Chapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc.

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1 Chapter 5 Newton s Laws of Motion Copyright 2010 Pearson Education, Inc.

2 Force and Mass Copyright 2010 Pearson Education, Inc. Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The Vector Nature of Forces: Forces in Two Dimensions Weight Normal Forces

3 Force: push or pull 5-1 Force and Mass Force is a vector it has magnitude and direction Copyright 2010 Pearson Education, Inc.

4 5-1 Force and Mass Mass is the measure of how hard it is to change an object s velocity. Mass can also be thought of as a measure of the quantity of matter in an object. Copyright 2010 Pearson Education, Inc.

5 5-2 Newton s First Law of Motion If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest. This is also known as the law of inertia. Copyright 2010 Pearson Education, Inc.

6 5-2 Newton s First Law of Motion In order to change the velocity of an object magnitude or direction a net force is required. An inertial reference frame is one in which the first law is true. Accelerating reference frames are not inertial. Copyright 2010 Pearson Education, Inc.

7 Question 5.1a A book is lying at rest on a table. The book will remain there at rest because: Newton s First Law I a) there is a net force but the book has too much inertia b) there are no forces acting on it at all c) it does move, but too slowly to be seen d) there is no net force on the book e) there is a net force, but the book is too heavy to move

8 Question 5.1a A book is lying at rest on a table. The book will remain there at rest because: Newton s First Law I a) there is a net force but the book has too much inertia b) there are no forces acting on it at all c) it does move, but too slowly to be seen d) there is no net force on the book e) there is a net force, but the book is too heavy to move There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force.

9 Question 5.1b Newton s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero

10 Question 5.1b Newton s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck. Follow-up: Are there any forces acting on the puck? What are they?

11 Question 5.1c You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? Newton s First Law III a) a net force acted on it b) no net force acted on it c) it remained at rest d) it did not move, but only seemed to e) gravity briefly stopped acting on it

12 Question 5.1c You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? Newton s First Law III a) a net force acted on it b) no net force acted on it c) it remained at rest d) it did not move, but only seemed to e) gravity briefly stopped acting on it The book was initially moving forward (because it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state of motion, and therefore it slid forward off the seat. Follow-up: What is the force that usually keeps the book on the seat?

13 5-3 Newton s Second Law of Motion Two equal weights exert twice the force of one; this can be used for calibration of a spring: Copyright 2010 Pearson Education, Inc.

14 5-3 Newton s Second Law of Motion Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force: Copyright 2010 Pearson Education, Inc.

15 5-3 Newton s Second Law of Motion Acceleration is inversely proportional to mass: Copyright 2010 Pearson Education, Inc.

16 5-3 Newton s Second Law of Motion Combining these two observations gives Or, more familiarly, Copyright 2010 Pearson Education, Inc.

17 5-3 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: (5-1) Copyright 2010 Pearson Education, Inc.

18 5-3 Newton s Second Law of Motion Copyright 2010 Pearson Education, Inc.

19 Copyright 2010 Pearson Education, Inc.

20 Copyright 2010 Pearson Education, Inc.

21 Question 5.4a Off to the Races I From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only ½ F, how long would it have to be applied to reach the same final speed? a) 16 s b) 8 s c) 4 s d) 2 s e) 1 s F v

22 Question 5.4a From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only ½ F, how long would it have to be applied to reach the same final speed? Off to the Races I a) 16 s b) 8 s c) 4 s d) 2 s e) 1 s In the first case, the acceleration acts over time T = 4 s to give velocity v = at. In the second case, the force is half, therefore the acceleration is also half, so to achieve the same final speed, the time must be doubled. v F

23 ConcepTest 5.4b Off to the Races II From rest, we step on the gas of our Ferrari, providing a force F for 4 secs. During this time, the car moves 50 m. If the same force would be applied for 8 secs, how much would the car have traveled during this time? a) 250 m b) 200 m c) 150 m d) 100 m e) 50 m F v

24 ConcepTest 5.4b Off to the Races II From rest, we step on the gas of our a) 250 m Ferrari, providing a force F for 4 secs. b) 200 m During this time, the car moves 50 m. If the same force would be applied for c) 150 m 8 secs, how much would the car have d) 100 m traveled during this time? e) 50 m In the first case, the acceleration acts over time T = 4 s to give a distance of x = 2aT 2 (why is there no v 0 T term?). In the 2nd case, the time is doubled, so the distance is quadrupled because it goes as the square of the time. F1v

25 5-3 Newton s Second Law of Motion Free-body diagrams: A free-body diagram shows every force acting on an object. Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components Apply Newton s second law to each coordinate direction Copyright 2010 Pearson Education, Inc.

26 5-3 Newton s Second Law of Motion Example of a free-body diagram: Copyright 2010 Pearson Education, Inc.

27 5-4 Newton s Third Law of Motion Forces always come in pairs, acting on different objects: If object 1 exerts a force F r on object 2, then object 2 exerts a force F r on object 1. These forces are called action-reaction pairs. Copyright 2010 Pearson Education, Inc.

28 5-4 Newton s Third Law of Motion Some action-reaction pairs: Copyright 2010 Pearson Education, Inc.

29 5-4 Newton s Third Law of Motion Although the forces are the same, the accelerations will not be unless the objects have the same mass. Contact forces: The force exerted by one box on the other is different depending on which one you push. Copyright 2010 Pearson Education, Inc.

30 Question 5.9a A small car collides with a large truck. Which experiences the greater impact force? Collision Course I a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each

31 Question 5.9a A small car collides with a large truck. Which experiences the greater impact force? Collision Course I a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each According to Newton s Third Law, both vehicles experience the same magnitude of force.

32 Question 5.9b Collision Course II In the collision between the car and the truck, which has the greater acceleration? a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each

33 Question 5.9b Collision Course II In the collision between the car and the truck, which has the greater acceleration? a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, because it has the smaller mass.

34 Question 5.10a If you push with force F on either the heavy box (m 1 ) or the light box (m 2 ), in which of the two cases below is the contact force between the two boxes larger? Contact Force I a) case A b) case B c) same in both cases A F m 2 m 1 B m F m 1 2

35 Question 5.10a If you push with force F on either the heavy box (m 1 ) or the light box (m 2 ), in which of the two cases below is the contact force between the two boxes larger? Contact Force I a) case A b) case B c) same in both cases The acceleration of both masses together is the same in either case. But the contact force is the only force that accelerates m 1 in case A (or m 2 in case B). Because m 1 is the larger mass, it requires the larger contact force to achieve the same acceleration. Follow-up: What is the acceleration of each mass? A F m 2 m 1 B m F m 1 2

36 Question 5.10b Contact Force II Two blocks of masses 2m and m are in contact on a horizontal frictionless surface. If a force F is applied to mass 2m, what is the force on mass m? a) 2F b) F c) ½F d) 1 / 3 F e) ¼F F 2m m

37 Question 5.10b Contact Force II Two blocks of masses 2m and m a) 2F are in contact on a horizontal b) F frictionless surface. If a force F c) ½ F is applied to mass 2m, what is d) 1 / 3 F the force on mass m? e) ¼ F The force F leads to a specific acceleration of the entire system. In order for mass m to accelerate at the same rate, the force on it must be F 2m m smaller! How small?? Let s see... Follow-up: What is the acceleration of each mass?

38 Hint: draw free-body diagrams for both objects

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42 5-5 The Vector Nature of Forces: Forces in Two Dimensions The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics. Copyright 2010 Pearson Education, Inc.

43 Newton s Second Law r a r F r = or F = m r ma F = ma F = ma F = ma x x y y z z Newton s laws can be applied to each component of the forces independently Copyright 2010 Pearson Education, Inc.

44 Summary of Chapter 5 Force: a push or pull Mass: measures the difficulty in accelerating an object Newton s first law: if the net force on an object is zero, its velocity is constant Inertial frame of reference: one in which the first law holds Newton s second law: Free-body diagram: a sketch showing all the forces on an object Copyright 2010 Pearson Education, Inc.

45 Summary of Chapter 5 Newton s third law: If object 1 exerts a force F r on object 2, then object 2 exerts a force F r on object 1. Contact forces: an action-reaction pair of forces produced by two objects in physical contact Forces are vectors Newton s laws can be applied to each component of the forces independently Copyright 2010 Pearson Education, Inc.