# Chapter 8: Newton s Third law

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Warning: My approach is a soewhat abbreviated and siplified version of what is in the text, yet just as coplete. Both y treatent and the text s will prepare you to solve the sae probles. Restating Newton s Third law fro Chapter 4: When two bodies interact, the forces exerted by each body on the other are always equal in agnitude and opposite in direction. Less precisely: For every action there is an equal and opposite reaction. SMU PHYS1100.1, fall 2008, Prof. Clarke 1

2 A syste and its environent. Often, there will be ore than one object of interest in a proble, such as these two asses being pushed by a single force. F M Each object of interest (e.g., and M) is referred to as a syste; everything else (e.g., earth, table) is referred to as the environent. Typically, systes will interact (exert forces) with each other and with their environent. SMU PHYS1100.1, fall 2008, Prof. Clarke 2

3 Internal and external forces Forces exerted by one syste of interest on another are internal forces. e.g., ass pushes on ass M: P on M ass M pushes on ass : P M on Forces exerted on systes of interest by agents in the environent are external forces. e.g., the Earth exerts a gravitational force on : w E on the table exerts a noral force on : n T on the table exerts a frictional force on M: f k,t on M the external force F exerted on : F X on etc. The notation: P on M eans the force P exerted by on M. SMU PHYS1100.1, fall 2008, Prof. Clarke 3

4 Free-body diagras for and M: y P M on f k,t on n T on w E on a x F X on Using the F A on B notation, it is easy assign the correct forces to each syste. Only forces with on are put on the FBD for, and only forces with on M are put on the FBD for M. y M f k,t on M n T on M a P on M w E on M x In particular, the force driving the two asses, F, becoes F X on in this notation (X being soe unknown, external agent), and is applied only to the FBD for! SMU PHYS1100.1, fall 2008, Prof. Clarke 4

5 Action/reaction pairs y P M on f k,t on n T on a x F X on Note the syetry between the two internal forces: P on M y M f k,t on M n T on M a P on M x w E on P M on w E on M The two internal forces constitute an action/reaction pair. Newton s 3 rd Law states that every force has a corresponding reaction force, but only internal forces have their reaction forces labeled on the FBDs, and never on the sae FBD. SMU PHYS1100.1, fall 2008, Prof. Clarke 5

6 External forces (e.g., n T on ) are also part of an action-reaction pair, but the reaction force (e.g., n on T, the noral force exerts on the table) is irrelevant to the dynaics of or M. Thus, external forces do not appear in action/reaction pairs on the FBDs, only the internal forces do. Action/reaction: a bit of a isnoer? This ter sees to iply that one force, being the reaction to the action, soehow happens after the action. This is incorrect: one cannot exist without the other. The two forces co-exist siultaneously, no exceptions. SMU PHYS1100.1, fall 2008, Prof. Clarke 6

7 Identifying action/reaction pairs Easy!!! In our notation F A on B, just swap the labels A and B! Thus, if F A on B is the action force, the reaction force is F B on A e.g.: You (Y) are pushing a box (B) across the floor. If the action force is P Y on B, the reaction force is the box pushing back on you, P B on Y. P B on Y Y B P Y on B B Y Note that P Y on B and P B on Y appear on different FBDs!! P Y on B ended here, 16/10/08 SMU PHYS1100.1, fall 2008, Prof. Clarke 7 B P B on Y Y

8 More exaples. Two boxes, A and B, sit on a table, T, which sits on the earth, E. a) If the action force is the noral force of the table, T, on box A, (n T on A ), what is the reaction force? A n T on A n A on T = the noral force of box A on the table, T. T E B w E on B b) If the action force is the gravitational force the earth, E, exerts on box B (w E on B, otherwise known B s weight), what is the reaction force? w B on E = the gravitational force box B exerts on the earth, E. SMU PHYS1100.1, fall 2008, Prof. Clarke 8

9 Alert: A very coon isconception: Regardless of what you ay have learned or thought you learned elsewhere, the reaction force to the weight of is NOT the noral force fro the table! First, gravitational and noral forces are entirely different kinds of forces. Action/reaction pairs are ALWAYS the sae type of force. Second, both the weight and noral force are put on the sae FBD. Action/reaction pairs are NEVER put on the sae FBD. w n T E n SMU PHYS1100.1, fall 2008, Prof. Clarke 9 w

10 Alert: A very coon isconception: Regardless of what you ay have learned or thought you learned elsewhere, the reaction force to the weight of is NOT the noral force fro the table! First, gravitational and noral forces are entirely different kinds of forces. Action/reaction pairs are always the sae type of force. n T on w E on T Second, both the weight and noral force are put on the sae FBD. Action/reaction pairs are NEVER put on the sae FBD. E n T on Using the notation F A on B will help you avoid this trap. w E on SMU PHYS1100.1, fall 2008, Prof. Clarke 10

11 Newton s Third Law does ore than just pair up forces into action/reaction pairs. It also states that the two forces are equal in agnitude and opposite in direction. Thus, if P on M and P M on are an action/reaction pair, the two are related by: P on M = P M on exaple: If your weight is 150 pounds, this eans the earth is pulling you down with a gravitational force of 150 pounds. At the very sae tie, your body is pulling up on the earth with a gravitational force of the sae agnitude: 150 pounds! Who knew! SMU PHYS1100.1, fall 2008, Prof. Clarke 11

12 Clicker question 8.1 Solve a high-schooler s conundru: If I try to push a box across the floor, doesn t its reaction force on e cancel y action force on it? If so, why a I able to push boxes across the floor? a) the box doesn t push back with quite the sae force, and so the difference in forces allows it to ove. b) The friction force on y feet is greater than the friction force on the botto of the box, so it oves. c) The two forces act on different bodies (e and the box), and thus don t even get the chance to cancel out. d) Newton s 3 rd Law doesn t apply in this case. SMU PHYS1100.1, fall 2008, Prof. Clarke 12

13 Clicker question 8.1 Solve a high-schooler s conundru: If I try to push a box across the floor, doesn t its reaction force on e cancel y action force on it? If so, why a I able to push boxes across the floor? Buffalo uffins! a) the box doesn t push back with quite the sae force, and so the difference in forces allows it to ove. b) The friction force on y feet is greater than the friction force on the botto of the box, so it oves. ay be correct, but doesn t answer the question c) The two forces act on different bodies (e and the box), and thus don t even get the chance to cancel out. d) Newton s 3 rd Law doesn t apply in this case. Oh yes it does! SMU PHYS1100.1, fall 2008, Prof. Clarke 13

14 Clicker question 8.2 Car B is stopped for a red light. Car A, whose ass is greater than Car B, doesn t see the red light and runs into the back of Car B. Which of the following stateents is true? v a) B exerts a force on A, but A doesn t exert a force on B. b) B exerts a larger force on A than A exerts on B. c) B exerts the sae aount of force on A as A exerts on B. d) A exerts a larger force on B than B exerts on A. e) A exerts a force on B but B doesn t exert a force on A. SMU PHYS1100.1, fall 2008, Prof. Clarke 14

15 Clicker question 8.2 Car B is stopped for a red light. Car A, whose ass is greater than Car B, doesn t see the red light and runs into the back of Car B. Which of the following stateents is true? v a) B exerts a force on A, but A doesn t exert a force on B. b) B exerts a larger force on A than A exerts on B. c) B exerts the sae aount of force on A as A exerts on B. d) A exerts a larger force on B than B exerts on A. e) A exerts a force on B but B doesn t exert a force on A. SMU PHYS1100.1, fall 2008, Prof. Clarke 15

16 Clicker question 8.3 Consider yourself sitting in your chair. If the action force is your weight (i.e., the Earth s pull on you), what is the reaction force? a) the noral force you exert against the chair (pointing down); b) the noral force the chair exerts against you (pointing up); c) your gravitational pull on the Earth; d) the chair pushing against the floor. SMU PHYS1100.1, fall 2008, Prof. Clarke 16

17 Clicker question 8.3 Consider yourself sitting in your chair. If the action force is your weight (i.e., the Earth s pull on you), what is the reaction force? a) the noral force you exert against the chair (pointing down); b) the noral force the chair exerts against you (pointing up); c) your gravitational pull on the Earth; d) the chair pushing against the floor. SMU PHYS1100.1, fall 2008, Prof. Clarke 17

18 Challenge exaple. a) In the syste shown, ass is pushed to the right with a force F X. Given the asses and M and the coefficient of kinetic friction between the table and M (µ k,tm ), what conditions ust exist on µ k,m (coefficient of kinetic friction between M and ) and F X if is to slide across M and M is to slide across the table? y f k,m on n M on w E on a x F X on y f k,t on M notes 8.1 n T on M M a M x F X on M µ k,m µ k,tm T n on M f k, on M w E on M E SMU PHYS1100.1, fall 2008, Prof. Clarke 18

19 y f k,m on n M on w E on a x F X on FBD for Two forces internal to the syste + M: n M on (noral force exerted by M on ) f k,m on (kinetic friction exerted by M on ) The action/reaction counterparts to these forces ust appear on the FBD for M. They do not appear here!!! All other forces are external to the syste + M their action/ reaction counterparts do not appear on either FBD. x/ F X f k,m = a y/ n M g = 0 n M = g 1 f k,m = µ k,m n M = µ k,m g 2 a = F X µ k,m g F a = X µ k,m g 3 SMU PHYS1100.1, fall 2008, Prof. Clarke 19

20 f k,t on M y n on M n T on M M a M f k, on M w E on M x FBD for M In the equations, I drop the on and on M part of the notation to ake the less awkward to write. They were needed to help us put the forces on the correct FBD but serve no purpose in the equations. Newton s 2 nd Law x/ f k, f k,t = Ma M y/ n T n Mg = 0 n T = n + Mg Newton s 3 rd Law n = n M = g (fro 1 ) f k, = f k,m = µ k,m g (fro 2 ) f k,t = µ k,tm n T = µ k,tm (n + Mg) = µ k,tm ( + M)g f Thus, a M = k, f k,t a M = g µ k,m µ [ k,tm ( + 1)] 4 M M M SMU PHYS1100.1, fall 2008, Prof. Clarke 20

21 We can now answer the question asked: What are the constraints on F X and µ k,m so that slips on M and M slips on the table, i.e., for a > a M > 0? Fro 4 : a M = g [ µ k,m µ ( k,tm + 1 )] > 0 M M µ k,m > µ ( k,tm + 1 ) µ k,m > µ ( M k,tm 1 + ) 5 M M Next, using 3 and 4 : a > a M F X µ k,m g > g [ µ k,m µ ( k,tm + 1 )] M M Solving for F X, we get: F X > g (µ k,m µ k,tm )( + 1 ) 6 M SMU PHYS1100.1, fall 2008, Prof. Clarke 21

22 Challenge exaple. b) Let = 2.0 kg, M = 3.0 kg, F X = 20 N, µ k,tm = 0.2, and µ k,m = 0.8. Verify that both asses will slip over their respective surfaces. fro 5 : µ ( M k,tm 1 + ) 3 = (0.2)(1+ ) = 0.5 < 0.8 = µ 2 k,m fro 6 : g (µ k,m µ k,tm )( + 1 ) 2 = (2.0)(9.8)( )( +1) M 3 = 19.6 N < 20 N = F X c) If M has width W = 0.45 and starts directly over the centre of M, how uch tie passes before is pushed off M? Fro 3, a = 2.16 s 2 and fro 4, a M = 1.96 s 2. Thus, 1 2 s = a t 2 ; s M = a M t 2 s s M = = (a a M ) t 2 t 2 = W/(a a M ) = 0.45/(0.2) = t = 1.5 s SMU PHYS1100.1, fall 2008, Prof. Clarke 22 W 2 1 2

23 Acceleration Constraints If objects are connected together as they ove, their accelerations will be related to each other: perhaps but not necessarily equal. The relationships aong the accelerations are called acceleration constraints. So long as the rope is under tension, the accelerations of the truck and car will be equal. a C = a T So long as the rope doesn t stretch, the agnitudes of the accelerations of blocks A and B are equal, though their directions are different. a A = a B SMU PHYS1100.1, fall 2008, Prof. Clarke 23

24 Note: In the iddle of page 216 where the text discusses this exaple, it gives the acceleration constraint as: a Ax = a By which relates the x-coponent of a A with the y- coponent of a B : The constraint on the previous slide (a A = a B ) relates the agnitudes of the accelerations, and thus no negative sign. SMU PHYS1100.1, fall 2008, Prof. Clarke 24

25 Acceleration constraints can often provide the issing piece of inforation needed to solve a proble, but soeties they can be tricky. Consider the proble below. a 1 s 1 s 2 a 2 SMU PHYS1100.1, fall 2008, Prof. Clarke 25

26 Acceleration constraints can often provide the issing piece of inforation needed to solve a proble, but soeties they can be tricky. Consider the proble below. In tie t, the length of rope that disappears in front of 1, s 1, ust be accounted for by the two extra lengths of rope, s 2, that appear above 2. a 1 s 1 s 1 = 2 s 2 s 2 but s 1 = ½ a 1 t 2 ; s 2 = ½ a 2 t 2 a 1 = 2a 2. and this is the acceleration constraint. a 2 SMU PHYS1100.1, fall 2008, Prof. Clarke 26

27 Clicker question 8.4 Rope 1 is fixed to a wall at one end and pulled at the other end with a force of 100N (top). Rope 2 is pulled at both ends by a force of 100 N each (botto). Which stateent is correct? a) The tension in rope 2 is the sae as the tension in rope 1. b) The tension in rope 2 is twice that of the tension in rope 1. c) The tension in rope 2 is less than the tension in rope 1. SMU PHYS1100.1, fall 2008, Prof. Clarke 27

28 Clicker question 8.4 Rope 1 is fixed to a wall at one end and pulled at the other end with a force of 100N (top). Rope 2 is pulled at both ends by a force of 100 N each (botto). Which stateent is correct? a) The tension in rope 2 is the sae as the tension in rope 1. b) The tension in rope 2 is twice that of the tension in rope 1. c) The tension in rope 2 is less than the tension in rope 1. SMU PHYS1100.1, fall 2008, Prof. Clarke 28

29 Explanation to Clicker question 8.4 : Break up the rope into three bits: left (L), iddle (M), and right (R) (or as any bits as you like). Newton s 3 rd Law identifies two action/reaction pairs: F M on L = F L on M and F R on M = F M on R. Nothing oves. Thus Newton s 2 nd Law requires that F S on L = F M on L, F L on M = F R on M, and F M on R = F W on R. Thus 100 N = F S on L = F M on L = F L on M = F R on M = F M on R = F W on R, and this is equivalent to the situation where two people are pulling. 100 N F S on L L F M on L F L on M M F R on M F M on R R F W on R Sa action/reaction pairs Wall SMU PHYS1100.1, fall 2008, Prof. Clarke 29

30 8.4 Ropes and Pulleys 1. A stationary rope transits an action/reaction pair so that the pull at one end of the rope is equal in agnitude and opposite in direction to the pull at the other end. If a rope of ass is used to accelerate an object of ass M, and is not negligible, then T 1 T 2 = a, and T 1 > T 2. T T Massless string approxiation: If = 0, we recover T 1 = T 2. Thus, the tension along a assless rope (string) is constant even if the rope is accelerating. M a T 2 T 2 a T 1 SMU PHYS1100.1, fall 2008, Prof. Clarke 30

31 If a ass M hangs at the end of a rope of ass, the tension at the top of the rope is greater than at the botto since the top has to support both and M, while the botto only needs to support M. T top = T bot + g; T bot = Mg T top = Mg + g a/r T top T top M If we use the assless string approxiation, = 0 and T top = T bot. Once again the tension in the string is constant. For a vertical syste, we need to assue the string is assless even if the syste is not accelerating. SMU PHYS1100.1, fall 2008, Prof. Clarke 31 Mg g a/r T bot T bot

32 2. An ideal pulley is assless and frictionless, so that its only effect on the proble is to redirect the tension in the string. The approxiations of ideal pulleys and assless strings allow us to write: T S on A = T S on B = T. We ll do this particular proble as our first exaple. SMU PHYS1100.1, fall 2008, Prof. Clarke 32

33 Exaple. Mass A (1.0 kg) is held in place on a frictionless table and is attached via a assless string that passes over an ideal pulley to ass B (0.5 kg) that dangles freely, as shown. a) When A is released, find the acceleration of the asses and the tension in the string. For ass A: For ass B: y x/ T = A a 1 x/ irrelevant y A n T on A w E on A a T S on A x y/ irrelevant y/ T B g = B a 2 Substitute 1 into 2 : A a B g = B a B Solve for a: a = g = 3.27 s -2 A + B Evaluate T fro 1 : T = (1.0)(3.27) = 3.27 N a B T S on B x w E on B SMU PHYS1100.1, fall 2008, Prof. Clarke 33

34 b) What was the tension in the string when ass A was being held in place? B y T S on B x w E on B Look at ass B again, but this tie with a = 0: x/ irrelevant y/ T B g = 0 T = (0.5)(9.8) = 4.9 N The tension in the string is less when the asses are accelerating than when they are being held still. SMU PHYS1100.1, fall 2008, Prof. Clarke 34

35 Clicker question 8.5 Blocks A and B are pulled with a force F across a frictionless table by assless strings. Let the tension in string 1 be T 1 and the tension in string 2 be T 2. Which of the following is true? a) T 2 < T 1 < F b) T 2 = T 1 = F c) T 2 > T 1 > F d) T 2 < T 1 = F e) We need to know about the asses before we can tell. F SMU PHYS1100.1, fall 2008, Prof. Clarke 35

36 Clicker question 8.5 Blocks A and B are pulled with a force F across a frictionless table by assless strings. Let the tension in string 1 be T 1 and the tension in string 2 be T 2. Which of the following is true? a) T 2 < T 1 < F b) T 2 = T 1 = F c) T 2 > T 1 > F d) T 2 < T 1 = F e) We need to know about the asses before we can tell. F SMU PHYS1100.1, fall 2008, Prof. Clarke 36

37 Clicker question 8.6 In the diagra, consider the tension in the (assless) string when A is held in place (T held ) and the tension in the string when A is let go and B falls (T fall ). Which of the following stateents is true? a) T held > T fall b) T held = T fall c) T held < T fall SMU PHYS1100.1, fall 2008, Prof. Clarke 37

38 Clicker question 8.6 In the diagra, consider the tension in the (assless) string when A is held in place (T held ) and the tension in the string when A is let go and B falls (T fall ). Which of the following stateents is true? a) T held > T fall b) T held = T fall c) T held < T fall SMU PHYS1100.1, fall 2008, Prof. Clarke 38

39 Clicker question 8.7 In the syste shown, the string is assless and all pulleys are ideal. T 1 is the tension in the string between 1 and the pulley on the table. T 2 is the tension in the string between the pulley on the table and 2. T 3 is the tension in the string between the ceiling and 2. Which tension is the greatest? a) T 1 b) T 2 c) T 3 d) They are all the sae. T 1 T 2 T 3 SMU PHYS1100.1, fall 2008, Prof. Clarke 39

40 Clicker question 8.7 In the syste shown, the string is assless and all pulleys are ideal. T 1 is the tension in the string between 1 and the pulley on the table. T 2 is the tension in the string between the pulley on the table and 2. T 3 is the tension in the string between the ceiling and 2. Which tension is the greatest? a) T 1 b) T 2 c) T 3 d) They are all the sae. T 1 T 2 T 3 ended here, 21/10/08 SMU PHYS1100.1, fall 2008, Prof. Clarke 40

41 Exaple: Find the tension in the string and accelerations in ters of 1, 2, and g. Assue a assless string, ideal pulleys, and a frictionless table. a 1 y n T on 1 a 1 1 : x/ T = 1 a 1 y/ irrelevant 1 T x a 2 1 g SMU PHYS1100.1, fall 2008, Prof. Clarke 41

42 Exaple: Find the tension in the string and accelerations in ters of 1, 2, and g. Assue a assless string, ideal pulleys, and a frictionless table. a 1 y n T on 1 a 1 1 : x/ T = 1 a 1 y/ irrelevant 2 : x/ no forces 1 T x y/ 2T 2 g = 2 a 2 a 2 1 g y T T 2 x a 2 2 g SMU PHYS1100.1, fall 2008, Prof. Clarke 42

43 Exaple: Find the tension in the string and accelerations in ters of 1, 2, and g. Assue a assless string, ideal pulleys, and a frictionless table. y n T on 1 a 1 1 : x/ T = 1 a 1 y/ irrelevant a 1 2 : x/ no forces 1 T 1 g x 2 1 a 1 2 g = 2 a 2 y/ 2T 2 g = 2 a 2 acceleration constraint fro slide 26: a 1 = 2a 2 y a a 2 2 g = 2 a 2 a 2 ( ) = 2 g T T a 2 = 2 g 2 a 1 = 2 g T = g a 2 2 x 2 g SMU PHYS1100.1, fall 2008, Prof. Clarke 43

44 Exaple: Atwood s achine a) If 1 = 1.0 kg and 2 = 1.5 kg, with what iniu force F ust the ideal pulley be pulled so that both asses lift off the ground? b) What is the acceleration of the pulley? F P T 1 1 g F a 1 T 1 g = 1 a 1 T 2 g = 0 T = 2 g T a 1 = g = 2 1 g 1 ( ) 1 F 2T = 0 (assless pulley) F = 2 2 g = 29.4 N 1 s 1 P a 1 P acceleration constraint: s P = s 1 1 a P = a 1 = 1 = 2.45 s 2 ( ) g 2 2 T T 2 SMU PHYS1100.1, fall 2008, Prof. Clarke 44 T 2 2 g a 2 = 0 n G on 2 = 0 s P 1 2 F P

### ConcepTest 4.6 Force and Two Masses

ConcepTest 4.6 Force and Two Masses A force F acts on ass 1 giving acceleration a 1. The sae force acts on a different ass 2 giving acceleration a 2 = 2a 1. If 1 and 2 are glued together and the sae force

### Work, Energy, Conservation of Energy

This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and non-conservative forces, with soe

### Newton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1

Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is

### Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

### F=ma From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.edu

Chapter 4 F=a Fro Probles and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, orin@physics.harvard.edu 4.1 Introduction Newton s laws In the preceding two chapters, we dealt

### This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.

This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical

### Forces. Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies.

Forces Now we will discuss the part of mechanics known as dynamics. We will introduce Newton s three laws of motion which are at the heart of classical mechanics. We must note that Newton s laws describe

### Chapter 13 Simple Harmonic 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 13.1 Introduction to Periodic Motion Periodic otion is any otion that

### Answer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This print-out should have 4 questions. Multiple-choice questions ay continue on the next colun or page find all choices before aking your selection.

### BROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino

BROCK UNIVERSITY PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino 1. [10 marks] Clearly indicate whether each statement is TRUE or FALSE. Then provide a clear, brief,

### THE NATURE OF FORCES Forces can be divided into two categories: contact forces and non-contact forces.

SESSION 2: NEWTON S LAWS Key Concepts In this session we Examine different types of forces Review and apply Newton's Laws of motion Use Newton's Law of Universal Gravitation to solve problems X-planation

### Answer: Same magnitude total momentum in both situations.

Page 1 of 9 CTP-1. In which situation is the agnitude of the total oentu the largest? A) Situation I has larger total oentu B) Situation II C) Sae agnitude total oentu in both situations. I: v 2 (rest)

### Lecture 9. Friction in a viscous medium Drag Force Quantified

Lecture 9 Goals Describe Friction in Air (Ch. 6) Differentiate between Newton s 1 st, 2 nd and 3 rd Laws Use Newton s 3 rd Law in problem solving Assignment: HW4, (Chap. 6 & 7, due 10/5) 1 st Exam Thurs.,

### PHYS101 The Laws of Motion Spring 2014

The Laws of Motion 1. An object of mass m 1 = 55.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m 2

### Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. Dr Tay Seng Chuan

PC1221 Fundamentals of Physics I Lectures 9 and 10 he Laws of Motion Dr ay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while lecture

### Physics 101 Exam 1 NAME 2/7

Physics 101 Exam 1 NAME 2/7 1 In the situation below, a person pulls a string attached to block A, which is in turn attached to another, heavier block B via a second string (a) Which block has the larger

### Chapter 5 Newton s Laws of Motion

Chapter 5 Newton s Laws of Motion Sir Isaac Newton (1642 1727) Developed a picture of the universe as a subtle, elaborate clockwork slowly unwinding according to well-defined rules. The book Philosophiae

### A) N > W B) N = W C) N < W. speed v. Answer: N = W

CTN-12. Consider a person standing in an elevator that is moving upward at constant speed. The magnitude of the upward normal force, N, exerted by the elevator floor on the person's feet is (larger than/same

### College Physics 140 Chapter 4: Force and Newton s Laws of Motion

College Physics 140 Chapter 4: Force and Newton s Laws of Motion We will be investigating what makes you move (forces) and how that accelerates objects. Chapter 4: Forces and Newton s Laws of Motion Forces

### LAWS OF MOTION PROBLEM AND THEIR SOLUTION

http://www.rpauryascienceblog.co/ LWS OF OIO PROBLE D HEIR SOLUIO. What is the axiu value of the force F such that the F block shown in the arrangeent, does not ove? 60 = =3kg 3. particle of ass 3 kg oves

### Lesson 04: Newton s laws of motion

www.scimsacademy.com Lesson 04: Newton s laws of motion If you are not familiar with the basics of calculus and vectors, please read our freely available lessons on these topics, before reading this lesson.

### Ideal Cable. Linear Spring - 1. Cables, Springs and Pulleys

Cables, Springs and Pulleys ME 202 Ideal Cable Neglect weight (massless) Neglect bending stiffness Force parallel to cable Force only tensile (cable taut) Neglect stretching (inextensible) 1 2 Sketch a

### CHAPTER 3 NEWTON S LAWS OF MOTION

CHAPTER 3 NEWTON S LAWS OF MOTION NEWTON S LAWS OF MOTION 45 3.1 FORCE Forces are calssified as contact forces or gravitational forces. The forces that result from the physical contact between the objects

### 5. Forces and Motion-I. Force is an interaction that causes the acceleration of a body. A vector quantity.

5. Forces and Motion-I 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will

### What is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact?

Chapter 4: Forces What is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact? Application different forces (field forces, contact

### Version 001 Summer Review #04 tubman (IBII ) 1

Version 001 Suer Review #04 tuban (IBII20142015) 1 This print-out should have 20 questions. Multiple-choice questions ay continue on the next colun or page find all choices before answering. Conceptual

### = 4.0 N. For the upper magnet, F L on U. T on U. because these are an action/ reaction pair. Equilibrium for the upper magnet requires n T on U

7.8. (a) The upper magnet is labeled U, the lower magnet L. Each magnet eerts a long-range magnetic force on the other. Each magnet and the table eert a contact force (normal force) on each other. In addition,

### Chapter 4 Newton s Laws: Explaining Motion

Chapter 4 Newton s s Laws: Explaining Motion Newton s Laws of Motion The concepts of force, mass, and weight play critical roles. A Brief History! Where do our ideas and theories about motion come from?!

### 1 of 7 10/2/2009 1:13 PM

1 of 7 10/2/2009 1:13 PM Chapter 6 Homework Due: 9:00am on Monday, September 28, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

### AP Physics Newton's Laws Practice Test

AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a

### Chapter 4 Dynamics: Newton s Laws of Motion

Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

### Forces: Equilibrium Examples

Physics 101: Lecture 02 Forces: Equilibrium Examples oday s lecture will cover extbook Sections 2.1-2.7 Phys 101 URL: http://courses.physics.illinois.edu/phys101/ Read the course web page! Physics 101:

### Newton s Laws of Motion

Physics Newton s Laws of Motion Newton s Laws of Motion 4.1 Objectives Explain Newton s first law of motion. Explain Newton s second law of motion. Explain Newton s third law of motion. Solve problems

### physics 111N forces & Newton s laws of motion

physics 111N forces & Newton s laws of motion forces (examples) a push is a force a pull is a force gravity exerts a force between all massive objects (without contact) (the force of attraction from the

### Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of motion unless acted upon by net external forces.

Newton s Third Law Newton s First Law (Law of Inertia) F = 0 An object will remain at rest or in a constant state of motion unless acted upon by net external forces. Newton s First Law If F = 0 => No Change

### v v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )

Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### Lesson 44: Acceleration, Velocity, and Period in SHM

Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it akes sense that the object will accelerate. In Physics 20 you are only required to explain

### PH2213 : Examples from Chapter 4 : Newton s Laws of Motion. Key Concepts

PH2213 : Examples from Chapter 4 : Newton s Laws of Motion Key Concepts Newton s First and Second Laws (basically Σ F = m a ) allow us to relate the forces acting on an object (left-hand side) to the motion

### hoop disk M, R M, R Page 1 of 5

Page 1 of 5 CTot-1. Consider a rod of unifor density with an axis of rotation through its center and an identical rod with the axis of rotation through one end. Which has the larger oent of inertia? C

### Version 001 test 1 review tubman (IBII201516) 1

Version 001 test 1 review tuban (IBII01516) 1 This print-out should have 44 questions. Multiple-choice questions ay continue on the next colun or page find all choices before answering. Crossbow Experient

### For every action, there is an and.

SPH4C1 Lesson 03 Newton s Laws NEWTON S THIRD LAW LEARNING GOALS Students will: Be able to state Newton s 3 rd Law and apply it in qualitative and quantitative terms to explain the effect of forces acting

### If I have seen further than others, it is by standing upon the shoulders of giants.

Chapter 4: Dynaics If I have seen further than others, it is by standing upon the shoulders of giants. Sir Isaac Newton Objectives 1. Define ass and inertia and explain the eaning of Newton s 1st Law.

### PHYSICS 151 Notes for Online Lecture 2.2

PHYSICS 151 otes for Online Lecture. A free-bod diagra is a wa to represent all of the forces that act on a bod. A free-bod diagra akes solving ewton s second law for a given situation easier, because

### Newton s Laws Pre-Test

Newton s Laws Pre-Test 1.) Consider the following two statements and then select the option below that is correct. (i) It is possible for an object move in the absence of forces acting on the object. (ii)

### Newton s Law of Motion

chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating

### Chapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.

Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

### Force. A force is a push or a pull. Pushing on a stalled car is an example. The force of friction between your feet and the ground is yet another.

Force A force is a push or a pull. Pushing on a stalled car is an example. The force of friction between your feet and the ground is yet another. Force Weight is the force of the earth's gravity exerted

### 1. Newton s Laws of Motion and their Applications Tutorial 1

1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0

### Normal Force Example: Incline

Normal Force Example: Incline α The angle of the frictionless incline is α = 30. Mass slides down the incline, starting from rest. What is the speed of the mass after it slid 10 meters downhill? [use g

### Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4 Forces and Newton s Laws of Motion continued Clicker Question 4.3 A mass at rest on a ramp. How does the friction between the mass and the table know how much force will EXACTLY balance the gravity

### Lecture L9 - Linear Impulse and Momentum. Collisions

J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9 - Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,

### Mechanics 1: Motion of a Particle in 1 Dimension

Mechanics 1: Motion of a Particle in 1 Diension Motion of a Particle in One Diension eans that the particle is restricted to lie on a curve. If you think hard about this stateent you ight think that the

### Newton s Laws of Motion

Chapter 4 Newton s Laws of Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 7_8_2016 Goals for Chapter 4

### 04-1. Newton s First Law Newton s first law states: Sections Covered in the Text: Chapters 4 and 8 F = ( F 1 ) 2 + ( F 2 ) 2.

Force and Motion Sections Covered in the Text: Chapters 4 and 8 Thus far we have studied some attributes of motion. But the cause of the motion, namely force, we have essentially ignored. It is true that

### VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

### Friction and Newton s 3rd law

Lecture 4 Friction and Newton s 3rd law Pre-reading: KJF 4.8 Frictional Forces Friction is a force exerted by a surface. The frictional force is always parallel to the surface Due to roughness of both

### 2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was

### Best Angle for QUICK LAB. Analyze and Conclude. 22 MHR Unit 1 Forces and Motion: Dynamics

5. Pushing a grocery cart with a force of 95 N, applied at an angle of 35 down from the horizontal, makes the cart travel at a constant speed of 1.2 m/s. What is the frictional force acting on the cart?

### Serway_ISM_V1 1 Chapter 4

Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As

### Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

### Chapter 5 Problems. = 9ˆ i + 0 ˆ j F 2 F 1. = 8cos62 ˆ i + 8sin62 ˆ j. = (9 8cos62 ) i ˆ + (8sin62 ) ˆ j = i ˆ ˆ j =

Chapter 5 Problems 5.1 Only two horizontal forces act on a 3.0 kg body. One force is 9.0N, acting due east, and the other is 8.0N act 62 degrees North of west. What is the magnitude of the body s acceleration?

### Newton s Laws of Motion

Chapter 4 Newton s Laws of Motion PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 4 To understand the meaning

Section Review Answers Chapter 12 Section 1 1. Answers may vary. Students should say in their own words that an object at rest remains at rest and an object in motion maintains its velocity unless it experiences

### Homework 8. problems: 10.40, 10.73, 11.55, 12.43

Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks

### Physics 11 Chapter 4 HW Solutions

Physics 11 Chapter 4 HW Solutions Chapter 4 Conceptual Question: 5, 8, 10, 18 Problems: 3, 3, 35, 48, 50, 54, 61, 65, 66, 68 Q4.5. Reason: No. If you know all of the forces than you know the direction

### WEEK 8: PASSIVE FORCES AND NEWTON S LAWS

Name Date Partners WEEK 8: PASSIVE FORCES AND NEWTON S LAWS OBJECTIVES To explore interaction forces between objects as described by Newton s third law of motion. To explore tension forces and understand

### Newton s Laws of Motion

Newton s Laws of Motion FIZ101E Kazım Yavuz Ekşi My contact details: Name: Kazım Yavuz Ekşi Email: eksi@itu.edu.tr Notice: Only emails from your ITU account are responded. Office hour: Wednesday 10.00-12.00

### 4.3 The Graph of a Rational Function

4.3 The Graph of a Rational Function Section 4.3 Notes Page EXAMPLE: Find the intercepts, asyptotes, and graph of + y =. 9 First we will find the -intercept by setting the top equal to zero: + = 0 so =

### Q5.1. A. tension T 1 B. tension T 2 C. tension T 3 D. two of the above E. T 1, T 2, and T Pearson Education, Inc.

Q5.1 A car engine is suspended from a chain linked at O to two other chains. Which of the following forces should be included in the free-body diagram for the engine? A. tension T 1 B. tension T 2 C. tension

### Physics 211: Lab Oscillations. Simple Harmonic Motion.

Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.

### Lecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.8-4.12, second half of section 4.7

Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.8-4.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal

### Chapter 4. Forces I. 4.1 The Important Stuff Newton s First Law Newton s Second Law

Chapter 4 Forces I 4.1 The Important Stuff 4.1.1 Newton s First Law With Newton s Laws we begin the study of how motion occurs in the real world. The study of the causes of motion is called dynamics, or

### PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 1-7. February 13, 2013

PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 1-7 February 13, 2013 0.1 A 2.00-kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object

### Honors Physics. Momentum Review

Honors Physics Moentu Review Nae Date. A freight car of ass 0,000 kg oves along a frictionless level railroad track with a constant speed of 5 /s. What is the oentu of the car A. 30,000 kg /s B. 3,000

### W02D2-2 Table Problem Newton s Laws of Motion: Solution

ASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 W0D- Table Problem Newton s Laws of otion: Solution Consider two blocks that are resting one on top of the other. The lower block

### Clicker Question. A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road.

A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road. A. positive. B. negative. C. zero. Clicker Question The total work done on the

### Physics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion)

Physics 101 Prof. Ekey Chapter 5 Force and motion (Newton, vectors and causing commotion) Goal of chapter 5 is to establish a connection between force and motion This should feel like chapter 1 Questions

### KE =? v o. Page 1 of 12

Page 1 of 12 CTEnergy-1. A mass m is at the end of light (massless) rod of length R, the other end of which has a frictionless pivot so the rod can swing in a vertical plane. The rod is initially horizontal

### Simple Harmonic Motion

SHM-1 Siple Haronic Motion A pendulu, a ass on a spring, and any other kinds of oscillators ehibit a special kind of oscillatory otion called Siple Haronic Motion (SHM). SHM occurs whenever : i. there

### Imagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut.

A Resource for Free-standing Matheatics Qualifications Iagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut. Suppose both had a speed of

### 1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C. PHYS 11: Chap. 2, Pg 2

1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C PHYS 11: Chap. 2, Pg 2 1 1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All three A B PHYS 11: Chap. 2, Pg 3 C 1) more than

### Physics 123 Lab 5: Newton's 3rd Law and the Friction Force Physics 123: Electricity and Magnetism

Physics 123 Lab 5: Newton's 3rd Law and the Friction Force Physics 123: Electricity and Magnetism Instructor: Professor Andrew Boudreaux, Andrew.Boudreaux@wwu.edu Introduction and Overview In this lab

### Newton s Laws of Motion

Newton s Laws of Motion Newton s Laws and the Mousetrap Racecar Simple version of Newton s three laws of motion 1 st Law: objects at rest stay at rest, objects in motion stay in motion 2 nd Law: force

### LAB 6 - GRAVITATIONAL AND PASSIVE FORCES

L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies

### HW Set II page 1 of 9 PHYSICS 1401 (1) homework solutions

HW Set II page 1 of 9 4-50 When a large star becomes a supernova, its core may be compressed so tightly that it becomes a neutron star, with a radius of about 20 km (about the size of the San Francisco

### Chapter Test. Teacher Notes and Answers Forces and the Laws of Motion. Assessment

Assessment Chapter Test A Teacher Notes and Answers Forces and the Laws of Motion CHAPTER TEST A (GENERAL) 1. c 2. d 3. d 4. c 5. c 6. c 7. c 8. b 9. d 10. d 11. c 12. a 13. d 14. d 15. b 16. d 17. c 18.

### External vs. Internal Force

NEWTON'S THIRD LAW External vs. Internal Force External Force: Exerted on the system by something outside the system Internal Force: Exerted by one part of the system on another part Newton's Second Law:

### Version 001 Quest 3 Forces tubman (20131) 1

Version 001 Quest 3 Forces tubman (20131) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. l B Conceptual

### Newton s Second Law. First of only two important equations in this chapter: r =

Newton s First Law Unless they are acted upon by an external force, objects at rest will stay at rest, and object in motion will stay in motion with a constant velocity. Only applies in inertial reference

### Newton s Laws of Motion

Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first

### Physics 201 Fall 2009 Exam 2 October 27, 2009

Physics 201 Fall 2009 Exam 2 October 27, 2009 Section #: TA: 1. A mass m is traveling at an initial speed v 0 = 25.0 m/s. It is brought to rest in a distance of 62.5 m by a force of 15.0 N. The mass is

### E k = ½ m v 2. (J) (kg) (m s -1 ) FXA KINETIC ENERGY (E k ) 1. Candidates should be able to : This is the energy possessed by a moving object.

KINETIC ENERGY (E k ) 1 Candidates should be able to : This is the energy possessed by a oing object. Select and apply the equation for kinetic energy : E k = ½ 2 KINETIC ENERGY = ½ x MASS x SPEED 2 E

### MOTION AND FORCE: DYNAMICS

MOTION AND FORCE: DYNAMICS We ve been dealing with the fact that objects move. Velocity, acceleration, projectile motion, etc. WHY do they move? Forces act upon them, that s why! The connection between

### Physics-1 Recitation-3

Physics-1 Recitation-3 The Laws of Motion 1) The displacement of a 2 kg particle is given by x = At 3/2. In here, A is 6.0 m/s 3/2. Find the net force acting on the particle. (Note that the force is time

### More of Newton s Laws

More of Newton s Laws Announcements: Tutorial Assignments due tomorrow. Pages 19-21, 23, 24 (not 22,25) Note Long Answer HW due this week. CAPA due on Friday. Have added together the clicker scores so

### Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

### Laboratory Report Scoring and Cover Sheet

Laboratory Report Scoring and Cover Sheet Title of Lab _Newton s Laws Course and Lab Section Number: PHY 1103-100 Date _23 Sept 2014 Principle Investigator _Thomas Edison Co-Investigator _Nikola Tesla

### Dynamics Pulleys, Ramps, and Friction

Name School Date Purpose To investigate the vector nature of forces. To practice the use free-body diagrams (FBDs). To learn to apply Newton s Second Law to systems of masses connected by pulleys. Equipment

### Chapter 4: Newton s Laws of Motion

Chapter 4: Newton s Laws of Motion Dynamics: Study of motion and its causes. orces cause changes in the motion of an object. orce and Interactions Definition ( loose ): A force is a push or pull exerted

### Two-Body System: Two Hanging Masses

Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.