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projectile : an object that travels through the air and experiences only acceleration due to gravity | https://openstax.org/books/college-physics-2e/pages/3-glossary |
projectile motion : the motion of an object that is subject only to the acceleration of gravity | https://openstax.org/books/college-physics-2e/pages/3-glossary |
range : the maximum horizontal distance that a projectile travels | https://openstax.org/books/college-physics-2e/pages/3-glossary |
relative velocity : the velocity of an object as observed from a particular reference frame | https://openstax.org/books/college-physics-2e/pages/3-glossary |
relativity : the study of how different observers moving relative to each other measure the same phenomenon | https://openstax.org/books/college-physics-2e/pages/3-glossary |
resultant : the sum of two or more vectors | https://openstax.org/books/college-physics-2e/pages/3-glossary |
resultant vector : the vector sum of two or more vectors | https://openstax.org/books/college-physics-2e/pages/3-glossary |
scalar : a quantity with magnitude but no direction | https://openstax.org/books/college-physics-2e/pages/3-glossary |
tail : the start point of a vector; opposite to the head or tip of the arrow | https://openstax.org/books/college-physics-2e/pages/3-glossary |
trajectory : the path of a projectile through the air | https://openstax.org/books/college-physics-2e/pages/3-glossary |
vector : a quantity that has both magnitude and direction; an arrow used to represent quantities with both magnitude and direction | https://openstax.org/books/college-physics-2e/pages/3-glossary |
vector addition : the rules that apply to adding vectors together | https://openstax.org/books/college-physics-2e/pages/3-glossary |
velocity : speed in a given direction | https://openstax.org/books/college-physics-2e/pages/3-glossary |
The shortest path between any two points is a straight line. In two dimensions, this path can be represented by a vector with horizontal and vertical components. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
The horizontal and vertical components of a vector are independent of one another. Motion in the horizontal direction does not affect motion in the vertical direction, and vice versa. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Thegraphical method of adding vectorsAAandBBinvolves drawing vectors on a graph and adding them using the head-to-tail method. The resultant vectorRRis defined such thatA+B=RA+B=R. The magnitude and direction ofRRare then determined with a ruler and protractor, respectively. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Thegraphical method of subtracting vectorBBfromAAinvolves adding the opposite of vectorBB, which is defined asâBâB. In this case,AâB=A+(âB)=RAâB=A+(âB)=R. Then, the head-to-tail method of addition is followed in the usual way to obtain the resultant vectorRR. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Addition of vectors iscommutativesuch thatA+B=B+AA+B=B+A. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Thehead-to-tail methodof adding vectors involves drawing the first vector on a graph and then placing the tail of each subsequent vector at the head of the previous vector. The resultant vector is then drawn from the tail of the first vector to the head of the final vector. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
If a vectorAAis multiplied by a scalar quantitycc, the magnitude of the product is given bycAcA. Ifccis positive, the direction of the product points in the same direction asAA; ifccis negative, the direction of the product points in the opposite direction asAA. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
The steps to add vectorsAAandBBusing the analytical method are as follows:Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equationsAx=AcosθBx=BcosθAx=AcosθBx=BcosθandAy=AsinθBy=Bsinθ.Ay=AsinθBy=Bsinθ.Step 2: Add the horizon... | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
and | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Step 2: Add the horizontal and vertical components of each vector to determine the componentsRxRxandRyRyof the resultant vector,RR: | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
and | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Step 3: Use the Pythagorean theorem to determine the magnitude,RR, of the resultant vectorRR: | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Step 4: Use a trigonometric identity to determine the direction,θθ, ofRR: | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Projectile motion is the motion of an object through the air that is subject only to the acceleration of gravity. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
To solve projectile motion problems, perform the following steps:Determine a coordinate system. Then, resolve the position and/or velocity of the object in the horizontal and vertical components. The components of positionssare given by the quantitiesxxandyy, and the components of the velocityvvare given byvx=vcosθvx=... | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Determine a coordinate system. Then, resolve the position and/or velocity of the object in the horizontal and vertical components. The components of positionssare given by the quantitiesxxandyy, and the components of the velocityvvare given byvx=vcosθvx=vcosθandvy=vsinθvy=vsinθ, wherevvis the magnitude of the veloc... | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Analyze the motion of the projectile in the horizontal direction using the following equations:Horizontal motion(ax=0)Horizontal motion(ax=0)x=x0+vxtx=x0+vxtvx=v0x=vx=velocity is a constant.vx=v0x=vx=velocity is a constant. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Analyze the motion of the projectile in the vertical direction using the following equations:Vertical Motion(assuming positive is upay=âg=â9.80m/s2)Vertical Motion(assuming positive is upay=âg=â9.80m/s2)y=y0+12(v0y+vy)ty=y0+12(v0y+vy)tvy=v0yâgtvy=v0yâgty=y0+v0ytâ12gt2y=y0+v0ytâ12gt2vy2=v0y2â2g(yây0)... | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Recombine the horizontal and vertical components of location and/or velocity using the following equations:s=x2+y2s=x2+y2θ=tanâ1(y/x)θ=tanâ1(y/x)v=vx2+vy2v=vx2+vy2θv=tanâ1(vy/vx).θv=tanâ1(vy/vx). | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
The maximum heighthhof a projectile launched with initial vertical velocityv0yv0yis given byh=v0y22g.h=v0y22g. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
The maximum horizontal distance traveled by a projectile is called therange. The rangeRRof a projectile on level ground launched at an angleθ0θ0above the horizontal with initial speedv0v0is given byR=v02sin2θ0g.R=v02sin2θ0g. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Velocities in two dimensions are added using the same analytical vector techniques, which are rewritten asvx=vcosθvx=vcosθvy=vsinθvy=vsinθv=vx2+vy2v=vx2+vy2θ=tanâ1(vy/vx).θ=tanâ1(vy/vx). | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Relative velocity is the velocity of an object as observed from a particular reference frame, and it varies dramatically with reference frame. | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
Relativityis the study of how different observers measure the same phenomenon, particularly when the observers move relative to one another.Classical relativityis limited to situations where speed is less than about 1% of the speed of light (3000 km/s). | https://openstax.org/books/college-physics-2e/pages/3-section-summary |
acceleration : the rate at which an objectâs velocity changes over a period of time | https://openstax.org/books/college-physics-2e/pages/4-glossary |
carrier particle : a fundamental particle of nature that is surrounded by a characteristic force field; photons are carrier particles of the electromagnetic force | https://openstax.org/books/college-physics-2e/pages/4-glossary |
dynamics : the study of how forces affect the motion of objects and systems | https://openstax.org/books/college-physics-2e/pages/4-glossary |
external force : a force acting on an object or system that originates outside of the object or system | https://openstax.org/books/college-physics-2e/pages/4-glossary |
force : a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force | https://openstax.org/books/college-physics-2e/pages/4-glossary |
force field : a region in which a test particle will experience a force | https://openstax.org/books/college-physics-2e/pages/4-glossary |
free-body diagram : a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces are represented by vectors extending outward from the dot | https://openstax.org/books/college-physics-2e/pages/4-glossary |
free-fall : a situation in which the only force acting on an object is the force due to gravity | https://openstax.org/books/college-physics-2e/pages/4-glossary |
friction : a force past each other of objects that are touching; examples include rough surfaces and air resistance | https://openstax.org/books/college-physics-2e/pages/4-glossary |
inertia : the tendency of an object to remain at rest or remain in motion | https://openstax.org/books/college-physics-2e/pages/4-glossary |
inertial frame of reference : a coordinate system that is not accelerating; all forces acting in an inertial frame of reference are real forces, as opposed to fictitious forces that are observed due to an accelerating frame of reference | https://openstax.org/books/college-physics-2e/pages/4-glossary |
law of inertia : see Newtonâs first law of motion | https://openstax.org/books/college-physics-2e/pages/4-glossary |
mass : the quantity of matter in a substance; measured in kilograms | https://openstax.org/books/college-physics-2e/pages/4-glossary |
net external force : the vector sum of all external forces acting on an object or system; causes a mass to accelerate | https://openstax.org/books/college-physics-2e/pages/4-glossary |
Newtonâs first law of motion : a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force; also known as the law of inertia | https://openstax.org/books/college-physics-2e/pages/4-glossary |
Newtonâs second law of motion : the net external forceFnetFneton an object with massmmis proportional to and in the same direction as the acceleration of the object,aa, and inversely proportional to the mass; defined mathematically asa=Fnetma=Fnetm | https://openstax.org/books/college-physics-2e/pages/4-glossary |
Newtonâs third law of motion : whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts | https://openstax.org/books/college-physics-2e/pages/4-glossary |
normal force : the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the object rests | https://openstax.org/books/college-physics-2e/pages/4-glossary |
system : defined by the boundaries of an object or collection of objects being observed; all forces originating from outside of the system are considered external forces | https://openstax.org/books/college-physics-2e/pages/4-glossary |
tension : the pulling force that acts along a medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the weight of an object, the force on the object due to the rope is called a tension force | https://openstax.org/books/college-physics-2e/pages/4-glossary |
thrust : a reaction force that pushes a body forward in response to a backward force; rockets, airplanes, and cars are pushed forward by a thrust reaction force | https://openstax.org/books/college-physics-2e/pages/4-glossary |
weight : the forcewwdue to gravity acting on an object of massmm; defined mathematically as:w=mgw=mg, whereggis the magnitude and direction of the acceleration due to gravity | https://openstax.org/books/college-physics-2e/pages/4-glossary |
Dynamicsis the study of how forces affect the motion of objects. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Forceis a push or pull that can be defined in terms of various standards, and it is a vector having both magnitude and direction. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
External forcesare any outside forces that act on a body. Afree-body diagramis a drawing of all external forces acting on a body. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Newtonâs first law of motionstates that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as thelaw of inertia. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Inertiais the tendency of an object to remain at rest or remain in motion. Inertia is related to an objectâs mass. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Massis the quantity of matter in a substance. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Acceleration,aa, is defined as a change in velocity, meaning a change in its magnitude or direction, or both. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Newtonâs second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
In equation form, Newtonâs second law of motion isa=Fnetma=Fnetm. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
This is often written in the more familiar form:Fnet=maFnet=ma. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
The weightwwof an object is defined as the force of gravity acting on an object of massmm. The object experiences an acceleration due to gravitygg:w=mg.w=mg. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
If the only force acting on an object is due to gravity, the object is in free fall. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Friction is a force that opposes the motion past each other of objects that are touching. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Newtonâs third law of motionrepresents a basic symmetry in nature. It states: Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Athrustis a reaction force that pushes a body forward in response to a backward force. Rockets, airplanes, and cars are pushed forward by a thrust reaction force. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts perpendicular to and away from the surface. It is called a normal force,NN. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object:N=mg.N=mg. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
When objects rest on an inclined plane that makes an angleθθwith the horizontal surface, the weight of the object can be resolved into components that act perpendicular (wâ¥wâ¥) and parallel (wâ¥wâ¥)to the surface of the plane. These components can be calculated using:wâ¥=wsin(θ)=mgsin(θ)wâ¥=wsin(θ)=mgsin(θ... | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension,TT. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object:T=mg.T=mg. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
In any inertial frame of reference (one that is not accelerated or rotated), Newtonâs laws have the simple forms given in this chapter and all forces are real forces having a physical origin. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
To solve problems involving Newtonâs laws of motion, follow the procedure described:Draw a sketch of the problem.Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, an... | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Draw a sketch of the problem. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in direction... | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Write Newtonâs second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, thexx-direction) thenFnetx=0Fnetx=0. If the object does accelerate in that direction,Fnetx=maFnetx=ma. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Check your answer. Is the answer reasonable? Are the units correct? | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Newtonâs laws of motion can be applied in numerous situations to solve problems of motion. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Some problems will contain multiple force vectors acting in different directions on an object. Be sure to draw diagrams, resolve all force vectors into horizontal and vertical components, and draw a free-body diagram. Always analyze the direction in which an object accelerates so that you can determine whetherFnet=maFn... | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
The normal force on an object is not always equal in magnitude to the weight of the object. If an object is accelerating, the normal force will be less than or greater than the weight of the object. Also, if the object is on an inclined plane, the normal force will always be less than the full weight of the object. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Some problems will contain various physical quantities, such as forces, acceleration, velocity, or position. You can apply concepts from kinematics and dynamics in order to solve these problems of motion. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
The various types of forces that are categorized for use in many applications are all manifestations of thefour basic forcesin nature. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
The properties of these forces are summarized inTable 4.1. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
Everything we experience directly without sensitive instruments is due to either electromagnetic forces or gravitational forces. The nuclear forces are responsible for the submicroscopic structure of matter, but they are not directly sensed because of their short ranges. Attempts are being made to show all four forces ... | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
A force field surrounds an object creating a force and is the carrier of that force. | https://openstax.org/books/college-physics-2e/pages/4-section-summary |
deformation : change in shape due to the application of force | https://openstax.org/books/college-physics-2e/pages/5-glossary |
drag force : FDFD, found to be proportional to the square of the speed of the object; mathematicallyFDâv2FDâv2FD=12CÏAv2,FD=12CÏAv2,whereCCis the drag coefficient,AAis the area of the object facing the fluid, andÏÏis the density of the fluid | https://openstax.org/books/college-physics-2e/pages/5-glossary |
friction : a force that opposes relative motion or attempts at motion between systems in contact | https://openstax.org/books/college-physics-2e/pages/5-glossary |
Hookeâs law : proportional relationship between the forceFFon a material and the deformationÎLÎLit causes,F=kÎLF=kÎL | https://openstax.org/books/college-physics-2e/pages/5-glossary |
kinetic friction : a force that opposes the motion of two systems that are in contact and moving relative to one another | https://openstax.org/books/college-physics-2e/pages/5-glossary |
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