One-Dimensional Motion Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Time t Seconds Velocity v m/s

Size: px
Start display at page:

Download "One-Dimensional Motion Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Time t Seconds Velocity v m/s"

Transcription

1 One-Dimensional Motion Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Time t Seconds Velocity v m/s v x t Position x Meters Speed v m/s v t Length l Meters Acceleration a m/s a v Distance d t Gravity on g m/s g = 9.8 m/s Earth (Down) Name Equation Given? Notes Position as a unction o time, constant velocity. x vt No Position as a unction o x 0 0 time, constant acceleration. 1 at v t x Yes Velocity as a unction o time, constant acceleration. Velocity in terms o position and acceleration. v x 0 v at Yes v 0 x x a v Yes Position vs. Time (Constant Velocity) 0 0 Use i the velocity is constant or i you know initial and inal velocity (the average o those is v ). Use i there is acceleration, and time is involved in the problem, but no mention is made o inal velocity. Use i there is an acceleration and time in involved in the problem, no mention is made o position. Use to relate initial and inal position and velocity to acceleration, but no mention is made o time. THE SLOPE OF A POSITION VS. TIME GRAPH IS VELOCITY. Because velocity is constant, the slope is constant. This makes the graph a straight line. Position vs. Time (Constant Acceleration) THE SLOPE OF A POSITION VS. TIME GRAPH IS VELOCITY. Because the slope increases, the velocity increases. The shape o a position vs. time graph is a parabola or constant acceleration. Velocity vs. Time (Constant Velocity) THE SLOPE OF A VELOCITY VS. TIME GRAPH IS ACCELERATION. Because the slope is zero, acceleration is zero i velocity is constant. Constant velocity means constant y- value, so velocity vs. time or constant velocity is a lat line. THE AREA UNDER A VELOCITY VS. TIME GRAPH REPRESENTS A CHANGE IN POSITION.

2 Velocity vs. Time (Constant Acceleration) Acceleration vs. Time (Constant Velocity) Acceleration vs. Time (Constant Acceleration) THE SLOPE OF A VELOCITY VS. TIME GRAPH IS ACCELERATION. Because the acceleration is constant, the slope is constant. Constant slope means a straight line. THE AREA UNDER A VELOCITY VS. TIME GRAPH REPRESENTS A CHANGE IN POSITION. THE AREA UNDER AN ACCELERATION VS. TIME GRAPH REPRESENTS A CHANGE IN VELOCITY. Since velocity is constant, there is no acceleration. The graph o zero is a horizontal line at y = 0, which means there is no area which means that there is no change in velocity. THE AREA UNDER AN ACCELERATION VS. TIME GRAPH REPRESENTS A CHANGE IN VELOCITY. Since acceleration is constant, the y-value o the graph is a constant, which makes a lat line. Speed is the magnitude o velocity. Two cars, one traveling 60 mph north and the other 60 mph south, have the same speed but dierent velocities. Acceleration is a change in velocity. Since velocity is a vector, an object experiences an acceleration i either its speed or its direction changes. x Only use the equation v i speed is constant or you are asked or average speed! t v Only use the equation a i acceleration is constant or you are asked or average acceleration! Note t x that this equation can never be used at the same time as v. t Any object is considered to be in ree-all i gravity is the only orce acting on it. Big concept: Use kinematics whenever you have two o the ollowing and are asked or a third: position, velocity, time, and acceleration. Make sure that acceleration is constant beore using the constant acceleration equations (hint: simple harmonic motion is not const. accel. because a spring exerts a varying orce; circular motion is not const. accel. because the a keeps changing direction)

3 D Motion Review **Equations are the same as 1D motion just can be used in either X or Y direction. Horizontal Position vs. Time Remember that, in the horizontal direction, the motion is constant velocity. This makes the graph o x vs. t a line with slope v 0x. Vertical Position (Height) vs. Time In the vertical direction, the motion is constant acceleration, making the graph a parabola. The acceleration is downward, so the parabola opens downward. Horizontal Velocity vs. Time Remember that, in the horizontal direction, the motion is constant velocity. This makes the graph o v x vs. t a lat line with value v 0x. Vertical Velocity vs. Time In the vertical direction, the motion is constant acceleration, making the graph a line. The acceleration is 9.8 m/s, so the line has a constant negative slope o 9.8. Horizontal Acceleration vs. Time The motion in the horizontal direction is constant velocity, which automatically makes acceleration zero. Vertical Acceleration vs. Time The motion in the vertical direction is constant acceleration. The acceleration is 9.8 m/s, so the lat line has a constant negative value o 9.8. (Let g = 9.8 m/s ) Gravity subtracts 9.8 m/s rom the vertical velocity every second. Horizontal velocity never changes:

4 An object in ree all has only the orce o gravity acting on it. I an object is in ree all, it has an acceleration o 9.8 m/s downward, even i it is at the peak o its arc. They always try to trick you on this concept! The speed o an object in projectile motion is highest at the bottom o its path. The speed is slowest at the peak (though it may not be zero!). This is because the object s potential energy is the most at its peak, so its kinetic energy is least. The direction o velocity at a certain point is always tangent to the path that an object travels. The direction o acceleration at a certain point is always toward the center o the circle made by the curvature o the path. I a projectile is launched horizontally, then you can use the shorter projectile motion equations y 0 = ½gt and x = vt. These are good to memorize or the multiple choice.

5 Forces and Newton s Laws Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Force F N F ma Normal Force F N N None Tension Friction F Force T N None F Force N F FN Weight F Force W N F W mg Coeicient o Friction None None Mass m kg None Name Equation Given? Notes Newton s Second Law For a single orce, F ma. However, or (The most important F ma Yes several orces, it is the vector sum o all equation in all o physics!) orces equal mass times acceleration. I you have a problem taking place in D, Newton s Second Law in F ma x x then you need to create a sum-o-all orces No terms o components. F ma equation or the components in each y y individual dimension. Perpendicular Component o Weight on an Inclined Plane Parallel Component o Weight on an Inclined Plane F mg cos No F mg sin No Usually equal to the normal orce on an object on an inclined plane. Usually equal to the orce down the plane o an object on an inclined plane. Force vs. Acceleration (or a constant mass) AND Acceleration vs. Mass (or a constant orce) Slope o F vs. a is mass. As mass increases, acceleration decreases Newton s First Law: I the net orce on an object is zero (all orces balance), it will move with constant velocity in a straight line. Likewise, i an object travels with constant velocity in a straight line, the net orce on the object is zero. Note that an object can be in motion even i it has no net orce. Newton s Third Law: I object A exerts a orce on object B, then object B must exert an equal orce (but opposite in direction) on A. Note that action-reaction pairs are always on dierent objects (they always try to trick you into saying otherwise on the exam). Note also that, since they are on dierent objects, actionreaction pairs cannot cancel out. Weight orce is always directed down. Only a surace can exert normal orce. I there is no surace in the problem, there is no normal orce. The normal orce is perpendicular (normal) to the surace.

6 Only a rope or string can exert tension orce. I there is no rope or string in the problem, there is no tension orce. Normal and tension orces have no basic equations. They can only be ound by setting up a statement o Newton s Second Law, and then solving or them. A rope exerts the same tension orce at both ends, even i it is set through a pulley. A scale does not measure mass or weight. It measures the normal orce it exerts. Friction is always parallel to the plane, directed to oppose relative motion. This does not necessarily mean that it is in the opposite direction as velocity. A box in the back o a pick-up truck has riction that prevents it rom sliding o o the truck, but that riction is in the same direction as the velocity o the truck. Two types o riction: Static riction acts when the object is not sliding on the surace. Kinetic riction acts when the object is sliding on the surace. Both types o riction have separate coeicients o riction, oten labeled s and k. Note that 0 < k < s < 1. MAJOR NOTE ON FRICTION: The orce o riction is F FN. But or static riction, the riction orce could be less than this! This ormula only gives the maximum possible static riction! Big concept: Use orces you are asked to solve or a orce or ind an object s acceleration. When dealing with orces in two dimensions, split any orce into components that makes a odd angle with the acceleration vector: All orces and components perpendicular to the acceleration balance (add to zero). All orces and components parallel to the acceleration add to massacceleration.

7 Work, Energy, and Power Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Work W J W Fx Energy E J None Kinetic Energy K J 1 K mv p m Potential Energy (Gravity) Ug Power P W Name Equation Given? Notes Work done by Friction (also energy lost to riction) Conservation o Energy Power in terms o Force and Velocity K i W F x No U K U No i P Fv Yes J U g mgh Energy P time Friction takes some energy out o the system. Note that energy lost to riction becomes heat, so sometimes this is reerred to as thermal energy. The sum o all dierent energies beore equals the sum o all dierent energies ater. These could be kinetic, potential, thermal, etc. energies. Note that dot products imply that you are multiplying the two vectors and the cosine o the angle between them. Force vs. Displacement The area under a orce vs. displacement graph is work. (Could be anything) NO WORK IS DONE IF FORCE IS PERPENDICULAR TO AN OBJECTS MOTION!!! USE ENERGY EQUATIONS IF YOU ARE ASKED FOR VELOCITY IN TERMS OF POSITION, OR POSITION IN TERMS OF VELOCITY! Note that the equations W Fx and P Fv are equivalent to W F x and P F v and W Fx cos and P Fv cos. Cosine does the job o inding the parallel component or you. Work is a transer o energy rom one orm to another. I energy goes rom kinetic to potential, potential to kinetic, kinetic to thermal, kinetic to another object s kinetic, etc., work was done. A orce does positive work i the orce is in the same direction as displacement. Likewise a orce does negative work i the orce is opposite displacement. A orce does positive work i the potential energy related to that orce decreases. Likewise, a orce does negative work i the potential energy related to that orce decreases. A orce does positive work i the kinetic energy o the object increases.

8 Potential energy increases i an object is orced to do the opposite o what it wants to do. Likewise, potential energy decreases i an object is allowed to do what it wants to do. o Objects want to all down. So raising an object up increases its potential energy. o Objects in space want to attract each other due to gravity. Thereore, moving objects apart in space increases their potential energy. Example: I lit a book rom a low shel to a high shel. I do positive work because the orce I exert (up) is in the same direction as displacement (up), and my potential energy decreases because I had to burn calories to lit the book. On the other hand, gravity did negative work because the orce o gravity (down) was opposite the direction as displacement (up), and gravitational potential energy increased. Big concept: Use energy whenever are given a position and asked or a velocity, OR given a velocity and asked or a position. Example: A block is released rom rest at the top o the incline (point A) as shown. I the incline is rictionless, how ast does the block move at point B? Potential energy becomes kinetic energy mgh 1 mv gh 1015 v = 17.3 m/s I the incline has a coeicient o riction 0.11, what is the speed at point B? P.E. becomes K.E. AND energy lost to riction mgh 1 mv F x (where F F mg cos ) mgh 1 mv mgx cos v gh gxcos 10 v = 16 m/s N I the incline and horizontal plane have a coeicient o riction o 0.11, what is the distance x traveled along the horizontal surace to point C? The speed at the bottom is v = 16 m/s rom beore. All o this kinetic energy becomes energy lost to riction: 1 mv mgx (no cosine because this is lat) x 1 x = 116 m

9 Momentum Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Momentum p kgm/s p mv Impulse J or p kgm/s p mv Ft Name Equation Given? Notes Conservation o Momentum i p p No Use i you are given any problem dealing with a collision. Keep in mind that momentum is a vector, so i an object travels backwards, then it has negative momentum. Force vs. Time (Could be anything) The area under a orce vs. time is equal to impulse. Impulse is the change in the momentum o the object the orce is applied to. I there is a collision o two objects, the impulse is applied to both objects, but in opposite directions (Newton s Third Law). Momentum vs. Time The slope o momentum vs. time is net orce, because F net p. t USE CONSERVATION OF MOMENTUM WHENEVER THERE IS ANY KIND OF COLLISION! DO NOT USE CONSERVATION OF ENERGY! An elastic collision is one in which no energy is lost to heat or deormation. In these problems, you must also set up a conservation o energy equation. An inelastic collision is one in which some kinetic energy is lost during the collision, but the objects may not stick together. In other words, total kinetic energy beore the collision is more than total kinetic energy ater the collision. A perectly inelastic collision is one in which the two objects stick together. The most possible energy is lost to heat and deormation during a perectly inelastic collision. DON T ASSUME that you know that a collision is elastic or inelastic unless you are told. DON T ASSUME that the objects stick together unless you are told. When setting up a conservation o momentum equation, remember that a velocity is negative i the object is moving to the let (or down). Big concept: Use momentum to solve collision problems!

Pre-AP Physics Chapter 1 Notes Yockers JHS 2008

Pre-AP Physics Chapter 1 Notes Yockers JHS 2008 Pre-AP Physics Chapter 1 Notes Yockers JHS 2008 Standards o Length, Mass, and Time ( - length quantities) - mass - time Derived Quantities: Examples Dimensional Analysis useul to check equations and to

More information

Fs (30.0 N)(50.0 m) The magnitude of the force that the shopper exerts is f 48.0 N cos 29.0 cos 29.0 b. The work done by the pushing force F is

Fs (30.0 N)(50.0 m) The magnitude of the force that the shopper exerts is f 48.0 N cos 29.0 cos 29.0 b. The work done by the pushing force F is Chapter 6: Problems 5, 6, 8, 38, 43, 49 & 53 5. ssm Suppose in Figure 6. that +1.1 1 3 J o work is done by the orce F (magnitude 3. N) in moving the suitcase a distance o 5. m. At what angle θ is the orce

More information

PRACTICE TEST for Midterm Exam

PRACTICE TEST for Midterm Exam South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v o t + ½ at 2 d = v o + v 2 t v = v o + at v 2 = v 2 o + 2ad v = v x 2 + v y 2 = tan 1 v y v v x = v cos

More information

Practice Test for Midterm Exam

Practice Test for Midterm Exam A.P. Physics Practice Test for Midterm Exam Kinematics 1. Which of the following statements are about uniformly accelerated motion? Select two answers. a) If an object s acceleration is constant then it

More information

Newton s Laws of Motion

Newton s Laws of Motion Newton s Laws of Motion Observation #1 An object at rest remains at rest, unless something makes it move. Observation #2 A object in motion continues in motion with constant velocity, unless something

More information

Distance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is:

Distance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is: Chapter 1 Kinematics 1.1 Basic ideas r(t) is the position of a particle; r = r is the distance to the origin. If r = x i + y j + z k = (x, y, z), then r = r = x 2 + y 2 + z 2. v(t) is the velocity; v =

More information

Physics 231 Lecture 9

Physics 231 Lecture 9 Physics 31 Lecture 9 Mi Main points o today s lecture: Potential energy: ΔPE = PE PE = mg ( y ) 0 y 0 Conservation o energy E = KE + PE = KE 0 + PE 0 Reading Quiz 3. I you raise an object to a greater

More information

Exam 2--PHYS 101--F11--Chapters 4, 5, & 6

Exam 2--PHYS 101--F11--Chapters 4, 5, & 6 ame: Exam 2--PHYS 101--F11--Chapters 4, 5, & 6 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Consider this figure. What is the normal force acting on

More information

Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms

Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW Dynaics is the study o the causes o otion, in particular, orces. A orce is a push or a pull. We arrange our knowledge o orces into three laws orulated

More information

Work Up an Incline. Work = Force x Distance. Push up: 1500J. What is the PE at the top? mg = 500N. An incline is a simple machine!

Work Up an Incline. Work = Force x Distance. Push up: 1500J. What is the PE at the top? mg = 500N. An incline is a simple machine! Quick Question Work Up an Incline The block o ice weighs 500 Newtons. How much work does it take to push it up the incline compared to liting it straight up? Ignore riction. Work Up an Incline Work = Force

More information

0J2 - Mechanics Lecture Notes 2

0J2 - Mechanics Lecture Notes 2 0J2 - Mechanics Lecture Notes 2 Work, Power, Energy Work If a force is applied to a body, which then moves, we say the force does work. In 1D, if the force is constant with magnitude F, and the body moves

More information

MOMENTUM, IMPULSE & MOMENTS

MOMENTUM, IMPULSE & MOMENTS the Further Mathematics network www.fmnetwork.org.uk V 07 1 3 REVISION SHEET MECHANICS 1 MOMENTUM, IMPULSE & MOMENTS The main ideas are AQA Momentum If an object of mass m has velocity v, then the momentum

More information

NEWTONS LAWS OF MOTION AND FRICTIONS STRAIGHT LINES

NEWTONS LAWS OF MOTION AND FRICTIONS STRAIGHT LINES EWTOS LAWS O OTIO AD RICTIOS STRAIGHT LIES ITRODUCTIO In this chapter, we shall study the motion o bodies along with the causes o their motion assuming that mass is constant. In addition, we are going

More information

AP Mechanics Summer Assignment

AP Mechanics Summer Assignment 2012-2013 AP Mechanics Summer Assignment To be completed in summer Submit for grade in September Name: Date: Equations: Kinematics (For #1 and #2 questions: use following equations only. Need to show derivation

More information

Kinematics 1D Kinematics 2D Dynamics Work and Energy

Kinematics 1D Kinematics 2D Dynamics Work and Energy Kinematics 1D Kinematics 2D Dynamics Work and Energy Kinematics 1 Dimension Kinematics 1 Dimension All about motion problems Frame of Reference orientation of an object s motion Used to anchor coordinate

More information

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,

More information

Solutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 6

Solutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 6 CHAPTER 6 1. Because there is no acceleration, the contact orce must have the same magnitude as the weight. The displacement in the direction o this orce is the vertical displacement. Thus, W = F Æy =

More information

Today s lecture. WEST VIRGINIA UNIVERSITY Physics

Today s lecture. WEST VIRGINIA UNIVERSITY Physics Today s lecture Review of chapters 1-14 Note: I m taking for granted that you ll still know SI/cgs units, order-of-magnitude estimates, etc., so I m focusing on problems. Velocity and acceleration (1d)

More information

SPRING 2003 Final Exam, Part A

SPRING 2003 Final Exam, Part A Physics 151 SPRING 2003 Final Exam, Part A Roster No.: Score: 17 pts. possible Exam time limit: 2 hours. You may use calculators and both sides of 2 sheets of notes, handwritten only. Closed book; no collaboration.

More information

PRACTICE TEST for Midterm Exam

PRACTICE TEST for Midterm Exam South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v ot + ½ at d = v o + v t v = v o + at v = v o + ad v = v x + v y = tan 1 v y v v x = v cos v y = v sin

More information

1. A sphere with a radius of 1.7 cm has a volume of: A) m 3 B) m 3 C) m 3 D) 0.11 m 3 E) 21 m 3

1. A sphere with a radius of 1.7 cm has a volume of: A) m 3 B) m 3 C) m 3 D) 0.11 m 3 E) 21 m 3 1. A sphere with a radius of 1.7 cm has a volume of: A) 2.1 10 5 m 3 B) 9.1 10 4 m 3 C) 3.6 10 3 m 3 D) 0.11 m 3 E) 21 m 3 2. A 25-N crate slides down a frictionless incline that is 25 above the horizontal.

More information

Physics 231 Lecture 12

Physics 231 Lecture 12 Physics 31 Lecture 1 Work energy theorem W Potential energy o gravity: ΔPE total = = PE KE PE KE 0 mg Conservation o energy ( y ) 0 y 0 E = KE + PE = KE 0 + PE 0 Potential energy o a spring = PE = 1 kx

More information

Review D: Potential Energy and the Conservation of Mechanical Energy

Review D: Potential Energy and the Conservation of Mechanical Energy MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department o Physics 8. Spring 4 Review D: Potential Energy and the Conservation o Mechanical Energy D.1 Conservative and Non-conservative Force... D.1.1 Introduction...

More information

v (m/s) 10 d. displacement from 0-4 s 28 m e. time interval during which the net force is zero 0-2 s f. average velocity from 0-4 s 7 m/s x (m) 20

v (m/s) 10 d. displacement from 0-4 s 28 m e. time interval during which the net force is zero 0-2 s f. average velocity from 0-4 s 7 m/s x (m) 20 Physics Final Exam Mechanics Review Answers 1. Use the velocity-time graph below to find the: a. velocity at 2 s 6 m/s v (m/s) 1 b. acceleration from -2 s 6 c. acceleration from 2-4 s 2 m/s 2 2 4 t (s)

More information

Module 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis

Module 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis Module 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis 27.1 Introduction We shall analyze the motion o systems o particles and rigid bodies that are undergoing translational and rotational

More information

There are two types of forces: conservative (gravity, spring force) nonconservative (friction)

There are two types of forces: conservative (gravity, spring force) nonconservative (friction) Chapter 8: Conservation o Energy There are two types o orces: conservative (gravity, spring orce) nonconservative (riction) Conservative Forces Conservative Force the work done by the orce on an object

More information

The... of a particle is defined as its change in position in some time interval.

The... of a particle is defined as its change in position in some time interval. Distance is the. of a path followed by a particle. Distance is a quantity. The... of a particle is defined as its change in position in some time interval. Displacement is a.. quantity. The... of a particle

More information

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam.

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam. WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system is always

More information

Ground Rules. PC1221 Fundamentals of Physics I. Introduction to Energy. Energy Approach to Problems. Lectures 13 and 14. Energy and Energy Transfer

Ground Rules. PC1221 Fundamentals of Physics I. Introduction to Energy. Energy Approach to Problems. Lectures 13 and 14. Energy and Energy Transfer PC11 Fundamentals o Physics I Lectures 13 and 14 Energy and Energy Transer A/Pro Tay Seng Chuan 1 Ground Rules Switch o your handphone and pager Switch o your laptop computer and keep it No talking while

More information

GRADE 12 JUNE 2017 PHYSICAL SCIENCES P1

GRADE 12 JUNE 2017 PHYSICAL SCIENCES P1 NATIONAL SENIOR CERTIFICATE GRADE 1 JUNE 017 PHYSICAL SCIENCES P1 MARKS: 150 TIME: 3 hours *JPHSCE1* This question paper consists o 1 pages, including a page data sheet. PHYSICAL SCIENCES P1 (EC/JUNE 017)

More information

Name. VCE Physics Unit 3 Preparation Work

Name. VCE Physics Unit 3 Preparation Work Name. VCE Physics Unit 3 Preparation Work Transition into 2019 VCE Physics Unit 3+4 Units 3 and 4 include four core areas of study plus one detailed study. Unit 3: How do fields explain motion and electricity?

More information

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time.

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time. Mechanics Symbols: Equations: Kinematics The Study of Motion s = distance or displacement v = final speed or velocity u = initial speed or velocity a = average acceleration s u+ v v v u v= also v= a =

More information

Chapter 11 Collision Theory

Chapter 11 Collision Theory Chapter Collision Theory Introduction. Center o Mass Reerence Frame Consider two particles o masses m and m interacting ia some orce. Figure. Center o Mass o a system o two interacting particles Choose

More information

Newton s 3 Laws of Motion

Newton s 3 Laws of Motion Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet 3. F = F 1 on 2 2 on 1 Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of

More information

STEP Support Programme. Mechanics STEP Questions

STEP Support Programme. Mechanics STEP Questions STEP Support Programme Mechanics STEP Questions This is a selection of mainly STEP I questions with a couple of STEP II questions at the end. STEP I and STEP II papers follow the same specification, the

More information

Motion. Argument: (i) Forces are needed to keep things moving, because they stop when the forces are taken away (evidence horse pulling a carriage).

Motion. Argument: (i) Forces are needed to keep things moving, because they stop when the forces are taken away (evidence horse pulling a carriage). 1 Motion Aristotle s Study Aristotle s Law of Motion This law of motion was based on false assumptions. He believed that an object moved only if something was pushing it. His arguments were based on everyday

More information

CHAPTER 4. Impulse and momentum. CHAPTER s Objectives

CHAPTER 4. Impulse and momentum. CHAPTER s Objectives 60 CHAPTER 4 Impulse and momentum CHAPTER s Objectives To understand the interaction between objects through the impulse and momentum concepts To introduce the law o conservation o momentum, and apply

More information

Physics 20 Lesson 18 Pulleys and Systems

Physics 20 Lesson 18 Pulleys and Systems Physics 20 Lesson 18 Pulleys and Systes I. Pulley and syste probles In this lesson we learn about dynaics probles that involve several asses that are connected and accelerating together. Using the pulley

More information

Broward County Schools AP Physics 1 Review

Broward County Schools AP Physics 1 Review Broward County Schools AP Physics 1 Review 1 AP Physics 1 Review 1. The Basics of the Exam Important info: No penalty for guessing. Eliminate one or two choices and then take a shot. Multi-select questions

More information

Chapter 1 about science 1. Differentiate between hypothesis and theory.

Chapter 1 about science 1. Differentiate between hypothesis and theory. Physics A Exam Review Name Hr PHYSICS SCIENTIFIC METHOD FACT HYPOTHESIS LAW THEORY PHYSICAL SCIENCE UNITS VECTOR MAGNITUDE FORCE MECHANICAL EQUILIBRIUM NET FORCE SCALAR RESULTANT TENSION SUPPORT FORCE

More information

Version PREVIEW Semester 1 Review Slade (22222) 1

Version PREVIEW Semester 1 Review Slade (22222) 1 Version PREVIEW Semester 1 Review Slade () 1 This print-out should have 48 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A

More information

Lecture 11. Impulse/Momentum. Conservation of Momentum. Cutnell+Johnson: Impulse and Momentum

Lecture 11. Impulse/Momentum. Conservation of Momentum. Cutnell+Johnson: Impulse and Momentum Lecture 11 Impulse/Momentum Conservation of Momentum Cutnell+Johnson: 7.1-7.3 Impulse and Momentum We learned about work, which is the force times distance (times the cosine of the angle in between the

More information

Physics B Newton s Laws AP Review Packet

Physics B Newton s Laws AP Review Packet Force A force is a push or pull on an object. Forces cause an object to accelerate To speed up To slow down To change direction Unit: Newton (SI system) Newton s First Law The Law of Inertia. A body in

More information

Chapter 6: Work and Kinetic Energy

Chapter 6: Work and Kinetic Energy Chapter 6: Work and Kinetic Energy Suppose you want to find the final velocity of an object being acted on by a variable force. Newton s 2 nd law gives the differential equation (for 1D motion) dv dt =

More information

Preparing for Six Flags Physics Concepts

Preparing for Six Flags Physics Concepts Preparing for Six Flags Physics Concepts uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given

More information

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively.

More information

= v 0 x. / t = 1.75m / s 2.25s = 0.778m / s 2 nd law taking left as positive. net. F x ! F

= v 0 x. / t = 1.75m / s 2.25s = 0.778m / s 2 nd law taking left as positive. net. F x ! F Multiple choice Problem 1 A 5.-N bos sliding on a rough horizontal floor, and the only horizontal force acting on it is friction. You observe that at one instant the bos sliding to the right at 1.75 m/s

More information

Phys 1401: General Physics I

Phys 1401: General Physics I 1. (0 Points) What course is this? a. PHYS 1401 b. PHYS 1402 c. PHYS 2425 d. PHYS 2426 2. (0 Points) Which exam is this? a. Exam 1 b. Exam 2 c. Final Exam 3. (0 Points) What version of the exam is this?

More information

Unit 5 Forces I- Newtonʼ s First & Second Law

Unit 5 Forces I- Newtonʼ s First & Second Law Unit 5 orces I- Newtonʼ s irst & Second Law Unit is the NEWTON(N) Is by definition a push or a pull Does force need a Physical contact? Can exist during physical contact(tension, riction, Applied orce)

More information

Solving Physics Problems

Solving Physics Problems Solving Physics Problems Vectors Characteristic Displacement, velocity, acceleration, forces, momentum, impulse, electric field, magnetic field Break each vector into x and y components Add up x components

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 Work and Energy Midterm exams will be available next Thursday. Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 5 1. On page 162 of Giancoli, problem 4. 2.

More information

Review. Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91

Review. Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91 Review Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91 The unit of work is the A. Newton B. Watt C. Joule D. Meter E. Second 2/91 The unit of work is the A. Newton

More information

Energy present in a variety of forms. Energy can be transformed form one form to another Energy is conserved (isolated system) ENERGY

Energy present in a variety of forms. Energy can be transformed form one form to another Energy is conserved (isolated system) ENERGY ENERGY Energy present in a variety of forms Mechanical energy Chemical energy Nuclear energy Electromagnetic energy Energy can be transformed form one form to another Energy is conserved (isolated system)

More information

Chapter 6 Energy and Oscillations

Chapter 6 Energy and Oscillations Chapter 6 Energy and Oscillations Conservation of Energy In this chapter we will discuss one of the most important and fundamental principles in the universe. Energy is conserved. This means that in any

More information

Newton s Laws of Motion

Newton s Laws of Motion Chapter 4 Newton s Second Law: in vector form Newton s Laws of Motion σ റF = m റa in component form σ F x = ma x σ F y = ma y in equilibrium and static situations a x = 0; a y = 0 Strategy for Solving

More information

Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.

Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?

More information

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At

More information

PHYS 1114, Lecture 33, April 10 Contents:

PHYS 1114, Lecture 33, April 10 Contents: PHYS 1114, Lecture 33, April 10 Contents: 1 This class is o cially cancelled, and has been replaced by the common exam Tuesday, April 11, 5:30 PM. A review and Q&A session is scheduled instead during class

More information

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²)

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²) Practice A car starts from rest and travels upwards along a straight road inclined at an angle of 5 from the horizontal. The length of the road is 450 m and the mass of the car is 800 kg. The speed of

More information

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction. Newton s Laws Newton s first law: An object will stay at rest or in a state of uniform motion with constant velocity, in a straight line, unless acted upon by an external force. In other words, the bodies

More information

PHYS 124 Section A1 Mid-Term Examination Spring 2006 SOLUTIONS

PHYS 124 Section A1 Mid-Term Examination Spring 2006 SOLUTIONS PHYS 14 Section A1 Mid-Term Examination Spring 006 SOLUTIONS Name Student ID Number Instructor Marc de Montigny Date Monday, May 15, 006 Duration 60 minutes Instructions Items allowed: pen or pencil, calculator

More information

Impulse/Momentum And Its Conservation

Impulse/Momentum And Its Conservation Impulse/Momentum And Its Conservation Which is easier to stop? Truck, car, bowling ball, or baseball all moving at 30 mph. Baseball -it is the least massive. Baseball at 30 mph or a baseball at 90 mph.

More information

Scaler Quantity (definition and examples) Average speed. (definition and examples)

Scaler Quantity (definition and examples) Average speed. (definition and examples) Newton s First Law Newton s Second Law Newton s Third Law Vector Quantity Scaler Quantity (definition and examples) Average speed (definition and examples) Instantaneous speed Acceleration An object at

More information

AP PHYSICS 1. Energy 2016 EDITION

AP PHYSICS 1. Energy 2016 EDITION AP PHYSICS 1 Energy 2016 EDITION Copyright 2016 National Math + Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. 1 Pre-Assessment Questions Consider a system which could

More information

Circular Motion.

Circular Motion. 1 Circular Motion www.njctl.org 2 Topics of Uniform Circular Motion (UCM) Kinematics of UCM Click on the topic to go to that section Period, Frequency, and Rotational Velocity Dynamics of UCM Vertical

More information

Unit 1: Mechanical Equilibrium

Unit 1: Mechanical Equilibrium Unit 1: Mechanical Equilibrium Chapter: Two Mechanical Equilibrium Big Idea / Key Concepts Student Outcomes 2.1: Force 2.2: Mechanical Equilibrium 2.3: Support Force 2.4: Equilibrium for Moving Objects

More information

Chapter 4. Dynamics: Newton s Laws of Motion. That is, describing why objects move

Chapter 4. Dynamics: Newton s Laws of Motion. That is, describing why objects move Chapter 4 Dynamics: Newton s Laws of Motion That is, describing why objects move orces Newton s 1 st Law Newton s 2 nd Law Newton s 3 rd Law Examples of orces: Weight, Normal orce, Tension, riction ree-body

More information

Name (please print): UW ID# score last first

Name (please print): UW ID# score last first Name (please print): UW ID# score last first Question I. (20 pts) Projectile motion A ball of mass 0.3 kg is thrown at an angle of 30 o above the horizontal. Ignore air resistance. It hits the ground 100

More information

Dynamics: Forces. Lecture 7. Chapter 5. Course website:

Dynamics: Forces. Lecture 7. Chapter 5. Course website: Lecture 7 Chapter 5 Dynamics: Forces Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Today we are going to discuss: Chapter 5: Some leftovers from rotational motion Ch.4 Force,

More information

General Physics I Spring Forces and Newton s Laws of Motion

General Physics I Spring Forces and Newton s Laws of Motion General Physics I Spring 2011 Forces and Newton s Laws of Motion 1 Forces and Interactions The central concept in understanding why things move is force. If a tractor pushes or pulls a trailer, the tractor

More information

Physics 5A Final Review Solutions

Physics 5A Final Review Solutions Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone

More information

Review for 3 rd Midterm

Review for 3 rd Midterm Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The moment-of-inertia about the center-of-mass

More information

Work and Energy. Chapter 7

Work and Energy. Chapter 7 Work and Energy Chapter 7 Scalar Product of Two Vectors Definition of the scalar, or dot, product: A B A Alternatively, we can write: x B x A y B y A z B z Work Work Done by a Constant Force The work done

More information

11th Grade. Review for General Exam-3. decreases. smaller than. remains the same

11th Grade. Review for General Exam-3. decreases. smaller than. remains the same 1. An object is thrown horizontally with a speed of v from point M and hits point E on the vertical wall after t seconds as shown in the figure. (Ignore air friction.). Two objects M and S are thrown as

More information

ConcepTest PowerPoints

ConcepTest PowerPoints ConcepTest PowerPoints Chapter 6 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

Which iceboat crosses the finish line with more kinetic energy (KE)?

Which iceboat crosses the finish line with more kinetic energy (KE)? Two iceboats (one of mass m, one of mass 2m) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Which iceboat

More information

Concepts in Physics. Friday, October 16th

Concepts in Physics. Friday, October 16th 1206 - Concepts in Physics Friday, October 16th Notes Assignment #4 due Wednesday, October 21 st in class (no later than noon) There are still assignments #1 and #2 in my office to be picked up... If you

More information

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm!

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm! Wiley Plus Final Assignment (5) Is Due Today: Before 11 pm! Final Exam Review December 9, 009 3 What about vector subtraction? Suppose you are given the vector relation A B C RULE: The resultant vector

More information

Momentum & Energy Review Checklist

Momentum & Energy Review Checklist Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at

More information

Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)

Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction) Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position

More information

Lecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws

Lecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,

More information

Dynamics Review Checklist

Dynamics Review Checklist Dynamics Review Checklist Newton s Laws 2.1.1 Explain Newton s 1 st Law (the Law of Inertia) and the relationship between mass and inertia. Which of the following has the greatest amount of inertia? (a)

More information

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits?

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits? Name Period Date Honor Physics Final Exam Review Circuits You should be able to: Calculate the total (net) resistance of a circuit. Calculate current in individual resistors and the total circuit current.

More information

Physics 231. Topic 5: Energy and Work. Alex Brown October 2, MSU Physics 231 Fall

Physics 231. Topic 5: Energy and Work. Alex Brown October 2, MSU Physics 231 Fall Physics 231 Topic 5: Energy and Work Alex Brown October 2, 2015 MSU Physics 231 Fall 2015 1 What s up? (Friday Sept 26) 1) The correction exam is now open. The exam grades will be sent out after that on

More information

Physics 111. Lecture 18 (Walker: 8.3-4) Energy Conservation I March 11, Conservation of Mechanical Energy

Physics 111. Lecture 18 (Walker: 8.3-4) Energy Conservation I March 11, Conservation of Mechanical Energy Physics 111 Lecture 18 (Walker: 8.3-4) Energy Conservation I March 11, 2009 Lecture 18 1/24 Conservation o Mechanical Energy Deinition o mechanical energy: (8-6) I the only work done in going rom the initial

More information

Lecture 2 - Force Analysis

Lecture 2 - Force Analysis Lecture 2 - orce Analysis A Puzzle... Triangle or quadrilateral? 4 distinct points in a plane can either be arrange as a triangle with a point inside or as a quadrilateral. Extra Brownie Points: Use the

More information

Multiple-Choice Answer Key

Multiple-Choice Answer Key Multiple-Choice Answer Key The following contains the answers to the multiple-choice questions in this exam. Answer Key for AP Physics 1 Practice Exam, Section I Question 1: C Question : A Question 3:

More information

Ground Rules. PC1221 Fundamentals of Physics I. Introduction to Energy. Energy Approach to Problems. Lectures 13 and 14. Energy and Energy Transfer

Ground Rules. PC1221 Fundamentals of Physics I. Introduction to Energy. Energy Approach to Problems. Lectures 13 and 14. Energy and Energy Transfer PC1221 Fundamentals o Physics I Lectures 13 and 14 Energy and Energy Transer Dr Tay Seng Chuan 1 Ground Rules Switch o your handphone and pager Switch o your laptop computer and keep it No talking while

More information

Module 17: Systems, Conservation of Momentum and Center of Mass

Module 17: Systems, Conservation of Momentum and Center of Mass Module 17: Systems, Conservation of Momentum and Center of Mass 17.1 External and Internal Forces and the Change in Momentum of a System So far we have restricted ourselves to considering how the momentum

More information

Class 11 Physics NCERT Exemplar Solutions Motion in a Straight Line

Class 11 Physics NCERT Exemplar Solutions Motion in a Straight Line Class 11 Physics NCERT Exemplar Solutions Motion in a Straight Line Multiple Choice Questions Single Correct Answer Type Q1. Among the four graphs shown in the figure, there is only one graph for which

More information

Mechanics 2. Revision Notes

Mechanics 2. Revision Notes Mechanics 2 Revision Notes October 2016 2 M2 OCTOER 2016 SD Mechanics 2 1 Kinematics 3 Constant acceleration in a vertical plane... 3 Variable acceleration... 5 Using vectors... 6 2 Centres of mass 7 Centre

More information

Example force problems

Example force problems PH 105 / LeClair Fall 2015 Example force problems 1. An advertisement claims that a particular automobile can stop on a dime. What net force would actually be necessary to stop a 850 kg automobile traveling

More information

PHYSICS 231 INTRODUCTORY PHYSICS I

PHYSICS 231 INTRODUCTORY PHYSICS I PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 6 Last Lecture: Gravity Normal forces Strings, ropes and Pulleys Today: Friction Work and Kinetic Energy Potential Energy Conservation of Energy Frictional Forces

More information

Kinematics and Dynamics

Kinematics and Dynamics AP PHYS 1 Test Review Kinematics and Dynamics Name: Other Useful Site: http://www.aplusphysics.com/ap1/ap1- supp.html 2015-16 AP Physics: Kinematics Study Guide The study guide will help you review all

More information

PH 2213 : Chapter 05 Homework Solutions

PH 2213 : Chapter 05 Homework Solutions PH 2213 : Chapter 05 Homework Solutions Problem 5.4 : The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave

More information

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam #2, Chapters 5-7 Name PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The quantity 1/2 mv2 is A) the potential energy of the object.

More information

Physics for Scientists and Engineers 4th Edition, 2017

Physics for Scientists and Engineers 4th Edition, 2017 A Correlation of Physics for Scientists and Engineers 4th Edition, 2017 To the AP Physics C: Mechanics Course Descriptions AP is a trademark registered and/or owned by the College Board, which was not

More information

Tutorial 1 Calculating the Kinetic Energy of a Moving Object

Tutorial 1 Calculating the Kinetic Energy of a Moving Object 5. Energy As you learned in Section 5.1, mechanical work is done by applying orces on objects and displacing them. How are people, machines, and Earth able to do mechanical work? The answer is energy:

More information

Unit 2: Vector Dynamics

Unit 2: Vector Dynamics Multiple Choice Portion Unit 2: Vector Dynamics 1. Which one of the following best describes the motion of a projectile close to the surface of the Earth? (Assume no friction) Vertical Acceleration Horizontal

More information

Physics 1 Second Midterm Exam (AM) 2/25/2010

Physics 1 Second Midterm Exam (AM) 2/25/2010 Physics Second Midterm Eam (AM) /5/00. (This problem is worth 40 points.) A roller coaster car of m travels around a vertical loop of radius R. There is no friction and no air resistance. At the top of

More information