Chapter 5 Newton’s Laws of Motion

Announcements, 9/24 Homework due Friday, 10 PM Next Readiness Quiz: Chapter 6, Monday Extra Credit Opportunity: Street Corner Science! –Look at news item on eLearn, follow the link to two videos. In them, a Nobel Laureate sits on a street corner and answers science questions. Pick the question / answer that is most interesting, do a little more internet research, and write a 250+ word summary of the topic in your own words. Post the file in the dropbox labeled "Street Corner Science".

Units of Chapter 5 Force and Mass 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

5-1 Force and Mass Force: push or pull Force is a vector – it has magnitude and direction

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.

Identifying Forces The first thing to do with force problems is be able to identify the forces Every problem is divided into the system and the environment Every force must have an agent –An identifiable cause in the environment –Not necessarily a person!!! Almost every force is a contact force –Agent must physically touch the system –Gravity is one of the only exceptions

Identifying Forces - Procedure Divide the problem into “the system” and “the environment” –The system is just the thing whose motion you want to study, the environment is everything else Draw a picture of the problem, showing the object and everything in the environment that touches the object. Ropes, springs, surfaces and so on are part of the environment Draw a closed curve around the system, with the object inside the curve and everything else (mostly) outside the curve.

Identifying Forces - Procedure Locate every point on the boundary of this curve where the environment touches or contacts the system. These are the points where the environment exerts contact forces on the object. Don’t forget any! Identify by name the contact force or forces (there are probably more than one!) at each point of contact, then give each an appropriate symbol. Identify any long range forces acting on the object. Name the force, and write a symbol for it beside your picture

Standard Names for Some Forces The force due to gravity: Weight, often called The push up on things by floor/ground: Normal Force, often called Force of friction, often called Pull by a rope/string: Tension, often called

Examples System Everything else is the environment System

Group Exercise A car is pulled up a slope by a chain. Friction is present. Draw a sketch, and identify the forces on the car.

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.

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. 5-2 Newton’s First Law of Motion

ConcepTest 5.1aNewton’s First Law I ConcepTest 5.1a Newton’s First Law I 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because:

There are forces acting on the book leaving no net force 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. ConcepTest 5.1aNewton’s First Law I ConcepTest 5.1a Newton’s First Law I 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because:

ConcepTest 5.1bNewton’s First Law II ConcepTest 5.1b Newton’s First Law II 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero A hockey puck slides on ice at constant velocity. What is the net force acting on the puck?

constant velocity not accelerating no net force 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. ConcepTest 5.1bNewton’s First Law II ConcepTest 5.1b Newton’s First Law II 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? Follow-up: Are there any forces acting on the puck? What are they?

Newton’s First Law IV 1) the force pushing the stone forward finally stopped pushing on it 2) no net force acted on the stone 3) a net force acted on it all along 4) the stone simply “ran out of steam” 5) the stone has a natural tendency to be at rest You kick a smooth flat stone out on a frozen pond. The stone slides, slows down and eventually stops. You conclude that:

some forceto slow it down and stop it After the stone was kicked, no force was pushing it along! However, there must have been some force acting on the stone to slow it down and stop it. This would be friction!! Newton’s First Law IV 1) the force pushing the stone forward finally stopped pushing on it 2) no net force acted on the stone 3) a net force acted on it all along 4) the stone simply “ran out of steam” 5) the stone has a natural tendency to be at rest You kick a smooth flat stone out on a frozen pond. The stone slides, slows down and eventually stops. You conclude that: Follow-up: What would you have to do to keep the stone moving?

5-3 Newton’s Second Law of Motion Acceleration is proportional to force:

Announcements, 9/26 Homework due tonight, 10 PM Group Office Hours this afternoon, 1:30 PM, Room 139 Next Readiness Quiz: Chapter 6, due Monday

5-3 Newton’s Second Law of Motion Acceleration is inversely proportional to mass:

5-3 Newton’s Second Law of Motion Combining these two observations gives In words: acceleration equals net force over mass Or,

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)

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

5-3 Newton’s Second Law of Motion Example of a free-body diagram:

5-3 Newton’s Second Law of Motion A more complicated problem:

Practice

5-4 Newton’s Third Law of Motion 1. Every force occurs as one member of a pair of interaction forces 2. The two members of a pair of interaction forces act on two different objects. 3. The two members of an interaction pair are equal in magnitude but opposite in direction. Or, These forces are called action-reaction pairs.

5-4 Newton’s Third Law of Motion Some action-reaction pairs:

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.

Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down

When you pull down on the rope, the rope pulls up on you!! reaction rope on youyou exerted on the rope When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the “reaction” force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton’s 3 rd Law. Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down

Collision Course I A small car collides with a large truck. Which experiences the greater impact force? 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each

Collision Course I A small car collides with a large truck. Which experiences the greater impact force? 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each According to Newton’s 3 rd Law, both vehicles experience the same magnitude of force.

1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each In the collision between the car and the truck, which has the greater acceleration? Collision Course II

1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each In the collision between the car and the truck, which has the greater acceleration? Collision Course II F/mcar larger acceleration smaller mass 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, since it has the smaller mass.

Announcements, 9/29 Quiz Wednesday: On forces / free-body diagrams. Will be similar to the first example we do in class today and Example 5-4 in the book Homework due Friday, Chapter 5

Example A force of magnitude 7.50 N pushes three boxes with masses m 1 = 1.30 kg, m 2 = 3.20 kg and m 3 = 4.90 kg as shown in the figure. Find the magnitude of the contact force (a) between boxes 1 and 2, and (b) between boxes 2 and 3. Ignore friction

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.

Example Two adults and a child want to push a wheeled cart in the direction marked x in the figure below. The two adults push with forces F 1 and F 2 as shown in the figure. (a) Find the magnitude and direction of the smallest force that the child should exert to move the cart in the x direction only. (b) If the child exerts the minimum force found in part (a), the cart accelerates at 2.0 m/s 2 in the +x direction. What is the weight of the cart?

5-6 Weight The weight of an object on the Earth’s surface is the gravitational force exerted on it by the Earth.

Announcements, 10/1 Homework due Friday Next Readiness Quiz: Chapter 7 (Note this is different than in syllabus) New Extra Credit Opportunity: Lecture abut Dr. King, Humanities Auditorium, Wed Oct 8 th, 12:40 pm –Attend lecture, write a 250 word essay about what you learned, and what it meant to you

5-6 Weight If your surroundings are accelerating, your apparent weight may be more or less than your actual weight.

5-7 Normal Forces The normal force is the force exerted by a surface on an object.

5-7 Normal Forces The normal force may be equal to, greater than, or less than the weight.

5-7 Normal Forces The normal force is always perpendicular to the surface.

ConcepTest 5.14Normal Force ConcepTest 5.14 Normal Force Case 1 Case 2 Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle . In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface

down in addition to mg larger up lessened In Case 1, the force F is pushing down (in addition to mg), so the normal force needs to be larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. ConcepTest 5.14Normal Force ConcepTest 5.14 Normal Force Case 1 Case 2 Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle . In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface

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

Summary of Chapter 5 Newton’s third law: If object 1 exerts a force F on object 2, then object 2 exerts a force –F 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 Weight: gravitational force exerted by the Earth on an object

Summary of Chapter 5 On the surface of the Earth, W = mg Apparent weight: force felt from contact with a floor or scale Normal force: force exerted perpendicular to a surface by that surface Normal force may be equal to, lesser than, or greater than the object’s weight