is the result of a "centrifugal tendency" caused by inertia. Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is reported in "G's". If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string. There is a net force on the stone in the horizontal plane. In an inertial frame of reference, were it not for this net force acting on the stone, the stone would travel in a straight line, according to Newton's first law of motion.
In order to keep the stone moving in a circular path, a centripetal force, in this case provided by the string, must be continuously applied to the stone. As soon as it is removed the stone moves in a straight line. In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by the string is still acting on the stone. If one were to apply Newton's laws in their usual form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotatio
Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, is a function of time. Velocity is equivalent to a specification of an object's direction of motion. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity; the scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI as metres per second or as the SI base unit of. For example, "5 metres per second" is a scalar. If there is a change in speed, direction or both the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes.
Hence, the car is considered to be undergoing an acceleration. Speed describes only how fast an object is moving, whereas velocity gives both how fast it is and in which direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified; the big difference can be noticed. When something moves in a circular path and returns to its starting point, its average velocity is zero but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle; this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, which may be referred to as the instantaneous velocity to emphasize the distinction from the average velocity.
In some applications the "average velocity" of an object might be needed, to say, the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval, v, over some time period Δt. Average velocity can be calculated as: v ¯ = Δ x Δ t; the average velocity is always equal to the average speed of an object. This can be seen by realizing that while distance is always increasing, displacement can increase or decrease in magnitude as well as change direction. In terms of a displacement-time graph, the instantaneous velocity can be thought of as the slope of the tangent line to the curve at any point, the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity; the average velocity is the same as the velocity averaged over time –, to say, its time-weighted average, which may be calculated as the time integral of the velocity: v ¯ = 1 t 1 − t 0 ∫ t 0 t 1 v d t, where we may identify Δ x = ∫ t 0 t 1 v d t and Δ t = t 1 − t 0.
If we consider v as velocity and x as the displacement vector we can express the velocity of a particle or object, at any particular time t, as the derivative of the position with respect to time: v = lim Δ t → 0 Δ x Δ t = d x d t. From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity function v is the displacement function x. In the figure, this corresponds to the yellow area under the curve labeled s. X = ∫ v d t. Since the derivative of the position with respect to time gives the change in position divided by the change in time, velocity is measured in metres per second. Although the concept of an instantaneous velocity might at first seem counter-intuitive, it
Moon
The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, the largest among planetary satellites relative to the size of the planet that it orbits; the Moon is after Jupiter's satellite Io the second-densest satellite in the Solar System among those whose densities are known. The Moon is thought to have formed not long after Earth; the most accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body called Theia. The Moon is in synchronous rotation with Earth, thus always shows the same side to Earth, the near side; the near side is marked by dark volcanic maria that fill the spaces between the bright ancient crustal highlands and the prominent impact craters. After the Sun, the Moon is the second-brightest visible celestial object in Earth's sky, its surface is dark, although compared to the night sky it appears bright, with a reflectance just higher than that of worn asphalt.
Its gravitational influence produces the ocean tides, body tides, the slight lengthening of the day. The Moon's average orbital distance is 1.28 light-seconds. This is about thirty times the diameter of Earth; the Moon's apparent size in the sky is the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly during a total solar eclipse; this matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is increasing. The Moon was first reached in September 1959 by an unmanned spacecraft; the United States' NASA Apollo program achieved the only manned lunar missions to date, beginning with the first manned orbital mission by Apollo 8 in 1968, six manned landings between 1969 and 1972, with the first being Apollo 11. These missions returned lunar rocks which have been used to develop a geological understanding of the Moon's origin, internal structure, the Moon's history. Since the Apollo 17 mission in 1972, the Moon has been visited only by unmanned spacecraft.
Both the Moon's natural prominence in the earthly sky and its regular cycle of phases as seen from Earth have provided cultural references and influences for human societies and cultures since time immemorial. Such cultural influences can be found in language, lunar calendar systems and mythology; the usual English proper name for Earth's natural satellite is "the Moon", which in nonscientific texts is not capitalized. The noun moon is derived from Old English mōna, which stems from Proto-Germanic *mēnô, which comes from Proto-Indo-European *mḗh₁n̥s "moon", "month", which comes from the Proto-Indo-European root *meh₁- "to measure", the month being the ancient unit of time measured by the Moon; the name "Luna" is used. In literature science fiction, "Luna" is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of Earth's moon; the modern English adjective pertaining to the Moon is lunar, derived from the Latin word for the Moon, luna. The adjective selenic is so used to refer to the Moon that this meaning is not recorded in most major dictionaries.
It is derived from the Ancient Greek word for the Moon, σελήνη, from, however derived the prefix "seleno-", as in selenography, the study of the physical features of the Moon, as well as the element name selenium. Both the Greek goddess Selene and the Roman goddess Diana were alternatively called Cynthia; the names Luna and Selene are reflected in terminology for lunar orbits in words such as apolune and selenocentric. The name Diana comes from the Proto-Indo-European *diw-yo, "heavenly", which comes from the PIE root *dyeu- "to shine," which in many derivatives means "sky and god" and is the origin of Latin dies, "day"; the Moon formed 4.51 billion years ago, some 60 million years after the origin of the Solar System. Several forming mechanisms have been proposed, including the fission of the Moon from Earth's crust through centrifugal force, the gravitational capture of a pre-formed Moon, the co-formation of Earth and the Moon together in the primordial accretion disk; these hypotheses cannot account for the high angular momentum of the Earth–Moon system.
The prevailing hypothesis is that the Earth–Moon system formed after an impact of a Mars-sized body with the proto-Earth. The impact blasted material into Earth's orbit and the material accreted and formed the Moon; the Moon's far side has a crust, 30 mi thicker than that of the near side. This is thought to be; this hypothesis, although not perfect best explains the evidence. Eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, Jeff Taylor challenged fellow lunar scientists: "You have eighteen months. Go back to your Apollo data, go back to your computer, do whatever you have to, but make up your mind. Don't come to our conference unless you have something to say about the Moon's birth." At the 1984 conference at Kona, the giant impact hypothesis emerged as the most consensual theory. Before the conference, there were parti
Impulse (physics)
In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum in the same direction; the SI unit of impulse is the newton second, the dimensionally equivalent unit of momentum is the kilogram meter per second. The corresponding English engineering units are the slug-foot per second. A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly. J = F average The impulse is the integral of the resultant force with respect to time: J = ∫ F d t Impulse J produced from time t1 to t2 is defined to be J = ∫ t 1 t 2 F d t where F is the resultant force applied from t1 to t2.
From Newton's second law, force is related to momentum p by F = d p d t Therefore, J = ∫ t 1 t 2 d p d t d t = ∫ p 1 p 2 d p = p 2 − p 1 = Δ p where Δp is the change in linear momentum from time t1 to t2. This is called the impulse-momentum theorem; as a result, an impulse may be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant: J = ∫ t 1 t 2 F d t = Δ p = m v 2 − m v 1 where F is the resultant force applied, t1 and t2 are times when the impulse begins and ends m is the mass of the object, v2 is the final velocity of the object at the end of the time interval, v1 is the initial velocity of the object when the time interval begins. Impulse has the same dimensions as momentum. In the International System of Units, these are kg⋅m/s = N⋅s. In English engineering units, they are slug⋅ft/s = lbf⋅s; the term "impulse" is used to refer to a fast-acting force or impact. This type of impulse is idealized so that the change in momentum produced by the force happens with no change in time.
This sort of change is a step change, is not physically possible. However, this is a useful model for computing the effects of ideal collisions. Additionally, in rocketry, the term "total impulse" is used and is considered synonymous with the term "impulse"; the application of Newton's second law for variable mass allows impulse and momentum to be used as analysis tools for jet- or rocket-propelled vehicles. In the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse; this fact can be used to derive the Tsiolkovsky rocket equation, which relates the vehicle's propulsive change in velocity to the engine's specific impulse and the vehicle's propellant-mass ratio. Wave–particle duality defines the impulse of a wave collision; the preservation of momentum in the collision is called phase matching. Applications include: Compton effect Nonlinear optics Acousto-optic modulator Electron phonon scattering Serway, Raymond A..
Physics for Scientists and Engineers. Brooks/Cole. ISBN 0-534-40842-7. Tipler, Paul. Physics for Scientists and Engineers: Mechanics and Waves, Thermodynamics. W. H. Freeman. ISBN 0-7167-0809-4. Dynamics
Escape velocity
In physics, escape velocity is the minimum speed needed for a free object to escape from the gravitational influence of a massive body. It is slower the further away from the body an object is, slower for less massive bodies; the escape velocity from Earth is about 11.186 km/s at the surface. More escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching, but never reaching, zero speed. Once escape velocity is achieved, no further impulse need to be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing, will asymptotically approach zero speed as the object's distance approaches infinity, never to come back. Speeds higher than escape velocity have a positive speed at infinity.
Note that the minimum escape velocity assumes that there is no friction, which would increase the required instantaneous velocity to escape the gravitational influence, that there will be no future acceleration or deceleration, which would change the required instantaneous velocity. For a spherically symmetric, massive body such as a star, or planet, the escape velocity for that body, at a given distance, is calculated by the formula v e = 2 G M r, where G is the universal gravitational constant, M the mass of the body to be escaped from, r the distance from the center of mass of the body to the object; the relationship is independent of the mass of the object escaping the massive body. Conversely, a body that falls under the force of gravitational attraction of mass M, from infinity, starting with zero velocity, will strike the massive object with a velocity equal to its escape velocity given by the same formula; when given an initial speed V greater than the escape speed v e, the object will asymptotically approach the hyperbolic excess speed v ∞, satisfying the equation: v ∞ 2 = V 2 − v e 2.
In these equations atmospheric friction is not taken into account. A rocket moving out of a gravity well does not need to attain escape velocity to escape, but could achieve the same result at any speed with a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape. Escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass M; the existence of escape velocity is a consequence of conservation of energy and an energy field of finite depth. For an object with a given total energy, moving subject to conservative forces it is only possible for the object to reach combinations of locations and speeds which have that total energy. By adding speed to the object it expands the possible locations that can be reached, with enough energy, they become infinite. For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to be able to "escape" from the gravity.
Escape velocity is a speed because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field. The simplest way of deriving the formula for escape velocity is to use conservation of energy. For the sake of simplicity, unless stated otherwise, we assume that an object is attempting to escape from a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. In its initial state, i, imagine that a spaceship of mass m is at a distance r from the center of mass of the planet, whose mass is M, its initial speed is equal to v e. At its final state, f, it will be an infinite distance away from the planet, its speed will be negligibly small and assumed to be 0. Kinetic energy K and gravitational potential energy Ug are the only types of energy that we will deal with, so by the conservation of energy, i = f Kƒ = 0 because final velocity is zero, Ugƒ = 0 because its final distance is infinity, so ⇒ 1 2 m v e 2 + − G M m r
Newton (unit)
The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics Newton's second law of motion. See below for the conversion factors. One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force. In 1946, Conférence Générale des Poids et Mesures Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name newton for this force; the MKS system became the blueprint for today's SI system of units. The newton thus became the standard unit of force in the Système international d'unités, or International System of Units; this SI unit is named after Isaac Newton. As with every International System of Units unit named for a person, the first letter of its symbol is upper case.
However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter —except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case. Newton's second law of motion states that F = ma, where F is the force applied, m is the mass of the object receiving the force, a is the acceleration of the object; the newton is therefore: where the following symbols are used for the units: N for newton, kg for kilogram, m for metre, s for second. In dimensional analysis: F = M L T 2 where F is force, M is mass, L is length and T is time. At average gravity on Earth, a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force. 1 N = 0.10197 kg × 9.80665 m/s2 The weight of an average adult exerts a force of about 608 N. 608 N = 62 kg × 9.80665 m/s2 It is common to see forces expressed in kilonewtons where 1 kN = 1000 N.
For example, the tractive effort of a Class Y steam train locomotive and the thrust of an F100 fighter jet engine are both around 130 kN. One kilonewton, 1 kN, is about 100 kg of load. 1 kN = 102 kg × 9.81 m/s2 So for example, a platform that shows it is rated at 321 kilonewtons, will safely support a 32,100 kilograms load. Specifications in kilonewtons are common in safety specifications for: the holding values of fasteners, Earth anchors, other items used in the building industry. Working loads in tension and in shear. Rock climbing equipment. Thrust of rocket engines and launch vehicles clamping forces of the various moulds in injection moulding machines used to manufacture plastic parts