Download Newton`s Laws, Forces

Forces
Prof. Yury Kolomensky
Feb 9/12, 2007
- Hooke’s law
- String tension
- Gravity and Weight
- Normal force
- Friction
- Drag
-Review of Newton’s laws
Today’s Plan
• Catalog common forces around us


What you will use in problems
But also what you experience every day
 So that you can sound sophisticated when you tell your
mom what you learned 
• Remember Newton’s laws

Computational techniques: will use today again
 Review (again) on Monday
02/9-12/2007
YGK, Physics 8A
Spring Force
• Hooke’s law: force is
proportional to extension
 Demo: suspended block
 Mathematically
F = !kx

Warning: this cannot
continue to x∞
 Max tension
02/9-12/2007
YGK, Physics 8A
String Tension
• Force exerted by a rope, string, or cable on an object it
is attached to



Always directed along the string
Always points away from contact (pulls the object)
Approximations:
 Un-stretchable string: tension T constant along length
 Massless string: does not sag, has no weight
 Common pulley approximations (until Ch.10): frictionless, massless
02/9-12/2007
YGK, Physics 8A
Gravity
• Newton’s law of gravity:
 Fg = GNMm/r2
GN=6.6742(10)*10-11 N*m2/kg2 is the
Fg
Newton’s constant

Plug in Earth mass and radius:
 Mearth=6*1024 kg
Rearth=6400 km
Fg=mg, where g=GNMearth/Rearth2=9.8 m/s2
02/9-12/2007
YGK, Physics 8A
• My pet peeve


Weight
I think the book defines it incorrectly
Should not be equal to gravity
 Depends on acceleration, since, according to Einstein,
can’t distinguish gravity and acceleration
 Physicists define weight as force an object exerts on
support
 Have to be careful about this one and read carefully !
g
W
y
mg
02/9-12/2007
YGK, Physics 8A
Friction
• Force that resists relative
motion of dry surfaces
• Three kinds



Static friction
Kinetic friction
Rolling friction
 Demo on Friday
02/9-12/2007
YGK, Physics 8A
Properties of Friction
• Static friction


No relative motion: static friction balances externally applied force
 Directed opposite to external force along the surface
 0 ≤ Fstatic ≤ Fmax
Maximum friction force proportional to normal force at the surface
 Fmax=µsN
• Kinetic friction
 Once the motion starts, friction force is equal to
 Fkin = µkN
 Direction is opposite to velocity vector (opposes motion)
• Rolling friction
For rolling motion over surface
 Froll = µrN
 0 ≈ µr ≤ µ k ≤ µs
 Coefficients of friction: property of
materials and surface
02/9-12/2007

N
Fext
Ffr
mg
YGK, Physics 8A
Coefficients of Friction
Steel on steel
Al on steel
Rubber on concrete
Wood on wood
Glass on glass
Ice in ice
Teflon on teflon
Synovial joints in humans
µs
µk
0.7
0.6
1.0
0.25-0.5
0.9
0.1
0.04
0.01
0.6
0.5
0.8
0.2
0.4
0.03
0.04
0.003
 Measuring friction: demo
02/9-12/2007
YGK, Physics 8A
Drag Force and Terminal Speed
When an object moves through a fluid (gas or liquid) it experiences an opposing
force known as “drag”. Under certain conditions (turbulent, as opposed to
laminar, flow) the magnitude of the drag force is given by the expression:
1
D = C ! Av 2
2
C is a constant (depends on shape), A is the effective
cross sectional area of the moving object, ρ is the density
of the surrounding fluid, and v is the object’s speed.
Consider an object (a cat of mass m in this case) start
moving in air. Initially D = 0. As the cat accelerates D
Object at
increases and at a certain speed vt D = mg At this
terminal speed
point the net force and thus the acceleration become zero
and the cat moves with constant speed vt known the the
terminal speed (velocity)
1
D = C ! Avt2 = mg
2
02/9-12/2007
vt =
2mg
C! A
YGK, Physics 8A
Terminal Speed
02/9-12/2007
ρair=1.2 kg/m3
Object
C
Car
0.3-0.5
Smooth sphere
0.5
Human body
~1
Parachute
~1-1.2
Object
Shotput
Skydiver
Baseball
Basketball
vt (m/s)
145
60
42
20
Ping-pong ball
Raindrop
Parachutist
9
7
5
YGK, Physics 8A
Newton’s Laws: Summary
• 1st law: Relationship between inertial systems


v = v’ + V
a=a’
 v is velocity in fixed frame, v’ is velocity in moving
frame, V is velocity of moving frame wrt fixed
V=const : inertial frames
• 2nd law:

F = ma (remember vector form)
• 3rd law

02/9-12/2007
F12=-F21 for two interacting bodies
YGK, Physics 8A
Relationships
02/9-12/2007
YGK, Physics 8A
Problem-Solving Strategy
1.
2.
3.
4.
5.
6.
7.
8.
Visualize (draw a picture)
Write down “knowns” and “unknowns”
Split system into objects
Draw free-body diagrams for each object
 List and draw all forces: contact, long-distance
2nd law in vector form and projections
 2 or 3 equations per object
Write down constraints
 Additional equations
Solve for unknowns
Plug in numbers
 Demo: system of pulleys, mechanical advantage
02/9-12/2007
YGK, Physics 8A