Chapter 5: Forces andNewton’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 ofmechanics – dynamics - which does address the cause of motion- that cause is a force, a push or pull Force, , is a vector, has magnitude and direction How forces affect the motion of an object is describedby Newton’s Laws of Motion (Newtonian Mechanics) Objects are treated as point particles; in Chapter 10 wewill consider the shape of an object in more detail € r FNewton’s First Law of Motion An object at rest will remain at rest An object moving at a constant velocity will continue tomove at the constant velocity, unless acted upon by a netforce What does it mean?- tendency for an object’s motion not to change Net force = the sum of all applied forces0321=++=∑iiFFFFrrrr- No effect on the motion € r F 1 € r F 2 € r F 3According to the 1st law, zero velocity (at rest) isequivalent to constant velocityAn object with a constant velocity does not require aforce to maintain its velocity- forces act to change motion, not to sustain themotion (e.g., the speed of the Voyagers)- seems contrary to everyday experience Inertia – tendency for an object to remain at rest, or toremain 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 (anacceleration) € r F ii∑=r F ∑= mr a 1st law implies the 2nd law Meaning: if a net external force acts on an object ofmass m, it will be accelerated and the direction of theacceleration will be in the same direction as the netforce € r a =r F ∑mF1F2F3ΣFaDemo 8.2.2Eq. (5.1)All forces in Newton’s second law areexternal – a force exerted on an objectby some outside agentUnits: F=ma [mass][L/T2]->(kg)(m/s2)=N, Newton- The Newton is a derived unit- In British units, force is given by the lband mass is given by the slug-> slug=lb s2/ftThe Free Body Diagram (FBD) A schematic representation of an object and allthe external forces that act upon it Always draw in every problem!!!! From Newton’s 2nd law: € r F = mr a = 0∑r F G+r F table= 0r F table= −r F G € r F GtableFrBook atrest onthe tableFundamental Types of Forces1. Gravitational2. Electromagnetic – (electric and magnetic)3. Weak Nuclear4. Strong NuclearElectroweakWe will only consider the first twoGravitational ForceFrom our studies of free-fall motion and projectilemotion gravity causes an object to accelerate in thenegative y-direction€ r a y= −g ˆ y yApply thesecond lawym € r F G= −mg √ y This is only an approximation which holds only near thesurface 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 UniversalGravitation (the subject of Chapter 12(?))Example Problem Three forces acting on an object aregiven by =(-2.00 + 2.00 ) N, =(5.00– 3.00 ) N, and =-45.0 N. The objectexperiences an acceleration of magnitude3.75 m/s2. (a) What is the direction ofacceleration? (b) What is the mass of theobject? (c) If the object is initially at rest,what is its speed after 10.0 s? (d) Whatare the velocity components of the objectafter 10.0 s?€ i€ ˆ i € ˆ i € r F 1 € r F 2 € r F 3€ ˆ j € ˆ
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