Newton’s First Law

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