Forces
Course Virtual Worlds
INFOVW - 2010
Where are we?
• We have seen
– Mass and inertia properties
– Kinematics
• Now: Forces
– Forces together with the mass and inertia
properties supply the accelerations needed in
kinematics
• Force Fields
– Gravity
• Normal Force and Friction
• Fluid Dynamic Drag
• Springs and Dampers
• Pressure and Buoyancy is not done
Overview
Non--Contact Forces
Non
• Difference between contact and non-contact
forces
• Contact forces:
– Friction,
F i ti Normal,
N l CCollisions
lli i
• Non-Contact forces:
– Gravity
– Electro-magnetism
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Action--Reaction
Action
Force Fields
• Please remember the action-reaction principle
mention in an earlier lecture
• Every force has a equal but opposite reaction
force
Gravity
– The earth ‘pulls’ on you, but you ‘pull’ the earth
– If you push a box, the box also pushes you
Gravity
• Newton’s Law of Gravitation states that the
gravitation force is:
– Proportional to the product of the two masses
– Inversely proportional to the square of the
distance between the two C.o.M.
– Force acts on the line connecting the two centers
Fg  G
m1 m2 r
2
r
r
But what about 9.81 m/s2 ???
• Up to now we have used g = 9.81 m/s2
• Prove this…
mearth  5.98 10 24 kg
G  6.673 10 11 m 3 kg 1s  2
Rearth  6.38 106 m
2
Gravity acceleration
F  ma
– mmars = 6.421 1023 kg
– rmars= 3403 km
– gmars= 3.69 m/s2
m mearth r
G
 ma
2
r
r
G
m mearth
r
2
m a
mearth
G
a
( Rearth  h) 2
G
mearth
a
2
Rearth
5.98 10
a
(6.38 106 ) 2
9.81  a
6.673 10 11
• Mars
Gravity on the Moon and Mars
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Normal and Friction Forces
• Moon
– mmoon = 7.35 1022 kg
– rmoon= 1738 km
– gmoon= 1.62 m/s2
Normal forces
• Normal force is a reaction force
• If an object ‘rests’ on a surface, the reaction
force of the surface on the object is called the
normall fforce
Fn
Fg
3
Static Friction
• If an object rests on a surface, and a force is
applied on the object a friction force is acting
on the block from the surface
• There
Th iis a maximum
i
on thi
this ffriction
i ti fforce
– If applied force is smaller than this maximum,
object will remain static
– If applied force is larger than this maximum, the
object will start moving
On whiteboard…
Dynamic Friction or Kinetic Friction
• Once the object is moving, the friction changes
from static to dynamic friction
• Dynamic
D
i ffriction
i ti iis lless th
than static
t ti ffriction
i ti
Static Friction
fs
Fmax
  s Fn
Dynamic Friction or Kinetic Friction
F fk   k Fn
On whiteboard…
4
Friction Coefficients
DIY: Ice on Ice on the Moon
Static friction coefficient: 0.1
Mass of ice block: 20 kg
Gravity constant: 1.62 m/s2
Surface condition
static
dynamic
% difference
Ice on Ice
01
0.1
0 03
0.03
70%
Dry Iron on Iron
1.1
0.15
86%
Dry Teflon on Teflon
0.04
0.04
0%
Fg
Fluid Dynamic Drag
β
Complex Force
• Many factors influence the force
– Fluid/Matter properties
– Shape of object
– Motion of the fluids/air
– Etc. Etc.
• Most of the force are idealized
5
Ideal Viscous Drag
Fv  C lf v
• Applicable to slow moving objects
• Results in laminar flow (smooth flow)
Approximation
• These are not exact
• So don’t use them for real physics
Ideal Viscous Drag
Fv  C tf v 2
• Applicable to fast moving objects
• Results in turbulent flow (rough flow)
Springs and Dampers
• Very
V goodd for
f computer
t games
6
Springs
• Springs are used to connect two or more bodies
• They react (according to Hook’s Law) on
extension and compression
• Their
Th i length
l th relative
l ti tto th
the rest-length
t l th
determines the force they apply
Fs  k s ( L  r )
L
Fs  k s ( L  r )
L
Dampers
• Dampers try to slow down the motion between
two objects connected by a spring
• Depend on the relative speed between them
Fd  k d (v1  v2 )
Fd  k d
On whiteboard…
(v 1  v 2 )  L L
L
L
On whiteboard…
Combined

(v  v )  L  L
F1    k s ( L  r )  k d 1 2
 L
L


F1   F2
FORCES AND TORQUES
7
Torque
• Not only do these forces effect objects linearly
• Also torques are generated that make the
objects rotate
Torque
F
r
M  rF
Balance forces and torques
• Resulting force induces linear acceleration of
C.o.M
• Resulting
R lti ttorque induces
i d angular
l acceleration
l ti
around C.o.M.
General procedure
• Calculate objects mass properties
• Identify and quantify the forces and
torques/moments
• Sum
S th
these ((vector
t bbased)
d)
• Solve the equations of motion for accelerations
• Integrate over time for velocities
• Integrate over time for positions
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Tipping a box
All Force and Torques
w
w
Fp
Fp
h
h
Fn2
Fcg
Ff2
Rolling Cylinder
Fn1
Fcg
Ff1
All Force and Torques
Fn
Fcg
Ff
β
β
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Compare: Which one rolls faster?
DIY: Roll of wire
Mass of roll: 10 kg
Mass of block: 5 kg
Diameter of roll: 2 m
Height of block: 10 m
Gravity constant: g = 10 m/s2
β
β
Questions??
• Topic of the next lecture:
Next Lecture…
– Real-Time Simulation
• Read Chapter 4 of PfGD
– Makes it easier to follow the lecture
– No need to study it extensively, but prepare!
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