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This document provides information about projectile motion and uniform circular motion. It defines key terms like projectile, trajectory, horizontal and vertical components of motion. It gives examples of solving projectile motion problems for objects launched horizontally or at an angle. It also defines uniform circular motion, centripetal acceleration, centripetal force, and gives an example of calculating centripetal force for a mass attached to a string moving in a horizontal circle.
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Projectile motion
Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.
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This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.
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A projectile is an object upon which the only force acting is gravity. There are many examples of projectiles. An object dropped from rest is a projectile as long as that the influence of air resistance is negligible. An object that is thrown vertically upward is also a projectile provided that the influence of air resistance is negligible. And an object which is thrown upward at an angle to the horizontal is also a projectile as long as that the influence of air resistance is negligible. A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.
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The document discusses projectile motion, which is two-dimensional motion under constant acceleration. Projectiles follow a parabolic trajectory due to gravity acting downward. The horizontal and vertical motions can be analyzed separately, with the horizontal motion having constant velocity and the vertical following equations for constant acceleration. Key aspects include calculating the maximum height, range, and landing location of a projectile given initial velocity and angle.
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The document describes projectile motion and the key concepts involved. It defines a projectile as a particle thrown obliquely near the earth's surface that moves along a curved path. It discusses the trajectory, components of velocity and acceleration, equations of motion, time of flight, range, maximum height, and velocity of a projectile at any instant. Examples of projectile motion calculations are provided to illustrate how to determine initial velocities, maximum height, range, and the time and distance required for a bomb to hit a target from an airplane.
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Nehru Nagar is a residential area made by Siddhant and Saurabh. Their document discusses projectile motion through defining its components, equations of path and motion, time of flight, maximum height, horizontal range, and examples like cannon balls. Projectile motion results from independent horizontal and vertical motions. The path is a parabola defined by equations combining the horizontal and vertical components. Time of flight, maximum height, and horizontal range can be calculated from initial velocity and launch angle.
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Projectile motion
Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.
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this is all about projectile motion......first few slides are only for presentation ....if needed u can ignore them.....
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A projectile motion problem is given involving a projectile fired at an angle of 60 degrees with an initial speed of 30 m/s. The initial horizontal and vertical velocities are calculated. The range and time to highest point are also calculated. A second problem involves a shell fired from a cliff and calculations to determine the initial velocity and velocities when it hits the ground. A third problem involves calculating velocities and angle for a kicked football given the range and time.
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This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.
Projectile motion
A projectile is an object upon which the only force acting is gravity. There are many examples of projectiles. An object dropped from rest is a projectile as long as that the influence of air resistance is negligible. An object that is thrown vertically upward is also a projectile provided that the influence of air resistance is negligible. And an object which is thrown upward at an angle to the horizontal is also a projectile as long as that the influence of air resistance is negligible. A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.
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The document discusses projectile motion, which is two-dimensional motion under constant acceleration. Projectiles follow a parabolic trajectory due to gravity acting downward. The horizontal and vertical motions can be analyzed separately, with the horizontal motion having constant velocity and the vertical following equations for constant acceleration. Key aspects include calculating the maximum height, range, and landing location of a projectile given initial velocity and angle.
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Nehru Nagar is a residential area made by Siddhant and Saurabh. Their document discusses projectile motion through defining its components, equations of path and motion, time of flight, maximum height, horizontal range, and examples like cannon balls. Projectile motion results from independent horizontal and vertical motions. The path is a parabola defined by equations combining the horizontal and vertical components. Time of flight, maximum height, and horizontal range can be calculated from initial velocity and launch angle.
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Projectile motion is the motion of an object under the influence of gravity. It can be broken down into two components: horizontal motion and vertical motion. Horizontal motion is unaffected by gravity and follows the regular kinematic equations of straight line motion. Vertical motion is affected by the downward acceleration due to gravity and also follows straight line kinematic equations using the acceleration due to gravity. Understanding projectile motion requires analyzing the horizontal and vertical components separately using the appropriate kinematic equations for each direction.
Projectile motion
This document discusses projectile motion, which refers to two-dimensional motion under constant gravitational acceleration. Examples of projectiles include missiles, bombs, thrown balls, and objects thrown from windows. The motion is analyzed assuming constant gravitational acceleration directed downward, negligible air resistance, and ignoring Earth's rotation. The path of a projectile is called its trajectory. Equations are presented for the trajectory, range (horizontal distance between projection and landing), time of flight, and maximum height of a projectile based on its initial velocity and projection angle. The range is maximized when the projection angle is 45 degrees.
Projectile motion
1) Projectile motion involves objects moving through the air without propulsion, following a parabolic trajectory under constant acceleration due to gravity.
2) The horizontal and vertical components of motion are independent, with horizontal motion uniform and vertical motion accelerated.
3) Key equations given relate the total time, horizontal range, and maximum height of a projectile to its initial velocity and launch angle.
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Uniform circular motion requires a constant change in the direction of velocity but not necessarily the speed. The acceleration required is toward the center of the circle and depends on the velocity and radius of the circular path. For a banked road curve, the banking angle required to eliminate the need for any friction is given by the formula involving the vehicle's speed and the radius of the curve.
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The document discusses projectile motion, which refers to two-dimensional motion of objects subject to gravity. Examples of projectiles include balls and arrows. Projectiles follow a parabolic trajectory path. The range of a projectile is the maximum horizontal distance it can cover while returning to its original launch height. To analyze projectile motion, the initial velocity vector is resolved into horizontal and vertical components, and kinematic equations are applied to describe motion in each dimension throughout flight.
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This document discusses projectile motion and provides equations to model the motion. It states that:
1) The motion of a projectile can be thought of as the combination of horizontal and vertical motions, which act independently.
2) The equation of motion for the horizontal direction is x = ut cosθ, where u is the initial velocity and θ is the launch angle.
3) The equation of motion for the vertical direction is y = utsinθ - 1/2gt^2.
4) Combining the horizontal and vertical equations yields the equation of the projectile path, which is a parabola.
Physics -vectors-projectile motion
Projectile motion refers to the two-dimensional motion of an object under the influence of gravity. A projectile has both horizontal and vertical motion, with the horizontal motion being constant and the vertical motion accelerating due to gravity. The path of a projectile through the air is a parabolic curve. Examples of projectile motion include throwing a ball, kicking a field goal, or launching a rocket.
Uniform Circular Motion
1) Uniform circular motion is motion at a constant speed in a circular path. It requires centripetal acceleration towards the center.
2) The magnitude of centripetal acceleration depends on speed and radius, and is given by a=v^2/r.
3) A centripetal force is needed to produce the centripetal acceleration. This force can be provided by tension (in a rope), friction, or banking of the surface.
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Students conducted an experiment to study projectile motion. They built a launch pad with an adjustable angle and elastic band to launch projectiles at varying angles and velocities. Observations of the projectile's range and maximum height were recorded. The experiment demonstrated that a projectile's horizontal velocity remains constant while its vertical velocity changes, and that range is greatest at an angle of 45 degrees.
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This document discusses projectile motion, beginning with an overview of the objectives and definitions. It explains that a projectile experiences only gravity and air resistance, and its motion can be analyzed as independent vertical and horizontal components. Horizontal projectiles follow the simplest case where velocity is constant horizontally but follows parabolic free fall vertically. Non-horizontal projectiles require calculating initial velocity components and analyzing changes in vertical velocity over time. Solving projectile motion problems generally involves drawing diagrams, choosing a coordinate system, and applying the independent kinematic equations along each axis. Air resistance decreases a projectile's range from the ideal parabolic trajectory.
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This document provides an overview of projectile motion concepts including:
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- The horizontal motion of a projectile is independent of its vertical motion, with the horizontal velocity remaining constant and no horizontal acceleration. Vertically, gravity causes acceleration of -9.8 m/s2.
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1) Kinematics in two dimensions involves calculating displacement, velocity, and acceleration based on an object's initial position, velocity, acceleration, and time. Projectile motion can be analyzed by separating the horizontal and vertical motions.
2) For projectile motion, the horizontal velocity remains constant while the vertical velocity is affected by gravity. Objects thrown at an angle will hit the ground at the same time due to their downward acceleration.
3) The maximum range of a projectile is achieved at a launch angle of 45 degrees. Range can be calculated using the initial velocity, launch angle, and gravitational acceleration.
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1. The document discusses two dimensional projectile motion under constant acceleration due to gravity. It provides examples of projectiles moving horizontally and vertically, as well as equations of motion for two dimensional kinematic problems.
2. Key concepts covered include: the independence of horizontal and vertical motion, the parabolic trajectory of projectiles, and the equations needed to solve for displacement, velocity and acceleration in both the horizontal and vertical directions.
3. Examples include bullets fired from a moving car, balls dropped from the same height, and a ball reaching the edge of a surface at a constant horizontal velocity.
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This document discusses projectile motion and related concepts. It defines a projectile as any object moving only under the influence of gravity. The horizontal and vertical motions of a projectile are independent, allowing the use of kinematic equations separately in each direction. Galileo first discovered that objects fall at the same rate regardless of mass by dropping objects from the Leaning Tower of Pisa. The document provides examples of solving projectile motion problems by separating the horizontal and vertical components.
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This document discusses motion in two dimensions and projectile motion. It defines scalar and vector quantities, and how to resolve vectors into horizontal and vertical components using trigonometry. It presents the three equations of motion for constant acceleration, and applies them to examples of objects falling vertically and projectiles launched at an angle. It also discusses how air resistance affects projectile motion by decreasing height and range, and how launch angle and height can maximize the projectile's range.
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Free fall is the motion of an object under the influence of gravitational force only. During free fall, the acceleration due to gravity (g) is about 9.8 m/s2, causing the object's speed to increase by 9.8 m/s every second and its position to change according to the kinematic equations of motion. In a vacuum, where there is no air resistance, all objects in free fall accelerate at the same rate due to gravity regardless of their mass or shape.
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Projectile motion refers to the motion of objects through the air without propulsion. When objects are projected horizontally, their horizontal motion is uniform while their vertical motion is accelerated downward by gravity. This results in parabolic trajectories. The total time, horizontal range, and maximum height of a projectile depend on its initial velocity and height/angle of projection. When objects are projected at an angle, their horizontal and vertical motions can be treated independently, following the kinematic equations of uniform and accelerated motion respectively.
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Projectile motion is the motion of an object under the influence of gravity. It can be broken down into two components: horizontal motion and vertical motion. Horizontal motion is unaffected by gravity and follows the regular kinematic equations of straight line motion. Vertical motion is affected by the downward acceleration due to gravity and also follows straight line kinematic equations using the acceleration due to gravity. Understanding projectile motion requires analyzing the horizontal and vertical components separately using the appropriate kinematic equations for each direction.
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This document discusses projectile motion, which refers to two-dimensional motion under constant gravitational acceleration. Examples of projectiles include missiles, bombs, thrown balls, and objects thrown from windows. The motion is analyzed assuming constant gravitational acceleration directed downward, negligible air resistance, and ignoring Earth's rotation. The path of a projectile is called its trajectory. Equations are presented for the trajectory, range (horizontal distance between projection and landing), time of flight, and maximum height of a projectile based on its initial velocity and projection angle. The range is maximized when the projection angle is 45 degrees.
Projectile motion
1) Projectile motion involves objects moving through the air without propulsion, following a parabolic trajectory under constant acceleration due to gravity.
2) The horizontal and vertical components of motion are independent, with horizontal motion uniform and vertical motion accelerated.
3) Key equations given relate the total time, horizontal range, and maximum height of a projectile to its initial velocity and launch angle.
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Uniform circular motion requires a constant change in the direction of velocity but not necessarily the speed. The acceleration required is toward the center of the circle and depends on the velocity and radius of the circular path. For a banked road curve, the banking angle required to eliminate the need for any friction is given by the formula involving the vehicle's speed and the radius of the curve.
Motion in two dimensions
The document discusses projectile motion, which refers to two-dimensional motion of objects subject to gravity. Examples of projectiles include balls and arrows. Projectiles follow a parabolic trajectory path. The range of a projectile is the maximum horizontal distance it can cover while returning to its original launch height. To analyze projectile motion, the initial velocity vector is resolved into horizontal and vertical components, and kinematic equations are applied to describe motion in each dimension throughout flight.
Projectile motionchemistory (4)
This document discusses projectile motion and provides equations to model the motion. It states that:
1) The motion of a projectile can be thought of as the combination of horizontal and vertical motions, which act independently.
2) The equation of motion for the horizontal direction is x = ut cosθ, where u is the initial velocity and θ is the launch angle.
3) The equation of motion for the vertical direction is y = utsinθ - 1/2gt^2.
4) Combining the horizontal and vertical equations yields the equation of the projectile path, which is a parabola.
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Projectile motion refers to the two-dimensional motion of an object under the influence of gravity. A projectile has both horizontal and vertical motion, with the horizontal motion being constant and the vertical motion accelerating due to gravity. The path of a projectile through the air is a parabolic curve. Examples of projectile motion include throwing a ball, kicking a field goal, or launching a rocket.
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1) Uniform circular motion is motion at a constant speed in a circular path. It requires centripetal acceleration towards the center.
2) The magnitude of centripetal acceleration depends on speed and radius, and is given by a=v^2/r.
3) A centripetal force is needed to produce the centripetal acceleration. This force can be provided by tension (in a rope), friction, or banking of the surface.
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Students conducted an experiment to study projectile motion. They built a launch pad with an adjustable angle and elastic band to launch projectiles at varying angles and velocities. Observations of the projectile's range and maximum height were recorded. The experiment demonstrated that a projectile's horizontal velocity remains constant while its vertical velocity changes, and that range is greatest at an angle of 45 degrees.
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This document discusses projectile motion, beginning with an overview of the objectives and definitions. It explains that a projectile experiences only gravity and air resistance, and its motion can be analyzed as independent vertical and horizontal components. Horizontal projectiles follow the simplest case where velocity is constant horizontally but follows parabolic free fall vertically. Non-horizontal projectiles require calculating initial velocity components and analyzing changes in vertical velocity over time. Solving projectile motion problems generally involves drawing diagrams, choosing a coordinate system, and applying the independent kinematic equations along each axis. Air resistance decreases a projectile's range from the ideal parabolic trajectory.
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Torque is a measure of the tendency of a force to rotate an object about an axis. It is defined mathematically as the cross product of the lever arm distance and the force applied, which tends to produce rotation. Newton's laws for linear motion can be applied to rotational motion by substituting torque for force, angular position for linear position, angular velocity for linear velocity, and angular acceleration for linear acceleration. Horsepower, a unit of power, was originally defined based on the work a horse could do in one minute.
Projectile motion 2
This document provides an overview of projectile motion concepts including:
- A projectile is any object upon which the only force acting is gravity and it moves in a parabolic trajectory.
- The horizontal motion of a projectile is independent of its vertical motion, with the horizontal velocity remaining constant and no horizontal acceleration. Vertically, gravity causes acceleration of -9.8 m/s2.
- Key equations presented include those relating the horizontal and vertical displacement and velocity as functions of time, as well as resolving initial velocity into horizontal and vertical components using trigonometry.
- Examples are provided of solving projectile motion problems by identifying knowns and unknowns, selecting appropriate equations, and applying a
Lecture 05 Kinematics in Two Dimensions
1) Kinematics in two dimensions involves calculating displacement, velocity, and acceleration based on an object's initial position, velocity, acceleration, and time. Projectile motion can be analyzed by separating the horizontal and vertical motions.
2) For projectile motion, the horizontal velocity remains constant while the vertical velocity is affected by gravity. Objects thrown at an angle will hit the ground at the same time due to their downward acceleration.
3) The maximum range of a projectile is achieved at a launch angle of 45 degrees. Range can be calculated using the initial velocity, launch angle, and gravitational acceleration.
Motion in two dimensions
1. The document discusses two dimensional projectile motion under constant acceleration due to gravity. It provides examples of projectiles moving horizontally and vertically, as well as equations of motion for two dimensional kinematic problems.
2. Key concepts covered include: the independence of horizontal and vertical motion, the parabolic trajectory of projectiles, and the equations needed to solve for displacement, velocity and acceleration in both the horizontal and vertical directions.
3. Examples include bullets fired from a moving car, balls dropped from the same height, and a ball reaching the edge of a surface at a constant horizontal velocity.
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This document discusses projectile motion and related concepts. It defines a projectile as any object moving only under the influence of gravity. The horizontal and vertical motions of a projectile are independent, allowing the use of kinematic equations separately in each direction. Galileo first discovered that objects fall at the same rate regardless of mass by dropping objects from the Leaning Tower of Pisa. The document provides examples of solving projectile motion problems by separating the horizontal and vertical components.
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This document discusses motion in two dimensions and projectile motion. It defines scalar and vector quantities, and how to resolve vectors into horizontal and vertical components using trigonometry. It presents the three equations of motion for constant acceleration, and applies them to examples of objects falling vertically and projectiles launched at an angle. It also discusses how air resistance affects projectile motion by decreasing height and range, and how launch angle and height can maximize the projectile's range.
Free fall
Free fall is the motion of an object under the influence of gravitational force only. During free fall, the acceleration due to gravity (g) is about 9.8 m/s2, causing the object's speed to increase by 9.8 m/s every second and its position to change according to the kinematic equations of motion. In a vacuum, where there is no air resistance, all objects in free fall accelerate at the same rate due to gravity regardless of their mass or shape.
Projectile motion (2)
Projectile motion refers to the motion of objects through the air without propulsion. When objects are projected horizontally, their horizontal motion is uniform while their vertical motion is accelerated downward by gravity. This results in parabolic trajectories. The total time, horizontal range, and maximum height of a projectile depend on its initial velocity and height/angle of projection. When objects are projected at an angle, their horizontal and vertical motions can be treated independently, following the kinematic equations of uniform and accelerated motion respectively.
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www.wsautter.com
and
http://www.youtube.com/results?search_query=wnsautter&aq=f
Lecture 1: Quadrotor
The document describes the anatomy and dynamics of a quadrotor unmanned aerial vehicle (UAV). It discusses the first manned quadrotor flight in 1907 and advantages of quadrotors such as vertical take-off and landing. Key components of quadrotor structure and motion including motors, frames of reference, state variables, and kinematic and dynamic equations are presented. Thrust forces from each motor and gravity are expressed as components of the total force acting on the quadrotor.
Chapter 11_0 velocity, acceleration.pdf
This problem involves analyzing the motion of a ball thrown vertically upwards in an elevator shaft, and an open-platform elevator moving upwards at a constant velocity.
The key steps are:
1) Use kinematic equations to find the velocity and position of the ball as a function of time, assuming constant downward acceleration due to gravity.
2) Determine the velocity and position of the elevator as a constant upward velocity.
3) Express the relative motion of the ball with respect to the elevator to determine when they meet.
By setting the position of the ball equal to the position of the elevator and solving for time, we can determine when the ball and elevator meet at 26.4 seconds after the ball is thrown
Circular Motion (AIS).ppt
The document discusses circular motion and related concepts such as radians, angular displacement, angular velocity, angular acceleration, centripetal acceleration, and centripetal force. It provides definitions and equations for these terms and concepts, including that centripetal acceleration is directed toward the center of the circular path, and is given by a=v2/r. Centripetal force is the net force providing the centripetal acceleration, and is given by Fc=mv2/r.
Unit iv dynamics of particles
The document defines key concepts in particle dynamics including:
1. D'Alembert's principle which states that an imaginary inertia force acts opposite to motion to maintain dynamic equilibrium.
2. The principle of work and energy which relates the work done by a force to the change in kinetic energy of a particle.
3. The impulse-momentum principle which states that the impulse of a force is equal to the change in linear momentum of a particle.
4. Uniform rectilinear motion as motion along a straight line at constant velocity.
chapter5_Phys201_Summer07.pdf
The document discusses uniform circular motion and centripetal force. It defines key terms like centripetal acceleration, centripetal force, and period of motion. It provides examples of calculating centripetal force and acceleration for objects moving in circular paths, including satellites in orbit. It also discusses concepts like apparent weight and applications to space stations designed to create artificial gravity environments.
Mechanics
A branch of physical science which deals with ( the states of rest or motion of ) bodies under action of forces
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Hpn6notescolor
- 1. II P6-1 CHAPTER6: MOTION IN TWO DIMENSIONS PLOJECTILE:ANY OBJECTTHAT ISPROJECTEDBY SOME FORCEAND CONTINUESIN MOTIONBY ITS OWNINERTIA (travelsin a curvedpath) TRAJECTORY:PATHOFA PROJECTILE -A curvedpathistheresultof two forces: 1)Theforceyouapplywhenyouthrowit makesit goforwardata constantspeed(theforwardspeeddoesnotchangebecausenootherforces areactingin thisdirectionafteryouthrowtheball) 2) All thetimetheballmoves,gravitykeepspullingontheball(gravity causesit's downwardspeedto keepincreasing) -thecombinationofforwardconstantspeedanddownwardincreasing speedcnusesthepath to curve o WE MUSTLOOK AT THEHORIZONTALAND VERTICAL COMPONENTSOFMOTIONSEPARATELY! PROJECTILELAUNCHEDHORIZONTALLY fra*e, of refuancl (sta^r'tr'ng .P ot i't) V;=inihalvetoct! Vix=Vi Viy=0 (no terttcal Corngonn* o? initial vclocity) tt
- 2. I I P6-2 PROJECTILENOT LATINCHEDHORIZONTALLY(AT AN ANGLE FROM HORIZONTAL) "F c,?. / a - / l r / l r Ay t., rnaxirrnurnheiql'rt oscrrsin h;lf tha ti nlc (alwaysg) (no.horz.acceleration) dx dx € also catle&t*...e-ttrang" " STEPSFORSOLVINGPROJECTILEMOTIONPROBLEMS Drawyourpicture Establishyoursignconvention Write outyourgivenandwhatyouwantto find (divideit up:andy) Breakyourinitialvelocityintohorizontalandverticalcomponents Apply equationsin onlyonedirection,horizontallyor vertically Lookatwhatyou'resolvingfor to determinewhatto donext. f o':v"'-)s" d -v,*!ot'- Jv ' ' i ' 2 - o - - l a,=ri**lo.t' 2 -no horizontalacceleration,e*:0 -vertically, accelerationis alwaysg! 1 . 2. 3. 4. 5. 6.
- 3. a a P6-3 EXAMPLE:(Projectilethrownhorizontally) A STONEIS THROWNHORIZONTALLYAT 15M/S. IT WAS THROWNFROMTHETOpOFA CLrFF44l|4HrcH. (A) HOWLONG DOESIT TAKE A STONETOREACHTHEBOTTOMOFTHE CLIFF?(B)HOWFARFROMTHEBASEOFTHECLIFFDOESTHE STONESTRIKE THE GROLTND? Gr-g,' * rnaKe x ' * g 'Y- ftx =O Vix=lsF t tDhere given (,q.) dy A1 LJnKnoarn: (Ot (h) d,x Vi? tSS &--.. $iven u -.#rarne of { rc+uenLa $=-q'8F/ V i $ = O r A9=*44'"'y' +D .firt ? tooKef tha slde of *hc Whuc Yoo aw 3 th rngs =vit + + gt' (viy=o) : i*' Lrgo,w*hj, -l"osofvc-R:t'L) tb) d* - d--r= Vix.::U+t artL [ar= Vlxt =(tstYs.os) O,alr.,4gtg) a d,r=E a
- 4. I a P6-4 EXAMPLE:(Projectilelaunched atanangle) A GOLFBALL ISHIT AND LEAVESTHETEEWITH A VELOCITY OF25M/SAT 35OWITH RESPECTTOTHEHORIZONTAL.WHAT IS THEHORIZONTALDISPLACEMENTOFTHEBALL? 9iuq' 4 r = o l g r - Q . 8 ? " Vip=th I u,y=fr ,...rSY- -^fl -.. $'{'=o- - fri', *he dx.S €rnfrre +rr,a] -b ((Ak inihd t Velocr inlr hori zon-fzrl and, Vgnt er"t CorvrgoAent-r ' V=ufuT,,,,,,viy--Visrn2s'=(zsgXsrn?J) --,+..lF )r €Ju'I Vix = vrcoszs': LzEbrXco.r3f) a eo.sf* Vix - tl,a +o{"^l {rrne J*he praSachlcis rn rrofion dcpr,rrclsontlnerhifral and ffnat Vcrhcr*l vslo(-tu - or",4orrtd{ eft- it startsr {"o whert tf cnatq #e- Ve,rfical d.isgtaceftLrf ls tefr (er.=o) dy=Viytr t %t?u o ={l.t..t?)c{.t F1,SF)ta; [usa 4bradmficor&c1.r. ouf,t) O = lt.qe - - *{^c hon ?ontzrldrJ?Ilt-emerl- 4'9t = lY't{ L*=V,x1,rt axt.l-D d* =Viri =.lgo.s?Xe"Qrls) . @ l.qtL + af, = ?,1+S a
- 5. a t P6-5 -uniformcircular motionresultswhena netforce, actingon a mass movingat a constantspeed,changesdirection in sucha way that theforce is alwaysacting at a right angle to thedirection in which themassis moving UNIFORM CIRCIJLAR MOTION: PARTICLESMOVING IN A CIRCULAR PATH AT A CONSTANTSPEED CENTRIPETAL ACCELERATION: ACCELERATION ALWAYS AT RIGHT ANGLES TO THE VELOCITY OF A PARTICLE -centripetalacceleration,like centripetalforce, is alwaysdirectedtoward thecenterof a circle. Thisis a resultof Ittewton'smqws. -"centripetal"meanscenter-seeking a"-centripetalacceleration(m/s2) v- velocity (m/s) r-radiusof circle(m) EXAMPLE:WHAT IS THE CENTRIPETALACCELERATIONOFAN OBJECTMOVINGIN A CIRCULARPATHOF2O.OM RADIUSWITH A SPEEDOF2O.OM/S? Lao.os" sD.oh Given: r=' lD.onn rf - at n ^..r, hh v - 4Ll.J 1 aL-*# J O.on1 I o
- 6. o t P6-6 *seepage153of textbookfor vectordiagramsdescribingcircularmotion v' (znr' t ' l 4tt2r T2 = 4 , 2nr , = , ) A " : ; ) A " CENTRIPETALFORCE:FORCEDIRECTEDTOWARDTHE CENTEROFA CIRCLE,KEEPSPARTICLESMOVING IN LTNIFORM CIRCULAR MOTION Fr"t = ffiQ, fY'? D,2S Kg r = t,DOrr., v : s . o ? Fc mvz r EXAMPLE:40.25KG MASSISATTACHEDTOA 1.00M LENGTH OFSTRING.THEMASSIS MOVING IN A HORIZONTALCIRCLE AT A SPEEDOF 15.0M/S. WHAT IS THECENTRIPETALFORCE ACTINGON THEMASS? Given: FtnA"Fe e =!1!.t =e r r4 ( o . e s r g X t s . o F )- T b ( l.oonn) w.rL Fc '- sb N Iradlalty tn WAr."L) -properlyengineeredcurvesin aroadarebankedto furnishsuchaforce. -asatellitefollowinganorbitaroundaplanetor aplanetgoingaroundthe sunis heldin orbitby thecentripetalforcefurnishedby the gravitational attraction -astheplanetsmovearoundthesuntheyundergocentripetalacceleration, butthesearenotconstantin magnitude.Theplanetsmovearoundthesun in circularorbits. t a