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

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 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.

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) OR A net force acting on an object produces an acceleration! ∑F  0  a

Newton’s 2nd Law Experiment: 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)/m OR: (total force!)  ∑F = ma

∑F = ma Newton’s 2nd Law: ∑F = ma ∑F = the net (TOTAL!) force acting on mass m 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!

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

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

Example 5.1: Accelerating Hockey Puck 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. Steps to Solve the Problem 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.

Example

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

Newton’s 3rd Law 2nd 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!)

Another Statement of Newton’s 3rd Law “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

Example: Newton’s 3rd Law

Action-Reaction Pairs: On Different Bodies