Transcript Newton`s Laws - AdvancedPlacementPhysicsC

Newton’s First & Second
Law
AP Physics C
Unit is the Newton(N) or pound (lb)
• Is by definition a …..
push or a pull
• Can exist during physical contact
(Tension, Friction, Applied Force)
• Can exist with NO physical contact
• called Fundamental Forces
(gravitational, electric, nuclear FIELDS)
•
Inerte in Galileo’s Italian meant “lazy”
INERTIA – the more of it you have, the harder it is
to get you moving.




Modern definition: a quantity of matter, also called …
MASS. Unit for MASS = kilogram.
NOTE: MASS and WEIGHT are NOT the same thing.
MASS never changes when an object moves to a
different planet.
Weight is a force due to Gravity. It is how your MASS is effected by gravity.
What is the weight of an 85.3-kg person on earth? On Mars=3.2 m/s/s)?
W  mg
W  mg  W  (85.3)(9.8)  835.94 N
WMARS  (85.3)(3.2)  272.96 N
An object in motion remains in motion in a
straight line and at a constant speed OR an
object at rest remains at rest, UNLESS acted
upon by an EXTERNAL (unbalanced) force.
acc  0   F  0
The bottom line: There is NO ACCELERATION (no change in velocity)
unless a force acts, but you can have MOTION even if there is NO force acting.
“Common sense” told us the opposite for generations, so inertia was a real
intellectual breakthrough.
EQUILIBRIUM
is when there are either NO FORCES acting or those that are acting
all cancel each other out.
A pictorial representation of forces complete
with labels.
FN
Ff
T
T
W1,Fg1
or m1g
m2g
•Weight(mg) – Always
drawn from the center,
straight down
•Force Normal(FN) – A
surface force always drawn
perpendicular to a surface.
•Tension(T or FT) – force in
ropes and always drawn
AWAY from object.
•Friction(Ff)- Always drawn
opposing the motion.
It helps if you first circle the object you are analyzing, and labe only the forces
acting ON IT. Other than gravity, these forces must involve physical contact.
Ff
FN
mg
Since the Fnet = 0, a system moving at a
constant speed or at rest MUST be at
EQUILIBRIUM.
TIPS for solving problems
• Draw a FBD
• Resolve anything at angles into
COMPONENTS
• Write equations of equilibrium
• Solve for unknowns
A 10-kg box is being pulled across the table to the
right at a constant speed with a force of 50N.
a)
b)
Calculate the Force of Friction
Calculate the Force Normal
FN
Ff
mg
Fa
Fa  F f  50 N
mg  Fn  (10)(9.8)  98N
Suppose the same box is now pulled at an angle of 30
degrees above the horizontal.
a)
Calculate the Force of Friction
b)
Calculate the Force Normal
Fax  Fa cos   50 cos 30  43.3N
F f  Fax  43.3N
FN
Ff
Fa
Fay
30
Fax
mg
FN  mg!
FN  Fay  mg
FN  mg  Fay  (10)(9.8)  50 sin 30
FN  73N
If an object is NOT at rest or moving at a
constant speed, that means the FORCES are
UNBALANCED. One force(s) in a certain
direction overpowers the others.
THEN THE OBJECT WILL…..
ACCELERATE.
The acceleration of an object is directly
proportional to the NET FORCE and
inversely proportional to the mass.
a  FNET
a
1
a
m
FNET
 FNET  ma
m
FNET   F
Tips:
•Draw an FBD
•Resolve vectors into components
•Write equations of motion by adding and
subtracting vectors to find the NET FORCE.
Always write larger force – smaller force.
•Solve for any unknowns
A 10-kg box is being pulled across the table to
the right by a rope with an applied force of
50N. Calculate the acceleration of the box if a
12 N frictional force acts upon it.
FN
Ff
mg
Fa
In which direction,
is this object
accelerating?
The X direction!
So N.S.L. is worked
out using the forces
in the “x” direction
only
FNet  ma
Fa  F f  ma
50  12  10a
a  3.8 m / s
2
A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected
to a cable that passes over a pulley and then is fastened to a hanging mass,
m2 = 11.0 kg as shown below. Find the acceleration of each mass and the
tension in the cable.
FN
FNet  ma
m2 g  T  m2 a
T
T
m1g
T  m1a
m2 g  m1a  m2 a
m2 g  m2 a  m1a
m2 g  a (m2  m1 )
m2g
a
m2 g
(11)(9.8)

 7.7 m / s 2
m1  m2
14
FNet  ma
m2 g  T  m2 a
T  m1a
T  (3)(7.7)  23.1 N
FNET
FNet  ma 
m
a
Rise
Slope 
Run
Where does the calculus fit in?
2


dv
d x
F  ma  m  m
dt
dt
First
derivative
Second
derivative
DON’T WORRY ABOUT THE STUFF ON THIS
SLIDE OR THE NEXT FOR NOW.
Where does the calculus fit in?


dv
d 2x
F  ma  m  m
dt
dt
There could be situations where you are
given a displacement function or velocity
function. The derivative will need to be
taken once or twice in order to get the
acceleration. Here is an example.
You are standing on a bathroom scale in an elevator in a tall
building. Your mass is 72-kg. The elevator starts from rest
and travels upward with a speed that varies with time
according to:
2
v(t )  3t  0.20t
When t = 4.0s , what is the reading on the bathroom scale
(a.k.a. Force Normal)?
Fnet  ma
dv d (3t  0.20t )
a

 3  0.40t FN  mg  ma  FN  ma  mg
dt
dt
FN  (72)(9.8)  (72)( 4.6) 
a(4)  3  0.40(4)  4.6 m/s/s
1036.8 N
DON’T WORRY ABOUT THE STUFF ON THIS SLIDE UNTIL
NOVEMBER
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