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Newton’s First Law

Learn about Newton's First, Second, and Third Laws of Motion, their mathematical statements, and their practical applications in physics. Explore the concepts of inertia, mass, force, acceleration, and action-reaction pairs. Discover how to solve problems using Newton's laws.

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Newton’s First Law

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  1. Newton’s First Law Mathematical Statement of Newton’s 1st Law: If v = constant, ∑F = 0 OR if v ≠ constant, ∑F ≠ 0

  2. Mass (Inertia) • Inertia Thetendency of a body to maintain its state of rest or motion. • MASS:Property of an object that specifies how much resistance an object exhibits to changes in it’s velocity. • A measure of the inertia of a body • Quantity of matter in a body • A scalar quantity • Quantify mass by having a standard mass =Standard Kilogram (kg)(Similar to standards for length & time). • SI Unit of Mass = Kilogram (kg) • cgs unit = gram (g) = 10-3 kg • Weight: (NOT the same as mass!) The force of gravity on an object.

  3. Newton’s Second Law(Lab) • 1st Law:If no net force acts, object remains at rest or in uniform motion in straight line. • What if a net force acts? DoExperiments. • Find, if the net force ∑F  0  Thevelocity v changes(in magnitude or direction or both). • A change in the velocity v (dv)  There is an acceleration a = (dv/dt) OR A net force acting on an object produces an acceleration!∑F  0  a

  4. Newton’s 2nd Law • Experiment:The net force ∑F on an object & the acceleration aof that object are related. • HOW? Answer by EXPERIMENTS! • Thousands of experiments over hundreds of years find (object of massm) : a  (∑F)/m(proportionality) • Choose the units of force so that this is not just a proportionality but an equation: a  (∑F)/m OR: (total force!) ∑F = ma

  5. Newton’s 2nd Law:∑F = ma ∑F = the net (TOTAL!) force acting on massm m= the mass (inertia) of the object. a = acceleration of the object. Description of the effect of ∑F.∑F is the cause of a. ∑F = ma The Vector Sum of All Forces Acting on Mass m!

  6. Based on experiment! Not derivable mathematically!! • Newton’s 2nd Law: ∑F = ma AVECTOR equation!! Holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!

  7. 2nd Law • Force = an action capable of accelerating an object. • Units of force: SI unit = the Newton (N) • ∑F = ma , units = kg m/s2  1N = 1 kg m/s2

  8. See Figure:A hockey puck, mass m = 0.3 kg, slides on the horizontal, frictionless surface of an ice rink.  Two hockey sticks strike the puck simultaneously, exerting forces F1 & F2 on it. Calculate the magnitude & direction of the acceleration. Example 5.1: Accelerating Hockey Puck 1.Sketch the force diagram (“Free Body Diagram”). 2.Choose a coordinate system. 3.Resolve Forces (find components) along x & y axes. 4.Write Newton’s 2nd Law equations x & y directions. 5.Use Newton’s 2nd Law equations & algebra to solve for unknowns in the problem. x & y directions. Steps to Solve the Problem

  9. Example

  10. Sect. 5.5: Gravitational Force & Weight • Weight  Force of gravity on an object. Varies (slightly) from location to location because g varies. Write as Fg  mg. (Read discussion of difference between inertial mass & gravitational mass). • Consider an object in free fall. Newton’s 2nd Law: ∑F = ma • If no other forces are acting, only Fg  mg acts (in vertical direction). ∑Fy = may or Fg = mg(down, of course) • SI Units: Newtons(just like any force!). g = 9.8 m/s2  If m = 1 kg, Fg = 9.8 N

  11. Newton’s 3rd Law • 2nd Law:A quantitative description of how forces affect motion. • BUT: Where do forces come from? • EXPERIMENTSFind: Forces applied to an object are ALWAYS applied byanotherobject.  Newton’s 3rd Law:“Whenever one object exerts a force F12 on a second object, the second object exerts an equal and opposite force -F12 on the first object.” • Law of Action-Reaction: “Every action has an equal & opposite reaction”. (Action-reaction forces act on DIFFERENTobjects!)

  12. “If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude & opposite in direction to the force F21 exerted by object 2 on object 1.” As in figure Another Statement of Newton’s 3rd Law

  13. Example: Newton’s 3rd Law

  14. Action-Reaction Pairs: On Different Bodies

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