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space-time : concept of space-time is that time is essentially another coordinate that is treated the same way as any individual spatial coordinate; in the equations that represent both special and general relativity, time appears in the same context as do the spatial coordinates | https://openstax.org/books/university-physics-volume-1/pages/13-key-terms |
spring tide : high tide created when the Moon, the Sun, and Earth are along one line | https://openstax.org/books/university-physics-volume-1/pages/13-key-terms |
theory of general relativity : Einsteinâs theory for gravitation and accelerated reference frames; in this theory, gravitation is the result of mass and energy distorting the space-time around it; it is also often referred to as Einsteinâs theory of gravity | https://openstax.org/books/university-physics-volume-1/pages/13-key-terms |
tidal force : differencebetween the gravitational force at the center of a body and that at any other location on the body; the tidal force stretches the body | https://openstax.org/books/university-physics-volume-1/pages/13-key-terms |
universal gravitational constant : constant representing the strength of the gravitational force, that is believed to be the same throughout the universe | https://openstax.org/books/university-physics-volume-1/pages/13-key-terms |
All masses attract one another with a gravitational force proportional to their masses and inversely proportional to the square of the distance between them. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Spherically symmetrical masses can be treated as if all their mass were located at the center. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Nonsymmetrical objects can be treated as if their mass were concentrated at their center of mass, provided their distance from other masses is large compared to their size. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The weight of an object is the gravitational attraction between Earth and the object. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The gravitational field is represented as lines that indicate the direction of the gravitational force; the line spacing indicates the strength of the field. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Apparent weight differs from actual weight due to the acceleration of the object. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Objects must have a minimum velocity, the escape velocity, to leave a planet and not return. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Objects with total energy less than zero are bound; those with zero or greater are unbounded. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Orbital velocities are determined by the mass of the body being orbited and the distance from the center of that body, and not by the mass of a much smaller orbiting object. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The period of the orbit is likewise independent of the orbiting objectâs mass. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Bodies of comparable masses orbit about their common center of mass and their velocities and periods should be determined from Newtonâs second law and law of gravitation. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
All orbital motion follows the path of a conic section. Bound or closed orbits are either a circle or an ellipse; unbounded or open orbits are either a parabola or a hyperbola. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The areal velocity of any orbit is constant, a reflection of the conservation of angular momentum. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The square of the period of an elliptical orbit is proportional to the cube of the semi-major axis of that orbit. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Earthâs tides are caused by the difference in gravitational forces from the Moon and the Sun on the different sides of Earth. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Spring or neap (high) tides occur when Earth, the Moon, and the Sun are aligned, and neap or (low) tides occur when they form a right triangle. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Tidal forces can create internal heating, changes in orbital motion, and even destruction of orbiting bodies. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Evidence for the existence of black holes is still circumstantial, but the amount of that evidence is overwhelming. | https://openstax.org/books/university-physics-volume-1/pages/13-summary |
Ï = m V Ï = m V | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
p = F A p = F A | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
p = p 0 + Ï g h p = p 0 + Ï g h | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
d p d y = â Ï g d p d y = â Ï g | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
p abs = p g + p atm p abs = p g + p atm | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
F 1 A 1 = F 2 A 2 F 1 A 1 = F 2 A 2 | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
Q = d V d t Q = d V d t | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
A 1 v 1 = A 2 v 2 A 1 v 1 = A 2 v 2 | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
Ï 1 A 1 v 1 = Ï 2 A 2 v 2 Ï 1 A 1 v 1 = Ï 2 A 2 v 2 | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
p + 1 2 Ï v 2 + Ï g y = constant p + 1 2 Ï v 2 + Ï g y = constant | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
η = F L v A η = F L v A | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
R = 8 η l Ï r 4 R = 8 η l Ï r 4 | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
Q = ( p 2 â p 1 ) Ï r 4 8 η l Q = ( p 2 â p 1 ) Ï r 4 8 η l | https://openstax.org/books/university-physics-volume-1/pages/14-key-equations |
absolute pressure : sum of gauge pressure and atmospheric pressure | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Archimedesâ principle : buoyant force on an object equals the weight of the fluid it displaces | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Bernoulliâs equation : equation resulting from applying conservation of energy to an incompressible frictionless fluid:p+12Ïv2+Ïgh=constant,p+12Ïv2+Ïgh=constant,throughout the fluid | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Bernoulliâs principle : Bernoulliâs equation applied at constant depth:p1+12Ïv12=p2+12Ïv22p1+12Ïv12=p2+12Ïv22 | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
buoyant force : net upward force on any object in any fluid due to the pressure difference at different depths | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
density : mass per unit volume of a substance or object | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
flow rate : abbreviatedQ, it is the volumeVthat flows past a particular point during a timet, orQ=dV/dtQ=dV/dt | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
fluids : liquids and gases; a fluid is a state of matter that yields to shearing forces | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
gauge pressure : pressure relative to atmospheric pressure | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
hydraulic jack : simple machine that uses cylinders of different diameters to distribute force | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
hydrostatic equilibrium : state at which water is not flowing, or is static | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
ideal fluid : fluid with negligible viscosity | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
laminar flow : type of fluid flow in which layers do not mix | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Pascalâs principle : change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Poiseuilleâs law : rate of laminar flow of an incompressible fluid in a tube:Q=(p2âp1)Ïr48ηl.Q=(p2âp1)Ïr48ηl. | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Poiseuilleâs law for resistance : resistance to laminar flow of an incompressible fluid in a tube:R=8ηlÏr4R=8ηlÏr4 | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
pressure : force per unit area exerted perpendicular to the area over which the force acts | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
Reynolds number : dimensionless parameter that can reveal whether a particular flow is laminar or turbulent | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
specific gravity : ratio of the density of an object to a fluid (usually water) | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
turbulence : fluid flow in which layers mix together via eddies and swirls | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
turbulent flow : type of fluid flow in which layers mix together via eddies and swirls | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
viscosity : measure of the internal friction in a fluid | https://openstax.org/books/university-physics-volume-1/pages/14-key-terms |
A fluid is a state of matter that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Density is the mass per unit volume of a substance or object, defined asÏ=m/V.Ï=m/V.The SI unit of density iskg/m3.kg/m3. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Pressure is the force per unit perpendicular area over which the force is applied,p=F/A.p=F/A.The SI unit of pressure is the pascal:1Pa=1N/m21Pa=1N/m2. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Pressure due to the weight of a liquid of constant density is given byp=Ïghp=Ïgh, wherepis the pressure,his the depth of the liquid,ÏÏis the density of the liquid, andgis the acceleration due to gravity. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Gauge pressure is the pressure relative to atmospheric pressure. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Absolute pressure is the sum of gauge pressure and atmospheric pressure. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Open-tube manometers have U-shaped tubes and one end is always open. They are used to measure pressure. A mercury barometer is a device that measures atmospheric pressure. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
The SI unit of pressure is the pascal (Pa), but several other units are commonly used. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Pressure is force per unit area. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
A hydraulic system is an enclosed fluid system used to exert forces. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Buoyant force is the net upward force on any object in any fluid. If the buoyant force is greater than the objectâs weight, the object will rise to the surface and float. If the buoyant force is less than the objectâs weight, the object will sink. If the buoyant force equals the objectâs weight, the object can re... | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Archimedesâ principle states that the buoyant force on an object equals the weight of the fluid it displaces. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Flow rateQis defined as the volumeVflowing past a point in timet, orQ=dVdtQ=dVdtwhereVis volume andtis time. The SI unit of flow rate ism3/s,m3/s,but other rates can be used, such as L/min. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Flow rate and velocity are related byQ=AvQ=AvwhereAis the cross-sectional area of the flow andvis its average velocity. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
The equation of continuity states that for an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out of the pipe. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Bernoulliâs equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid:p1+12Ïv12+Ïgh1=p2+12Ïv22+Ïgh2.p1+12Ïv12+Ïgh1=p2+12Ïv22+Ïgh2. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Bernoulliâs principle is Bernoulliâs equation applied to situations in which the height of the fluid is constant. The terms involving depth (or heighth) subtract out, yieldingp1+12Ïv12=p2+12Ïv22.p1+12Ïv12=p2+12Ïv22. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Bernoulliâs principle has many applications, including entrainment and velocity measurement. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Laminar flow is characterized by smooth flow of the fluid in layers that do not mix. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Turbulence is characterized by eddies and swirls that mix layers of fluid together. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Fluid viscosityηηis due to friction within a fluid. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
Flow is proportional to pressure difference and inversely proportional to resistance:Q=pâ2p1R.Q=pâ2p1R. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
The pressure drop caused by flow and resistance is given byp2âp1=RQp2âp1=RQ. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
The Reynolds numberNRNRcan reveal whether flow is laminar or turbulent. It isNR=2ÏvrηNR=2Ïvrη. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
ForNRNRbelow about 2000, flow is laminar. ForNRNRabove about 3000, flow is turbulent. For values ofNRNRbetween 2000 and 3000, it may be either or both. | https://openstax.org/books/university-physics-volume-1/pages/14-summary |
f = 1 T f = 1 T | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
Position in SHM with Ï = 0.00 Position in SHM with Ï = 0.00 | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
x ( t ) = A cos ( Ï t ) x ( t ) = A cos ( Ï t ) | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
x ( t ) = A cos ( Ï t + Ï ) x ( t ) = A cos ( Ï t + Ï ) | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
v ( t ) = â A Ï sin ( Ï t + Ï ) v ( t ) = â A Ï sin ( Ï t + Ï ) | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
a ( t ) = â A Ï 2 cos ( Ï t + Ï ) a ( t ) = â A Ï 2 cos ( Ï t + Ï ) | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
x max = A x max = A | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
| v max | = A Ï | v max | = A Ï | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
| a max | = A Ï 2 | a max | = A Ï 2 | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
Ï = k m Ï = k m | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
T = 2 Ï m k T = 2 Ï m k | https://openstax.org/books/university-physics-volume-1/pages/15-key-equations |
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