Chapter 5 Forces and Newton s Laws of Motion Previously we have studied kinematics which describes the motion of an object x v a does not explain the cause of the motion Now we begin the study of the second part of mechanics dynamics which does address the cause of motion that cause is a force a push or pull r Force F is a vector has magnitude and direction How forces affect the motion of an object is described by Newton s Laws of Motion Newtonian Mechanics Objects are treated as point particles in Chapter 10 we will consider the shape of an object in more detail Newton s First Law of Motion An object at rest will remain at rest An object moving at a constant velocity will continue to move at the constant velocity unless acted upon by a net force What does it mean tendency for an object s motion not to change Net force the sum of all applied forces r r r r Fi F1 F2 F3 0 r F2 i No effect on the motion r F1 r F3 According to the 1st law zero velocity at rest is equivalent to constant velocity An object with a constant velocity does not require a force to maintain its velocity forces act to change motion not to sustain the motion e g the speed of the Voyagers seems contrary to everyday experience Inertia tendency for an object to remain at rest or to remain in motion with a constant velocity all objects have inertia Mass a quantitative measure of inertia a scalar use symbol m unit is kg SI or slug British more mass means more inertia not equivalent to weight a force Newton s Second Law of Motion If there is a net force there is a change in velocity an acceleration r r r Fi F ma Eq 5 1 i 1st law implies the 2nd law Meaning if a net external force acts on an object of mass m it will be accelerated and the direction of the acceleration will be in the same direction as the net r force F F r a F m 1 F3 F2 a Demo 8 2 2 All forces in Newton s second law are external a force exerted on an object by some outside agent Units F ma mass L T2 kg m s2 N Newton The Newton is a derived unit In British units force is given by the lb and mass is given by the slug slug lb s2 ft The Free Body Diagram FBD A schematic representation of an object and all the external forces that act upon it Always draw in every problem From Newton s 2nd law r r F ma 0 r r FG Ftable 0 r r Ftable FG r Ftable r FG Book at rest on the table Fundamental Types of Forces 1 Gravitational 2 Electromagnetic electric and magnetic 3 Weak Nuclear Electroweak 4 Strong Nuclear We will only consider the first two Gravitational Force From our studies of free fall motion and projectile motion gravity causes an object to accelerate in the negative y direction y r ay g y y Apply the second law m r FG mg y This is only an approximation which holds only near the surface of the Earth as g is only constant near the surface But a good approximation We would like a more fundamental description of gravity g is an empirical number physicists don t like empirical numbers This lead Newton to devise his Law of Universal Gravitation the subject of Chapter 12 Example Problem Three forces r acting on an object rare j N F 5 00 i i given by F1 2 00 2 00 r 2 3 00 j N and F3 45 0 i N The object experiences an acceleration of magnitude 3 75 m s2 a What is the direction of of the acceleration b What is the mass object is initially at rest object c If the what is its speed after 10 0 s d What are the velocity components of the object after 10 0 s
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