Particle dynamics Physics 1A, UNSW

Size: px
Start display at page:

Download "Particle dynamics Physics 1A, UNSW"

Transcription

1 1 Particle dynaics Physics 1A, UNSW Newton's laws: S & J: Ch , 6.1 force, ass, acceleration also weight Physclips Chapter 5 Friction - coefficients of friction Physclips Chapter 6 Hooke's Law Dynaics of circular otion Question. Top view of ball. What is its trajectory after it leaves the race? e d c b a? then what? Aristotle: v_ = 0 is "natural" state (not in syllabus) Galileo & Newton: a_ = 0 is "natural" state Galileo: what if we reove the side of the bowl? Newton's Laws First law "zero (total) force zero acceleration" (It's actually a bit ore subtle. More forally, we should say: If Σ F_ = 0, there exist reference fraes in which a_ = 0 called Inertial fraes What is an inertial frae? One in which Newton's laws are true. observation: w.r.t. these fraes, distant stars don't accelerate Experient in the foyer

2 2 In inertial fraes: Second law Σ F_ = a_ Σ is iportant: it is the total force that deterines acceleration Σ F x = a x Σ F y = a y Σ F z = a z 3D > 3 equations 1st law is special case of 2nd What does the 2nd law ean? Σ F_ = i a_ and W_ = g g_ are i and g necessarily the sae? called inertial and gravitational asses F_ = a_ a_ is already defined, but this leaves us with a puzzle: i) Does this equation define? ii) Does this law define F_? iii) iv) v) How? Is it a physical law? All of the above? i) Given one ass, we could calibrate any forces by easuring the a they produced. ii) iii) Siilarly, for any one F, we could calibrate any 's by the accelerations produced The 2nd Law is the observation that the 's and F's thus defined are consistent. eg Having used standard to calibrate F, now produce 2F (eg two identical F systes). Is a now doubled? Every such experient is a test of Newton's second law. Or, for those who want it logically: NeNewton 1: "Every body persists in its state of rest or of unifor otion in a straight line unless it is copelled to change that state by forces ipressed on it." postulate An inertial frae of reference is one in which Newton's 1st law is true. Such fraes exist (and with respect to these fraes, distant stars don't accelerate) if Σ F = 0, _a = 0 w.r.t. distant stars. Force causes acceleration. F // a, F a definition observation: definition

3 3 Another way of writing Newton 2: To any body ay be ascribed a (scalar) constant, ass, such that the acceleration produced in two bodies by a given force is inversely proportional to their asses, i.e. for sae F, 2 1 = a 1 a 2 We already have etre, second, choose a standard body for kg, then choose units of F (Newtons) such that Σ F = a Newton's first and second laws (this eqn. is laws 1&2, definition of ass and units of force) So, how big are Newtons? Newton 3: "To every action there is always opposed an equal reaction; or the utual actions of two bodies upon each other are always equal and directed to contrary parts" Or Forces always occur in pairs, F and F, one acting on each of a pair of interacting bodies. Third law F AB = F BA Why so? What would it be like if internal forces didn t add to zero? Iportant conclusion: internal forces in a syste add to zero. So we can now write the 1st and 2nd laws: Σ F external = a Total external force = a

4 4 Exaple Where is centre of earth-oon orbit? F e = F = F g equal & opposite each akes a circle about coon centre of ass F g = a = ω 2 r F g = e a e = e ω 2 r e NB sign conventions r r e = e = kg kg = 81.3 (i) earth-oon distance r e + r = (ii) (two equations, two unknowns) r e ( ) = gives r = , r e = = 4700 k centre of both orbits is inside earth (later we'll see that it is the centre of ass of the two)

5 5 Using Newton's laws How do we use the to solve probles? Newton's 2nd ΣF = a the Σ is iportant: in principle, we have to consider the all. Newton's 3rd (forces coe in pairs, F and F), so: internal forces add to zero. They don't affect otion Therefore, applying Newton's 2nd, we use ΣF external = a draw diagras ('free body diagras') to show only the external forces on the body of interest Newton's second law is a vector equation write coponents of Newton's second law in 2 (or 3) directions Exaple. As the bus takes a steady turn with radius 8 at constant speed, you notice that a ass on a string hangs at 30 to the vertical. How fast is the bus going? Draw a diagra with physics string 30 T a T W W The ass (and the bus) are in circular otion, so we can apply Newton 2: F = a = v2 horiz r Only the tension has a horizontal coponent, so (the acceleration is centripetal) T sin 30 = v2 r (i) Need one ore eqn: ass is not falling down, ie vertical acceleration = 0, so T cos 30 = g (ii) Again, we have two equations in two unknowns Dived (i) by (ii) to eliinate T: tan 30 = v2 r 1 g > v = gr tan 30 = 6.7 /s > 20 kph. Don t stop yet! First, check the diensions. Reasonable? Suggestions? Probles? which we rearrange to give

6 6 Proble. Horse and cart. Wheels roll freely. Let's go! Why should I pull? The force of the cart on e equals y force on it, but opposes it. Σ F = 0. We'll never accelerate. What would you say to the horse? F c F c F c F c F g F g This is a good exercise in looking at the external forces Horizontal forces on cart (ass c ) F c Horizontal forces on horse (ass h ) F c = c a c = c a F c Horizontal forces on Earth (ass E ) F g F g F c = h a F g E >> h + c In principle, the earth accelerates to the left. But E >> h so a E << a h

7 7 "light" ropes etc. Here, light eans << other asses Truck ( t ) pulls wagon ( w ) with rope ( r ). All have sae a_. i) wagon: F 2 = w a. Let's apply Newton's second to each eleent: ii) iii) rope: F 1 - F 2 = r a truck: F 1 + F ext = t a (ii)/(i) > F 1 F 2 F 2 = ra w a if r << w, F 1 = F 2. iportant result: Forces at opposite ends of light ropes etc are equal and opposite. Again, see Physclips if this isn't clear Tension. When the ass of a string, coupling etc is negligible, forces at opposite ends are equal and opposite and we call this the tension in the string.

8 8 Exaple. (one diensional otion only) Consider a train. Wheels roll freely. Locootive exerts horizontal force F on the track. What are the tensions T 1 and T 2 in the two couplings? car 2 T car 1 2 T 1 Whole train accelerates together with a. F loco Look at the external forces acting on the train (horiz. only). F F F = (++)a > a = F/3 Look at external horiz forces on car 2: T 2 T 2 = a = F/3 and on cars 2 and 1 together T 1 T 1 = 2a Newton's 3rd: A question for you: How does floor "know" to exert N = W = g?

9 9 Hookes law Fro Physclips Ch 6.3 No applied force (x = 0) Under tension x > 0 Note that _F spring is in the opposite direction to x. Experientally (see Physclips exaple above), _F s x over sall range of x F = kx Hooke's Law. linear elastic behaviour - ore in S2. Linear approxiations are v. useful!

10 10 Why is linear elasticity so coon? Consider the interolecular forces F and energies U and separate into attractive and repulsive coponents: See hoework proble on interatoic forces We'll do energy later, and we'll see:

11 11 Mass and weight (inertial) ass defined by F = a observation: near earth's surface and without air, all bodies fall with sae a ( = g) weight W = g What is your weight? (so far. This is still subject to experiental test!) Warning: do not confuse ass and weight, or their units kg > ass N > force (kg..s -2 ) kg wt = weight of 1 kg = g = 9.8 N Why is W? Why is g i? a = F = W = (Grav field).(grav. property of body) Mach's Principle not in our syllabus Principle of General Relativity, but v. interesting questions Interactions with vacuu field,

12 Exaple Grav. field on oon g = 1.7 s -2. An astronaut weighs 800 N on Earth, and, while juping, exerts 2kN while body oves 0.3. What is his weight on oon? How high does he jup on earth and on oon? g E = W E > = 800 N 9.8 s-2 = 82 kg W = g = 82kg 1.7s -2 = 140 N Vertical (y) otion with constant acceleration. While feet are on ground, Σ F = 2 kn - W E = 1.2 kn (Earth) Moon: Σ F = 2 kn - g = 1.9 kn 12 Jup has two parts: feet on ground a = Σ F v i = 0, v f = v j feet off ground a = - g v i = v j, v f = 0 v y v j y h Δ y feet leave ground y easure y of centre of ass. While on ground: v j 2 v o 2 = 2a j Δy = 2 Σ F Earth > v j = 3.0 s 1 Δy Moon > v j = 3.7 s 1 While above ground: v 2 v j 2 = 2gh > h = v j 2 2g h E = 0.5. h = 4

13 13 Exaple (an iportant proble) Light pulley, light inextensible string. What are the accelerations of the asses? A nuber of different conventions are possible. The iportant thing is to define yours carefully and use it consistently. Let a be acceleration (down) of 1 = acceleration (up) of 2. Take up as positive, look at the free body diagra for 1 : we are only interested in the vertical direction. By assuption, the acceleration is down. T is up. 1 g is down. So Newton 2 for 1 gives: And Newton 2 for 2 : subtract: T 1 g = 1 a T 2 g = + 2 a 1 g + 2 g = 1 a 2 a a = g (Check: if 1 = 2, a = 0. If 2 = 0, a = g.) Alternatively, we ight have said a 1 be the acceleration up of 1 and a 2 be the acceleration of 2. Inextensible string so a 1 = a 2. etc.

14 14 Contact forces N F contact The noral coponent of a contact force is called the noral force N. The coponent in the plane of contact is called the friction force F f. F friction Noral force: at right angles to surface, is provided by deforation. If there is relative otion, kinetic friction (whose direction opposes relative otion) If there is no relative otion, static friction (whose direction opposes applied force) See the experient on Physclips Ch 6.5 Define coefficients of kinetic (k) and static (s) friction: F f = µ k N F f µ s N n.b.: Friction follows this approxiate epirical law µ and µ are approx. independent of N and of contact area. s k Often µ < µ. k s (It takes less force to keep sliding than to start sliding.)

15 15. Exaple. θ is gradually increased to θ c when sliding begins. What is θ c? What is a at θ c? (as before, free body diagra, N2:) Newton 2 in noral direction: N - g cos θ = 0 Newton 2 in direction down plane: g sin θ F f = a. (i) (ii) No sliding: a = 0 so total force is zero. (ii) g sin θ = F f µ s N (i) = µ s g cosθ g sin θ µ s g cosθ tan θ µ s, θ c = tan 1 µ s useful technique for µ s Sliding at θ = θ c : a > 0 (ii) a = g sin θ c F f = g sin θ c µ kn (i) = g sin θ c µ k g cosθ c we had θ c = tan 1 µ s so a = g cosθ c (µ s µ k )

16 16 Exaple. Rear wheel drive car, 3 kn weight on each front wheel, 2 kn on rear. Rubber-road: µ s = 1.5, µ k = 1.1 (ass of car)*g = weight = 2(3 kn + 2 kn) = 10 kn = 1 tonne Neglect rotation of car during accelerations. Assue that brakes produce 1.8 ties as uch force on front wheels as on back (why? Look at brake discs and pads). (i) What is ax forward acceleration without skidding? What is axiu deceleration for (ii) not skidding? (iii) 4 wheel skid? (i) F frs µ s N R = µ s W R on each rear wheel a ax = F = 1.5x2 kn = 2.9 kn on each rear wheel = 2*2.9kN = 5.8 s kg Stopping. For all wheels, F fs µ s N = µ s W F ff = 1.8 F fr. µ s W F = 1.5 µ s W R, front wheels skid first, when F ff > µ s W F. 2 front and 2 rear wheels. ax total friction = (front + rear) = µ sw F (brakes -> 1.8 ties as uch force on front wheels) ii) iii) = 1400 kg.wt = 14 kn a ax = F ax a = Σ F k = Σ µ kw = 14 kn 1000 kg = 14 s-2 =... = 11 s -2 Questions: Does area of rubber-road contact ake a difference? Does the size of the tire ake a difference?

17 17 Centripetal acceleration and force Circular otion with ω = const. and v const. eg bus going round a corner F = a centrip Or consider a haer thrower T resultant W Resultant force produces acceleration in the horizontal direction, towards the centre of the otion Centripetal force, centripetal acceleration

18 18 Exaple Conical pendulu. (Unifor circular otion.) What is the frequency? Free body diagra Apply Newton 2 in two directions: Vertical: a y = 0 Σ F y = 0 T cos θ W = 0 T = Horizontal: v 2 r v 2 r g cos θ = a c = T sin θ = g tan θ v = rg tan θ 2π r period = = rg tan θ g sin θ cos θ f = 1 period = 1 2π g tan θ r

19 19 Exaple. Foolhardy lecturer swings a bucket of bricks in a vertical circle. How fast should he swing so that the bricks stay in contact with the bucket at the top of the trajectory? r Draw diagra & identify iportant variables pose question atheatically. N W a centrip W and N provide centripetal force. g + N = a c For contact, we need N 0 so a c g how to express a c? a c = v2 r = rω 2 = r 2π T 2 T is easy to easure T = 2π r a c 2π r g r ~ 1 > T 2 s.

20 20 Exaple. (1,3) > stationary if F cos θ µ s N F cos θ µ s (g + F sin θ) (using (2)) F (cos θ µ s sin θ) µ s g (*) note iportance (cos θ µ s sin θ) Apply force F at θ to horizontal. Mass on floor, coefficients µ s and µ k. For any given θ, what F is required to ake the ass ove? Eliinate 2 unknowns N and F f > F(θ, µ s,,g) Stationary if F f µ s N (1) Newton 2 vertical: N = g + F sin θ (2) Newton 2 horizontal: F cos θ = F f (3) if (cos θ µ s sin θ) = 0, (F very large) θ = θ crit = tan 1 (1/µ s ). If θ < θ c, then (cos θ µ s sin θ) > 0 stationary if F i.e. oves when F > F crit = What if (cos θ µ s sin θ) = 0? θ = θ c,? µ s g cos θ µ s sin θ µ s g cos θ µ s sin θ (*) stationary if F µ s g cos θ µ s sin θ i.e. stationary no atter how large F becoes.

21 21

22 22 Exaple Plane travels in horizontal circle, speed v, radius r. For given v, what is the r for which the noral force exerted by the plane on the pilot = twice her weight? What is the direction of this force? Centripetal force F = v2 r = N cos θ Vertical forces: N sin θ = g eliinate θ: N 2 = 2 v4 r 2 + g2 N 2 2 g2 = v4 r 2 > r = v 2 N 2 2 g2 sin θ = g N = above horizontal, towards axis of rotation Question. Three identical bricks. What is the iniu force you ust apply to hold the still like this? N F f F f N g Vertical forces on iddle brick add to zero: 2 Ff = g Definition of µs Ff µs N N F f µs = g 2µs Bricks not accelerating horizontally, so noral force fro hands = noral force between bricks. (each) hand ust provide g 2µs horizontally. Vertically, two hands together provide 3g. 3g/2 iniu force fro hands g/2µ s

Physics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10

Physics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10 There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference

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

For a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ).

For a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ). Reading: Energy 1, 2. Key concepts: Scalar products, work, kinetic energy, work-energy theore; potential energy, total energy, conservation of echanical energy, equilibriu and turning points. 1.! In 1-D

More information

XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com

XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.co https://prootephysics.wordpress.co [MOTION] CHAPTER NO. 3 In this chapter we are going to discuss otion in one diension in which we

More information

Chapter 5, Conceptual Questions

Chapter 5, Conceptual Questions Chapter 5, Conceptual Questions 5.1. Two forces are present, tension T in the cable and gravitational force 5.. F G as seen in the figure. Four forces act on the block: the push of the spring F, sp gravitational

More information

F = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4.

F = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4. PHYSICS 151 Notes for Online Lecture.4 Springs, Strings, Pulleys, and Connected Objects Hook s Law F = 0 F = -k x 1 x = 0 x = x 1 Let s start with a horizontal spring, resting on a frictionless table.

More information

PHYSICS - CLUTCH CH 05: FRICTION, INCLINES, SYSTEMS.

PHYSICS - CLUTCH CH 05: FRICTION, INCLINES, SYSTEMS. !! www.clutchprep.co INTRO TO FRICTION Friction happens when two surfaces are in contact f = μ =. KINETIC FRICTION (v 0 *): STATIC FRICTION (v 0 *): - Happens when ANY object slides/skids/slips. * = Point

More information

3. In the figure below, the coefficient of friction between the center mass and the surface is

3. In the figure below, the coefficient of friction between the center mass and the surface is Physics 04A Exa October 9, 05 Short-answer probles: Do any seven probles in your exa book. Start each proble on a new page and and clearly indicate the proble nuber for each. If you attept ore than seven

More information

Lecture #8-3 Oscillations, Simple Harmonic Motion

Lecture #8-3 Oscillations, Simple Harmonic Motion Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.

More information

Question 1. [14 Marks]

Question 1. [14 Marks] 6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is

More information

Chapter 11 Simple Harmonic Motion

Chapter 11 Simple Harmonic Motion Chapter 11 Siple Haronic Motion "We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances." Isaac Newton 11.1 Introduction to Periodic Motion

More information

Q5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!

Q5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2! Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In

More information

For more Study Material and Latest Questions related to IIT-JEE visit

For more Study Material and Latest Questions related to IIT-JEE visit or ore Study Material and Latest Questions related to IIT-JEE visit www. ICTION Introduction If we slide or try to slide a body over a surface, the otion is resisted by a bonding between the body and the

More information

1. The property of matter that causes an object to resist changes in its state of motion is called:

1. The property of matter that causes an object to resist changes in its state of motion is called: SPH3U Exa Review 1. The property of atter that causes an object to resist changes in its state of otion is called: A. friction B. inertia C. the noral force D. tension 1. The property of atter that causes

More information

Chapter 3 Dynamics: Motion and Force 3.1 Newton's 2nd Law-1D Acceleration-Horizontal Motion Homework # 19

Chapter 3 Dynamics: Motion and Force 3.1 Newton's 2nd Law-1D Acceleration-Horizontal Motion Homework # 19 3.1 Newton's 2nd Law-1D Acceleration-Horizontal Motion Hoework # 19 01. A net force of 185.0 N is acting on a 25.0 kg object initially at rest. a.) What is the acceleration of the object? b.) What is the

More information

In the session you will be divided into groups and perform four separate experiments:

In the session you will be divided into groups and perform four separate experiments: Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track

More information

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40% NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity

More information

Systems of Masses. 1. Ignoring friction, calculate the acceleration of the system below and the tension in the rope. and (4.0)(9.80) 39.

Systems of Masses. 1. Ignoring friction, calculate the acceleration of the system below and the tension in the rope. and (4.0)(9.80) 39. Systes of Masses. Ignoring friction, calculate the acceleration of the syste below and the tension in the rope. Drawing individual free body diagras we get 4.0kg 7.0kg g 9.80 / s a?? g and g (4.0)(9.80)

More information

Honors Lab 4.5 Freefall, Apparent Weight, and Friction

Honors Lab 4.5 Freefall, Apparent Weight, and Friction Nae School Date Honors Lab 4.5 Freefall, Apparent Weight, and Friction Purpose To investigate the vector nature of forces To practice the use free-body diagras (FBDs) To learn to apply Newton s Second

More information

Uniform Circular Motion. Uniform Circular Motion

Uniform Circular Motion. Uniform Circular Motion Uniform Circular Motion Uniform Circular Motion Uniform Circular Motion An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion. Question: Why is uniform

More information

Name Period. What force did your partner s exert on yours? Write your answer in the blank below:

Name Period. What force did your partner s exert on yours? Write your answer in the blank below: Nae Period Lesson 7: Newton s Third Law and Passive Forces 7.1 Experient: Newton s 3 rd Law Forces of Interaction (a) Tea up with a partner to hook two spring scales together to perfor the next experient:

More information

Tutorial Exercises: Incorporating constraints

Tutorial Exercises: Incorporating constraints Tutorial Exercises: Incorporating constraints 1. A siple pendulu of length l ass is suspended fro a pivot of ass M that is free to slide on a frictionless wire frae in the shape of a parabola y = ax. The

More information

NB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016

NB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016 NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,

More information

15 Newton s Laws #2: Kinds of Forces, Creating Free Body Diagrams

15 Newton s Laws #2: Kinds of Forces, Creating Free Body Diagrams Chapter 15 ewton s Laws #2: inds of s, Creating ree Body Diagras 15 ewton s Laws #2: inds of s, Creating ree Body Diagras re is no force of otion acting on an object. Once you have the force or forces

More information

24/06/13 Forces ( F.Robilliard) 1

24/06/13 Forces ( F.Robilliard) 1 R Fr F W 24/06/13 Forces ( F.Robilliard) 1 Mass: So far, in our studies of mechanics, we have considered the motion of idealised particles moving geometrically through space. Why a particular particle

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 1

Physics 12. Unit 5 Circular Motion and Gravitation Part 1 Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting

More information

Dynamics II Motion in a Plane. Review Problems

Dynamics II Motion in a Plane. Review Problems Dynamics II Motion in a Plane Review Problems Problem 1 A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N thrust

More information

Isaac Newton ( )

Isaac Newton ( ) Isaac Newton (1642-1727) In the beginning of 1665 I found the rule for reducing any degree of binomial to a series. The same year in May I found the method of tangents and in November the method of fluxions

More information

BALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass

BALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass BALLISTIC PENDULUM INTRODUCTION: In this experient you will use the principles of conservation of oentu and energy to deterine the speed of a horizontally projected ball and use this speed to predict the

More information

Phys101 Second Major-162 Zero Version Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: 1

Phys101 Second Major-162 Zero Version Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: 1 Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: 1 Q1. Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 20 N, acting due east, and the other

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

Lecture 10. Example: Friction and Motion

Lecture 10. Example: Friction and Motion Lecture 10 Goals: Exploit Newton s 3 rd Law in problems with friction Employ Newton s Laws in 2D problems with circular motion Assignment: HW5, (Chapter 7, due 2/24, Wednesday) For Tuesday: Finish reading

More information

BIT1002 Newton's Laws. By the end of this you should understand

BIT1002 Newton's Laws. By the end of this you should understand BIT1002 Newton's Laws By the end of this you should understand Galileo's Law of inertia/newton's First Law What is an Inertial Frame The Connection between force and Acceleration: F=ma 4. The Third Law

More information

Solved Problems. 3.3 The object in Fig. 3-1(a) weighs 50 N and is supported by a cord. Find the tension in the cord.

Solved Problems. 3.3 The object in Fig. 3-1(a) weighs 50 N and is supported by a cord. Find the tension in the cord. 30 NEWTON'S LAWS [CHAP. 3 Solved Problems 3.1 Find the weight on Earth of a body whose mass is (a) 3.00 kg, (b) 200 g. The general relation between mass m and weight F W is F W ˆ mg. In this relation,

More information

2.003 Engineering Dynamics Problem Set 2 Solutions

2.003 Engineering Dynamics Problem Set 2 Solutions .003 Engineering Dynaics Proble Set Solutions This proble set is priarily eant to give the student practice in describing otion. This is the subject of kineatics. It is strongly recoended that you study

More information

Phys101 Second Major-162 Zero Version Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: N Ans:

Phys101 Second Major-162 Zero Version Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: N Ans: Coordinator: Dr. Kunwar S. Saturday, March 25, 2017 Page: 1 Q1. Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 20 N, acting due east, and the other

More information

= 1.49 m/s m. 2 kg. 2 kg

= 1.49 m/s m. 2 kg. 2 kg 5.6. Visualize: Please refer to Figure Ex5.6. Solve: For the diagra on the left, three of the vectors lie along the axes of the tilted coordinate sste. Notice that the angle between the 3 N force and the

More information

HSC PHYSICS ONLINE B F BA. repulsion between two negatively charged objects. attraction between a negative charge and a positive charge

HSC PHYSICS ONLINE B F BA. repulsion between two negatively charged objects. attraction between a negative charge and a positive charge HSC PHYSICS ONLINE DYNAMICS TYPES O ORCES Electrostatic force (force mediated by a field - long range: action at a distance) the attractive or repulsion between two stationary charged objects. AB A B BA

More information

Newton s Laws.

Newton s Laws. Newton s Laws http://mathsforeurope.digibel.be/images Forces and Equilibrium If the net force on a body is zero, it is in equilibrium. dynamic equilibrium: moving relative to us static equilibrium: appears

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter Exercises For all these exercises, assume that all strings are massless and all pulleys are both massless and frictionless. We will improve our model and learn how to account for the mass

More information

Study Questions/Problems Week 4

Study Questions/Problems Week 4 Study Questions/Problems Week 4 Chapter 6 treats many topics. I have selected on average less than three problems from each topic. I suggest you do them all. Likewise for the Conceptual Questions and exercises,

More information

Lesson 27 Conservation of Energy

Lesson 27 Conservation of Energy Physics 0 Lesson 7 Conservation o nergy In this lesson we will learn about one o the ost powerul tools or solving physics probles utilizing the Law o Conservation o nergy. I. Law o Conservation o nergy

More information

Tactics Box 2.1 Interpreting Position-versus-Time Graphs

Tactics Box 2.1 Interpreting Position-versus-Time Graphs 1D kineatic Retake Assignent Due: 4:32p on Friday, October 31, 2014 You will receive no credit for ites you coplete after the assignent is due. Grading Policy Tactics Box 2.1 Interpreting Position-versus-Tie

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics Physics 115.3 MIDTERM TEST October 22, 2008 Tie: 90 inutes NAME: (Last) Please Print (Given) STUDENT NO.: LECTURE SECTION (please

More information

Name Class Date. two objects depends on the masses of the objects.

Name Class Date. two objects depends on the masses of the objects. CHAPTER 12 2 Gravity SECTION Forces KEY IDEAS As you read this section keep these questions in ind: What is free fall? How are weight and ass related? How does gravity affect the otion of objects? What

More information

Lecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful

Lecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful Conseration Laws: The Most Powerful Laws of Physics Potential Energy gh Moentu p = + +. Energy E = PE + KE +. Kinetic Energy / Announceents Mon., Sept. : Second Law of Therodynaics Gie out Hoework 4 Wed.,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You are standing in a moving bus, facing forward, and you suddenly fall forward as the

More information

Lesson 24: Newton's Second Law (Motion)

Lesson 24: Newton's Second Law (Motion) Lesson 24: Newton's Second Law (Motion) To really appreciate Newton s Laws, it soeties helps to see how they build on each other. The First Law describes what will happen if there is no net force. The

More information

8.1 Force Laws Hooke s Law

8.1 Force Laws Hooke s Law 8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which

More information

Elastic Force: A Force Balance: Elastic & Gravitational Force: Force Example: Determining Spring Constant. Some Other Forces

Elastic Force: A Force Balance: Elastic & Gravitational Force: Force Example: Determining Spring Constant. Some Other Forces Energy Balance, Units & Proble Solving: Mechanical Energy Balance ABET Course Outcoes: 1. solve and docuent the solution of probles involving eleents or configurations not previously encountered (e) (e.g.

More information

Linear vs. Rotational Motion

Linear vs. Rotational Motion Linear vs. Rotational Motion Every term in a linear equation has a similar term in the analogous rotational equation. Displacements: s = r θ v t ω Speeds: v t = ω r Accelerations: a t = α r Every point

More information

Definition of Work, The basics

Definition of Work, The basics Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define

More information

Lecture 5. Dynamics. Forces: Newton s First and Second

Lecture 5. Dynamics. Forces: Newton s First and Second Lecture 5 Dynamics. Forces: Newton s First and Second What is a force? It s a pull or a push: F F Force is a quantitative description of the interaction between two physical bodies that causes them to

More information

EN40: Dynamics and Vibrations. Midterm Examination Tuesday March

EN40: Dynamics and Vibrations. Midterm Examination Tuesday March EN4: Dynaics and ibrations Midter Exaination Tuesday Marc 4 14 Scool of Engineering Brown University NAME: General Instructions No collaboration of any kind is peritted on tis exaination. You ay bring

More information

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision Physics 131: Lecture 16 Today s Agenda Elastic Collisions Definition Exaples Work and Energy Definition of work Exaples Physics 01: Lecture 10, Pg 1 Collisions Moentu is alost always consered during as

More information

OSCILLATIONS AND WAVES

OSCILLATIONS AND WAVES OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in

More information

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant Force varies with tie 7. The Ipulse-Moentu Theore DEFINITION

More information

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B.

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B. 2003 B1. (15 points) A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown above. One end of the rope is held by Student A of mass 70 kg, who is at rest on

More information

Physics 8 Wednesday, October 11, 2017

Physics 8 Wednesday, October 11, 2017 Physics 8 Wednesday, October 11, 2017 HW5 due Friday. It s really Friday this week! Homework study/help sessions (optional): Bill will be in DRL 2C6 Wednesdays from 4 6pm (today). Grace will be in DRL

More information

SRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES

SRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet

More information

Work, Energy and Momentum

Work, Energy and Momentum Work, Energy and Moentu Work: When a body oves a distance d along straight line, while acted on by a constant force of agnitude F in the sae direction as the otion, the work done by the force is tered

More information

Physics 204A FINAL EXAM Chapters 1-14 Spring 2006

Physics 204A FINAL EXAM Chapters 1-14 Spring 2006 Nae: Solve the following probles in the space provided Use the back of the page if needed Each proble is worth 0 points You ust show your work in a logical fashion starting with the correctly applied physical

More information

A. B. C. D. E. v x. ΣF x

A. B. C. D. E. v x. ΣF x Q4.3 The graph to the right shows the velocity of an object as a function of time. Which of the graphs below best shows the net force versus time for this object? 0 v x t ΣF x ΣF x ΣF x ΣF x ΣF x 0 t 0

More information

1. Replace the given system of forces acting on a body as shown in figure 1 by a single force and couple acting at the point A.

1. Replace the given system of forces acting on a body as shown in figure 1 by a single force and couple acting at the point A. Code No: Z0321 / R07 Set No. 1 I B.Tech - Regular Examinations, June 2009 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile

More information

+F N = -F g. F g = m٠a g

+F N = -F g. F g = m٠a g Force Normal = F N Force Normal (or the Normal Force, abbreviated F N ) = F N = The contact force exerted by a surface on an object. The word Normal means perpendicular to Therefore, the Normal Force is

More information

Physics 18 Spring 2011 Homework 3 - Solutions Wednesday February 2, 2011

Physics 18 Spring 2011 Homework 3 - Solutions Wednesday February 2, 2011 Phsics 18 Spring 2011 Hoework 3 - s Wednesda Februar 2, 2011 Make sure our nae is on our hoework, and please bo our final answer. Because we will be giving partial credit, be sure to attept all the probles,

More information

y scalar component x scalar component A. 770 m 250 m file://c:\users\joe\desktop\physics 2A\PLC Assignments - F10\2a_PLC7\index.

y scalar component x scalar component A. 770 m 250 m file://c:\users\joe\desktop\physics 2A\PLC Assignments - F10\2a_PLC7\index. Page 1 of 6 1. A certain string just breaks when it is under 400 N of tension. A boy uses this string to whirl a 10-kg stone in a horizontal circle of radius 10. The boy continuously increases the speed

More information

acceleration of 2.4 m/s. (b) Now, we have two rubber bands (force 2F) pulling two glued objects (mass 2m). Using F ma, 2.0 furlongs x 2.0 s 2 4.

acceleration of 2.4 m/s. (b) Now, we have two rubber bands (force 2F) pulling two glued objects (mass 2m). Using F ma, 2.0 furlongs x 2.0 s 2 4. 5.. 5.6. Model: An object s acceleration is linearl proportional to the net force. Solve: (a) One rubber band produces a force F, two rubber bands produce a force F, and so on. Because F a and two rubber

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

Chapter 5 Lecture. Pearson Physics. Newton's Laws of Motion. Prepared by Chris Chiaverina Pearson Education, Inc.

Chapter 5 Lecture. Pearson Physics. Newton's Laws of Motion. Prepared by Chris Chiaverina Pearson Education, Inc. Chapter 5 Lecture Pearson Physics Newton's Laws of Motion Prepared by Chris Chiaverina Chapter Contents Newton's Laws of Motion Applying Newton's Laws Friction Newton's Laws of Motion Two of the most important

More information

Physics 8 Monday, October 12, 2015

Physics 8 Monday, October 12, 2015 Physics 8 Monday, October 12, 2015 HW5 will be due Friday. (HW5 is just Ch9 and Ch10 problems.) You re reading Chapter 12 ( torque ) this week, even though in class we re just finishing Ch10 / starting

More information

26 Impulse and Momentum

26 Impulse and Momentum 6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction

More information

Student Book pages

Student Book pages Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..

More information

66 Chapter 6: FORCE AND MOTION II

66 Chapter 6: FORCE AND MOTION II Chapter 6: FORCE AND MOTION II 1 A brick slides on a horizontal surface Which of the following will increase the magnitude of the frictional force on it? A Putting a second brick on top B Decreasing the

More information

Energy and Momentum: The Ballistic Pendulum

Energy and Momentum: The Ballistic Pendulum Physics Departent Handout -10 Energy and Moentu: The Ballistic Pendulu The ballistic pendulu, first described in the id-eighteenth century, applies principles of echanics to the proble of easuring the

More information

the static friction is replaced by kinetic friction. There is a net force F net = F push f k in the direction of F push.

the static friction is replaced by kinetic friction. There is a net force F net = F push f k in the direction of F push. the static friction is replaced by kinetic friction. There is a net force F net = F push f k in the direction of F push. Exaple of kinetic friction. Force diagra for kinetic friction. Again, we find that

More information

HW 6 - Solutions Due November 20, 2017

HW 6 - Solutions Due November 20, 2017 Conteporary Physics I HW 6 HW 6 - Solutions Due Noveber 20, 2017 1. A 4 kg block is attached to a spring with a spring constant k 200N/, and is stretched an aount 0.2 [5 pts each]. (a) Sketch the potential

More information

1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy

1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy AP Physics Multiple Choice Practice Wor-Energy 1. A ass attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is

More information

Every object remains in a state of rest or move with constant velocity in a straight line unless forces acts on it to change that state

Every object remains in a state of rest or move with constant velocity in a straight line unless forces acts on it to change that state " NEWONʼS LAW OF MOION NEWONʼS FIRS LAW Newtonʼs First Law of Motion states that: Every object remains in a state of rest or move with constant velocity in a straight line unless forces acts on it to change

More information

Algebra Based Physics Uniform Circular Motion

Algebra Based Physics Uniform Circular Motion 1 Algebra Based Physics Uniform Circular Motion 2016 07 20 www.njctl.org 2 Uniform Circular Motion (UCM) Click on the topic to go to that section Period, Frequency and Rotational Velocity Kinematics of

More information

PSI AP Physics B Dynamics

PSI AP Physics B Dynamics PSI AP Physics B Dynamics Multiple-Choice questions 1. After firing a cannon ball, the cannon moves in the opposite direction from the ball. This an example of: A. Newton s First Law B. Newton s Second

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

dt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2

dt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2 v = v i + at a dv dt = d2 x dt 2 A sphere = 4πr 2 x = x i + v i t + 1 2 at2 x = r cos(θ) V sphere = 4 3 πr3 v 2 = v 2 i + 2a x F = ma R = v2 sin(2θ) g y = r sin(θ) r = x 2 + y 2 tan(θ) = y x a c = v2 r

More information

Flipping Physics Lecture Notes: Free Response Question #1 - AP Physics Exam Solutions

Flipping Physics Lecture Notes: Free Response Question #1 - AP Physics Exam Solutions 2015 FRQ #1 Free Response Question #1 - AP Physics 1-2015 Exa Solutions (a) First off, we know both blocks have a force of gravity acting downward on the. et s label the F & F. We also know there is a

More information

Force a push or a pull exerted on some object the cause of an acceleration, or the change in an objects velocity

Force a push or a pull exerted on some object the cause of an acceleration, or the change in an objects velocity Chapter 4 Physics Notes Changes in Motion Force a push or a pull exerted on some object the cause of an acceleration, or the change in an objects velocity Forces cause changes in velocity Causes a stationary

More information

Problem T1. Main sequence stars (11 points)

Problem T1. Main sequence stars (11 points) Proble T1. Main sequence stars 11 points Part. Lifetie of Sun points i..7 pts Since the Sun behaves as a perfectly black body it s total radiation power can be expressed fro the Stefan- Boltzann law as

More information

ma x = -bv x + F rod.

ma x = -bv x + F rod. Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous

More information

Angle recap. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:

Angle recap. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration: Angle recap Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Today s lecture

More information

Lecture PowerPoints. Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition. Giancoli

Lecture PowerPoints. Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition. Giancoli Lecture PowerPoints Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided solely

More information

PHYSICS 2210 Fall Exam 4 Review 12/02/2015

PHYSICS 2210 Fall Exam 4 Review 12/02/2015 PHYSICS 10 Fall 015 Exa 4 Review 1/0/015 (yf09-049) A thin, light wire is wrapped around the ri of a unifor disk of radius R=0.80, as shown. The disk rotates without friction about a stationary horizontal

More information

CIRCULAR MOTION AND GRAVITATION

CIRCULAR MOTION AND GRAVITATION CIRCULAR MOTION AND GRAVITATION An object moves in a straight line if the net force on it acts in the direction of motion, or is zero. If the net force acts at an angle to the direction of motion at any

More information

9. h = R. 10. h = 3 R

9. h = R. 10. h = 3 R Version PREVIEW Torque Chap. 8 sizeore (13756) 1 This print-out should have 3 questions. ultiple-choice questions ay continue on the next colun or page find all choices before answering. Note in the dropped

More information

Applying Newton s Laws

Applying Newton s Laws Chapter 5 Applying Newton s Laws PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Copyright 2008 Pearson Education Inc., publishing

More information

Momentum. February 15, Table of Contents. Momentum Defined. Momentum Defined. p =mv. SI Unit for Momentum. Momentum is a Vector Quantity.

Momentum. February 15, Table of Contents. Momentum Defined. Momentum Defined. p =mv. SI Unit for Momentum. Momentum is a Vector Quantity. Table of Contents Click on the topic to go to that section Moentu Ipulse-Moentu Equation The Moentu of a Syste of Objects Conservation of Moentu Types of Collisions Collisions in Two Diensions Moentu Return

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

Newton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics

Newton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics Lecture 2 Key Concepts Newtonian echanics and relation to Kepler's laws The Virial Theore Tidal forces Collision physics Newton's Laws 1) An object at rest will reain at rest and an object in otion will

More information

THE ROCKET EXPERIMENT 1. «Homogenous» gravitational field

THE ROCKET EXPERIMENT 1. «Homogenous» gravitational field THE OCKET EXPEIENT. «Hoogenous» gravitational field Let s assue, fig., that we have a body of ass Μ and radius. fig. As it is known, the gravitational field of ass Μ (both in ters of geoetry and dynaics)

More information

PHYSICS 221, FALL 2010 EXAM #1 Solutions WEDNESDAY, SEPTEMBER 29, 2010

PHYSICS 221, FALL 2010 EXAM #1 Solutions WEDNESDAY, SEPTEMBER 29, 2010 PHYSICS 1, FALL 010 EXAM 1 Solutions WEDNESDAY, SEPTEMBER 9, 010 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In

More information

SECOND MIDTERM -- REVIEW PROBLEMS

SECOND MIDTERM -- REVIEW PROBLEMS Physics 10 Spring 009 George A. WIllaims SECOND MIDTERM -- REVIEW PROBLEMS A solution set is available on the course web page in pdf format. A data sheet is provided. No solutions for the following problems:

More information

AP Physics 1 Work Energy and Power Practice Test Name

AP Physics 1 Work Energy and Power Practice Test Name AP Physics 1 Work Energy and Power Practice Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two objects, one of mass m and the other

More information