Intermediate Physics PHYS 151
Christopher Newport University
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This 12 page Class Notes was uploaded by Bart Thiel Jr. on Monday October 5, 2015. The Class Notes belongs to PHYS 151 at Christopher Newport University taught by Costa Gerousis in Fall. Since its upload, it has received 49 views. For similar materials see /class/219493/phys-151-christopher-newport-university in Physics 2 at Christopher Newport University.
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Date Created: 10/05/15
Chapter 5 Newton s Laws of Motion Chapter 5 Newton s Laws of Motion We will study classical motion No quantum mechanics No relativity We introduce the concept of force and define it in terms of the acceleration of a standard body Intuitively we know that force is a push or pull Forces come in different classes types I Contact I Macroscopic forces of contact friction viscosity the contact force from the oor supporting my feet I Field originally described as action at a distance I Examples Gravity Electromagnetism Force F is a vector quantity You push or pull in a specific direction F If force has direction what is it s measure The Empirical Feel of Forces We have a direct sensation of the forces that act on our body I As I stand on the oor I feel my shoes pushing up on my feet The nerves in the soles of my feet transmit this feeling to my brain I The nerves in our joints also give us a sense of the weight of our bodies I If you hit your toe or worse you feel the force against your toe What is the connection between Force and Motion Dynamics The ancient Greeks especially Aristotle had a very elegant philosophy of nature I Four elements Earth Air Fire Water I Two Forces Gravity Levity I Gravity pulled earth and water down Levity pushed Fire and Air up To Aristotle and perhaps to our common sense everything tended to its natural state For material obj ects earth amp water the natural state was at rest I To use modern language friction was seen as part of the fabric of space time c It was Galileo who suggested that friction was not essential but rather subject to technological manipulation and ideally elimination In 1686 Newton presented The Laws of Motion Newton s First Law An object at rest remains at rest and an object in motion continues in motion with constant velocity unless it experiences a net force Velocity constant acceleration 0 if there is no force or if all forces add to zero Remember Velocity constant does not mean velocity 0 LAN 4 Examples An object that is moving and that continues to move with constant velocity without any force acting on it A hockey puck sliding almost without friction across the ice An object at rest that remains at rest What about pushing a chair If the floor pushes just as hard friction the net force vector sum is zero What happens when you turn a comer quickly in your car The car would continue straight ahead unless the friction from the road pushes inwards to guide the car around the circle We know from experience that different objects resist a change in motion differently Example push a door push a semitrailer gt Not the same response Inertia The tendency of an object to resist a change in its velocity is called inertia The measure of inertia is mass I SI units measure mass as multiples of the standard kilogram kg1000g stored at the International Bureau of Weights and Measures in sevres France Newton s First Law tells us about motion if F 0 What if F at 0 Newton s Second Law The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass The direction of the acceleration is the direction of the resultant force Fma FNet ma Implicit and explicit meaning Force is a vector I The net force is the vector sum of all forces acting on the object In Mass is a scalar I The value of the mass of an object does not change with the direction of the acceleration Mass is invariant I If two objects are put together or separated the mass of the combined object is simply the arithmetic sum of the two masses m m1m2i I Chemical combination welding cutting does not change mass 0 Einstein corrected this but Relativistic effects are small for ordinary matter Force can be quantified by measuring the acceleration it produces on a standard kilogram or any multiple there of Example An object of mass 5 kg undergoes an acceleration of 8 ms2 9 8 ms2 in y direction What is the force on that object F ma 5 kg8 msz 9 40 lltgms2 9 9 vector on unit length no dimensions in y direction The force is in the same direction as the acceleration Units The SI unit of Force is the Newton defined as 1 N 1 kgms2 Notice pounds and kilograms do not directly convert The British unit of mass is the slug don t ask The force of gravity near Earth s surface acting on a 1 kg mass is 22 1hr 10 kg g 22111 Do not confuse ggram with g9i8mls2acceleration due to gravity Problem 1 A catcher stops a 92 mih pitch in his glove bringing it to rest with uniform deceleration in 015 m If the force exerted by the catcher is 803 N what is the mass of the ball 1 mi 21609 m Newton s Third Law If object 1 exerts a force F on object 2 then object 2 exerts a force F on object 1 I Forces come in pairs I The force pairs act on different objects I The forces have the same magnitude but opposite direction Example I push on the wall with a force of 20 N The wall pushes back on me with a force of 20 N in the opposite direction Problem 2 A force of magnitude 750 N pushes three boxes with masses m1 130 kg m2 320 kg and m3 490 Kg as shown in the Figure crucial assumption omitted in the problem no friction Find the contact force between a boxes 1 and 2 and b between boxes 2 and 3 z 7 aF21 F12 646 N b F23 F32 391 N A MAC truck and a Honda Civic have a head on collision Which vehicle experiences the greatest force Which vehicle experiences the greater acceleration The Vector Nature of Forces In the formula F ma F is the total net force acting on the object We must consider the vector sum of all forces acting on an object We can also consider each dimension separately 2 F x 2 ma x sz may 2FZ maZ Problem 3 A farm tractor tows a 4400 kg trailer up a 21 incline at a steady speed of 30 ms What force does the tractor exert on the trailer Ignore friction Weight The weight of any object on the Earth is the gravitational force exerted on it by the Earth W mg Note Weight is a force and therefore a vector Weight is not equivalent to mass Can a person s weight be zero When we say we want to lose weight what do we really mean 10 Apparent Weight Our sensation of weight comes from the force of the floor pushing up on us We can feel light or heavy if the floor is accelerating down or up The upward force of the floor on our feet is known as apparent weight Wag Physical picture It is your apparent weight that is measured on a scale Problem 4 As part of a physics experiment you stand on a bathroom scale in an elevator Though your normal weight is 610 N the scale at the moment reads 730 N a Is the acceleration of the elevator upward downward or zero b Calculate the magnitude of the elevator s acceleration ll Normal Forces Normal means perpendicular The normal force is a contact force and is perpendicular to the surface between the two objects in contact The table and the box are compressing each other s atoms slightly like springs The box pushes down on the table and the table pushes up on the box These two forces are reaction pairs If you lean against the wall the normal force from the wall is horizontal When the cart rolls down the incline in your physics lab the normal force is perpendicular to the incline Motion on an Incline Frictionless Xx Cart rolls without friction on incline Find the acceleration of the cart as a function of 6 o o 0 Draw a coordinate system parallel to incline N Free Body Diagram xycornponents of gravity OI quot N y mg 0 I WX rmg sin9 I Wy rmg cos9 12
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