15 N 5 N. Chapter 4 Forces and Newton s Laws of Motion. The net force on an object is the vector sum of all forces acting on that object.

Transcription

1 Chapter 4 orce and ewton Law of Motion Goal for Chapter 4 to undertand what i force to tudy and apply ewton irt Law to tudy and apply the concept of a and acceleration a coponent of ewton Second Law to learn ewton law of gravitation to differentiate between a and weight to tudy and apply ewton Third Law to be able to ue free body diagra to olve proble The concept of force and a A force i a puh or a pull. Contact force arie fro phyical contact. Action-at-a-ditance force do not require contact and include gravity and electrical force. Arrow are ued to repreent force (vector). The length of the arrow i proportional to the agnitude of the force. ewton firt law of otion The net force on an object i the vector u of all force acting on that object. The SI unit of force i the ewton (). Individual orce et orce Concept of force and a Individual orce 3 et orce 5 64 Dynaic, a new frontier A we entioned earlier, Mechanic can be divided into two ditinct part: Kineatic ( how object ove? ) Dynaic ( why object ove? ) 4 Ma i a eaure of the aount of tuff contained in an object. o, if oething accelerate, what caue it to accelerate? a force i the caue it i either puhing or pulling An object ove at contant velocity doe not require any force to keep it oving that way. Iaac ewton ( )

2 ewton irt Law We deterine the effect of the net force An object continue in a tate of ret or in a tate of otion at a contant peed along a traight line, unle it i forced to change that tate by a net force acting on it. If net force = 0 then velocity v = 0 or v = cont. The net force i the vector u of all of the force acting on an object. The reaon that ot object in otion tend to low down i due to the external frictional force equilibriu et i i 0 Relation between force and acceleration? Ye! nd law Inertia and Ma Inertia i the natural tendency of an object to reain at ret in otion at a contant peed along a traight line. The a of an object i a quantitative eaure of inertia. SI Unit of Ma: kilogra (kg) Inertial Reference rae An inertial reference frae i one in which ewton law of inertia i valid. All accelerating reference frae are noninertial. The earth i approxiately an inertial reference frae. An accelerating airplane i not an inertial reference frae. A erry-go-around i not an inertial reference frae. Any reference frae which ove with contant velocity to an inertial frae i alo an inertial frae. Inertial reference frae and non-inertial reference frae... The label depend on whether ewton 1 t law applie or not Concept of a force A we can ee fro our everyday experience there i a relation between force and otion Every reference frae which i oving with contant velocity relative to an inertial frae i alo an inertial reference frae. Thu there i no ingle inertial frae which i preferred over other. We ee that a force i required to change the tate of otion of an object

3 ewton econd law of otion When a net external force act on an object of a, the acceleration that reult i directly proportional to the net force and ha a agnitude that i inverely proportional to the a. The direction of the acceleration i the ae a the direction of the net force. a a kg kg SI Unit for orce Thi cobination of unit i called a newton (). Ma and ewton Second Law or a given object, the ratio of the agnitude of the force to the agnitude of the acceleration a i contant. We call thi ratio the inertial a. In other word: When a force with agnitude act on an object with a the agnitude of the acceleration a i: a Inertial: reit being accelerated 1-d VECTOR! a Exaple in 1-d : A box on ice A worker with pike on hi hoe pull with contant horizontal force of agnitude 0 on a box with a 40 kg reting on the flat, frictionle urface of a frozen lake. What i the acceleration of the box? x a x a x x 0 40kg x kg 0 40kg 0.5 ewton Second Law What i a force? A orce i a puh or a pull. A orce ha agnitude & direction Adding force i like adding vector. a 1 1 a ET ET VECTOR! a Exaple: Puhing a talled car Two people are puhing a talled car. The a of the car i 1850 kg. One peron applie a force of 75 to the car, while the other applie a force of 395. Both force are in the ae direction. A third force of 560 (due to friction) alo act on the car, but in the oppoite direction. ind the acceleration of the car. The net force in thi cae i: A free-body-diagra i a diagra that repreent the object and the force that act on it = +110 and i directed along the + x axi of the coordinate yte. If the a of the car i 1850 kg then, by ewton econd law, the acceleration i 110 a kg

4 Thi iage cannot currently be diplayed. A force ay be reolved into coponent The direction of force and acceleration vector can be taken into account by uing x and y coponent. a y a y i equivalent to x ax Exaple: The vector nature of ewton econd law A an tranded in a raft (a of an and raft = 1300 kg) caue an average force of 17 to the raft in a direction due eat ( + x direction). The wind exert a force of agnitude 15 which i pointing 67 o north of eat. Ignoring any reitance fro the water find the x- and y- coponent of the raft acceleration. Ue vector coponent The net force on the raft can be calculated in the following way: ewton Third Law orce 1 x coponent +17 +(15 ) co67 y coponent 0 +(15 ) in67 a a x y net x y kg kg An interacting ball and foot exert force on each other that are equal in agnitude and oppoite in direction Whenever one body exert a force on a econd body, the econd body exert an oppoitely directed force of equal agnitude on the firt body. Rifle recoil i a good exaple ewton Third Law 1 ay be called the action force and 1 the reaction force Actually, either force can be the action or the reaction force The action and reaction force act on different object orce: Haer - ail are oppoite in direction and equal in agnitude ewton Third Law or two interacting object A and B, the foral tateent of ewton third law i A on B Bon A You can not add action and reaction force together, becaue they are two force on two different object.

5 Thi iage cannot currently be diplayed. ewton Third Law There i a book on a table. The book exert a force P on the table. The table exert a force on the book. The earth exert a force g on the book. The book exert a force GM/r on the earth. Which force i the reaction force for? Exaple: ewton third law of otion g P GM/r Which force i the reaction force for g? Suppoe that the agnitude of the force i 36. If the a of the pacecraft i 11,000 kg and the a of the atronaut i 9 kg, what are the acceleration? ewton third law of otion P a P aa A 36 11,000 kg On the pacecraft On the atronaut 36 9 kg P. P. or two interacting object A and B, the foral tateent of ewton third law i A on B B on A Reaction pair are between two object, but for the otion of one object we have to conider force action on one object How can hore and cart tart oving? Look at net force on the hore Backward-pointing force of the cart and forward-pointing force that the road exert on hore. Thee two force are not part of an action-reaction pair, and thu can have different agnitude. 4.6 Different type of force undaental and non-fundaental force undaental orce 1. Gravitational force. Strong uclear force 3. Electroweak force (Electroagneti and weak force unified) Exaple of non-fundaental force - friction - tenion in a rope - noral or upport force

6 Thi iage cannot currently be diplayed. 4.7 The gravitational force undaental orce ewton Law of Gravitation Gravitational force i alway attractive. Directly proportional to the ae involved. Inverely proportional to the quare of the eparation between the ae. Mae ut be large to bring g to a ize even cloe to huanly perceptible force. ewton Law of Gravitation g i a vector along a line joining the center of the ae G r 1 Central force or two particle that have ae 1 and and are eparated by a ditance r, the force ha a agnitude given by attractive G kg ewton Law of Gravitation: Exaple 5 How to eaure the gravitational contant G The light attraction of the ae caue a nearly iperceptible rotation of the tring upporting the ae connected to the irror. Ue of the laer allow a point any eter away to ove through eaurable ditance a the angle allow the initial and final poition to diverge. G r kg 5 kg kg

7 4.7 The Gravitational orce Definition of Weight The weight of an object near the urface of the earth i the gravitational force that the earth exert on the object. The weight alway act downward, toward the center of the earth. 4.8 The oral orce Definition of the oral orce The noral force i one coponent of the force that a urface exert on an object with which it i in contact naely, the coponent that i perpendicular to the urface. On or above another atronoical body, the weight i the gravitational force exerted on the object by that body. SI Unit of Weight: newton () 4.8 The oral orce The oral orce Apparent Weight The apparent weight of an object i the reading of the cale. It i equal to the noral force the cale exert on the an The oral orce g a y g a 4.9 Static and Kinetic rictional orce When an object i in contact with a urface there i a force acting on that object. The coponent of thi force that i parallel to the urface i called the frictional force. apparent weight true weight

8 Thi iage cannot currently be diplayed. 4.9 Static and Kinetic rictional orce 4.9 Static and Kinetic rictional orce The agnitude of the tatic frictional force can have any value fro zero up to a axiu value. When the two urface are not liding acro one another the friction i called tatic friction. f MAX f f MAX 0 1 i called the coefficient of tatic friction. 4.9 Static and Kinetic rictional orce ote that the agnitude of the frictional force doe not depend on the contact area of the urface. 4.9 Static and Kinetic rictional orce Static friction oppoe the ipending relative otion between two object. Kinetic friction oppoe the relative liding otion otion that actually doe occur. f k k 0 1 i called the coefficient of kinetic friction. 4.9 Static and Kinetic rictional orce 4.9 Static and Kinetic rictional orce The led coe to a halt becaue the kinetic frictional force oppoe it otion and caue the led to low down.

9 4.9 Static and Kinetic rictional orce 4.10 The Tenion orce Cable and rope tranit force through tenion. Suppoe the coefficient of kinetic friction i 0.05 and the total a i 40kg. What i the kinetic frictional force? f k 0.05 k g k 40kg The Tenion orce A ale rope will tranit tenion undiinihed fro one end to the other. If the rope pae around a ale, frictionle pulley, the tenion will be tranitted to the other end of the rope undiinihed Equilibriu Application of ewton Law of Motion Definition of Equilibriu An object i in equilibriu when it ha zero acceleration. 0 x 0 y 4.11 Equilibriu Application of ewton Law of Motion Reaoning Strategy 4.11 Equilibriu Application of ewton Law of Motion Select an object() to which the equation of equilibriu are to be applied. Draw a free-body diagra for each object choen above. Include only force acting on the object, not force the object exert on it environent. Chooe a et of x, y axe for each object and reolve all force in the free-body diagra into coponent that point along thee axe. Apply the equation and olve for the unknown quantitie. T1 in 35 T in 35 0 T1 co35 T co35 0

10 4.11 Equilibriu Application of ewton Law of Motion 4.11 Equilibriu Application of ewton Law of Motion orce x coponent y coponent T 1 T W T 1 in10.0 T in T 1 co10.0 T co80.0 W W 3150 Suary orce add a vector Inertial reference frae ET a ewton law of gravitation 1 g G r