Presentation on theme: "Newton’s First Law Mathematical Statement of Newton’s 1st Law:"— Presentation transcript:
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 The tendency 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 bodyQuantity of matter in a bodyA scalar quantityQuantify 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 kgWeight: (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? Do Experiments.Find, if the net force ∑F 0 The velocity v changes (in magnitude or direction or both).A change in the velocity v (dv) There is an acceleration a = (dv/dt)ORA net force acting on an object produces an acceleration! ∑F 0 a
4 Newton’s 2nd LawExperiment: The net force ∑F on an object & the acceleration a of that object are related.HOW? Answer by EXPERIMENTS!Thousands of experiments over hundreds of years find (object of mass m) :a (∑F)/m (proportionality)Choose the units of force so that this is not just a proportionality but an equation:a (∑F)/mOR: (total force!) ∑F = ma
5 ∑F = ma Newton’s 2nd Law: ∑F = ma ∑F = the net (TOTAL!) force acting on mass mm = the mass (inertia) of the object.a = acceleration of the object. Description of theeffect of ∑F. ∑F is the cause of a.∑F = maThe VectorSum of All Forces Actingon Mass m!
6 FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!! Based on experiment!Not derivablemathematically!!Newton’s 2nd Law:∑F = maA VECTOR equation!! Holdscomponent by component.∑Fx = max, ∑Fy = may, ∑Fz = mazONE OF THE MOSTFUNDAMENTAL & IMPORTANTLAWS 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 Example 5.1: Accelerating Hockey Puck See Figure: A hockey puck, massm = 0.3 kg, slides on the horizontal,frictionless surface of an ice rink. Two hockey sticks strike the pucksimultaneously, exerting forcesF1 & F2 on it. Calculate themagnitude & direction of theacceleration.Steps to Solve the Problem1. 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.
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 = maIf no other forces are acting, only Fg mg acts(in vertical direction) ∑Fy = may orFg = 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 Law2nd Law: A quantitative description of how forces affect motion.BUT: Where do forces come from?EXPERIMENTS Find: Forces applied to an object are ALWAYS applied by another object. 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 DIFFERENT objects!)
12 Another Statement of Newton’s 3rd Law “If two objects interact,the force F12 exertedby object 1 on object 2is equal in magnitude& opposite in directionto the force F21 exertedby object 2 on object 1.”As in figure