Transcript Newton’s First Law Mathematical Statement of Newton’s 1 Law:

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
• 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.
The Vector
Sum of All 
Forces Acting
on Mass m!
∑F = ma
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!!!
nd
2
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).
Fg = mg
∑Fy = may
(down, of course)
• SI Units: Newtons (just like any force!).
g = 9.8 m/s2  If m = 1 kg,
Fg = 9.8 N
or
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