text
stringlengths
2
2.33k
source
stringclasses
826 values
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 : Einstein’s 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 Einstein’s 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 object’s 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 Newton’s 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
Earth’s 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
ρ = m V ρ = 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 + ρ g h p = p 0 + ρ g h
https://openstax.org/books/university-physics-volume-1/pages/14-key-equations
d p d y = − ρ g d p d y = − ρ 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
ρ 1 A 1 v 1 = ρ 2 A 2 v 2 ρ 1 A 1 v 1 = ρ 2 A 2 v 2
https://openstax.org/books/university-physics-volume-1/pages/14-key-equations
p + 1 2 ρ v 2 + ρ g y = constant p + 1 2 ρ v 2 + ρ 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 π r 4 R = 8 η l π r 4
https://openstax.org/books/university-physics-volume-1/pages/14-key-equations
Q = ( p 2 − p 1 ) π r 4 8 η l Q = ( p 2 − p 1 ) π 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
Archimedes’ 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
Bernoulli’s equation : equation resulting from applying conservation of energy to an incompressible frictionless fluid:p+12ρv2+ρgh=constant,p+12ρv2+ρgh=constant,throughout the fluid
https://openstax.org/books/university-physics-volume-1/pages/14-key-terms
Bernoulli’s principle : Bernoulli’s equation applied at constant depth:p1+12ρv12=p2+12ρv22p1+12ρv12=p2+12ρv22
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
Pascal’s 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
Poiseuille’s law : rate of laminar flow of an incompressible fluid in a tube:Q=(p2−p1)πr48ηl.Q=(p2−p1)πr48ηl.
https://openstax.org/books/university-physics-volume-1/pages/14-key-terms
Poiseuille’s law for resistance : resistance to laminar flow of an incompressible fluid in a tube:R=8ηlπr4R=8ηlπr4
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 asρ=m/V.ρ=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=ρghp=ρgh, wherepis the pressure,his the depth of the liquid,ρρis 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 object’s weight, the object will rise to the surface and float. If the buoyant force is less than the object’s weight, the object will sink. If the buoyant force equals the object’s weight, the object can re...
https://openstax.org/books/university-physics-volume-1/pages/14-summary
Archimedes’ 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
Bernoulli’s 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+12ρv12+ρgh1=p2+12ρv22+ρgh2.p1+12ρv12+ρgh1=p2+12ρv22+ρgh2.
https://openstax.org/books/university-physics-volume-1/pages/14-summary
Bernoulli’s principle is Bernoulli’s equation applied to situations in which the height of the fluid is constant. The terms involving depth (or heighth) subtract out, yieldingp1+12ρv12=p2+12ρv22.p1+12ρv12=p2+12ρv22.
https://openstax.org/books/university-physics-volume-1/pages/14-summary
Bernoulli’s 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=p−2p1R.Q=p−2p1R.
https://openstax.org/books/university-physics-volume-1/pages/14-summary
The pressure drop caused by flow and resistance is given byp2–p1=RQp2–p1=RQ.
https://openstax.org/books/university-physics-volume-1/pages/14-summary
The Reynolds numberNRNRcan reveal whether flow is laminar or turbulent. It isNR=2ρvrηNR=2ρvrη.
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 ϕ = 0.00 Position in SHM with ϕ = 0.00
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
x ( t ) = A cos ( ω t ) x ( t ) = A cos ( ω t )
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
x ( t ) = A cos ( ω t + ϕ ) x ( t ) = A cos ( ω t + ϕ )
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
v ( t ) = − A ω sin ( ω t + ϕ ) v ( t ) = − A ω sin ( ω t + ϕ )
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
a ( t ) = − A ω 2 cos ( ω t + ϕ ) a ( t ) = − A ω 2 cos ( ω t + ϕ )
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 ω | v max | = A ω
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
| a max | = A ω 2 | a max | = A ω 2
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
ω = k m ω = k m
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations
T = 2 π m k T = 2 π m k
https://openstax.org/books/university-physics-volume-1/pages/15-key-equations