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slide 1Physics 1401 - L 6 Frank Sciulli
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l Lecture todayu Complete Ch 6 on Force and Motionu Begin Ch 7 on Work and Energy
l Exam in one week will emphasize material up through chapter 6. Chapter 7 material (work, energy, …) will not be on the first midterm.
l Mention again at end of lecture
slide 2Physics 1401 - L 6 Frank Sciulli
Fluid Drag Forces
l Nonviscous flow = no drag force
l Viscous but laminaru η=viscosity
l Viscous and turbulent
dF K vη= −
dF C Avρ 212
=
review
slide 3Physics 1401 - L 6 Frank Sciulli
Terminal Speedl In either case,
D ∝ - v1 or 2 …
uObject will attain a terminal speed
u Text does the turbulent flow case
u Laminar flow case:η
η
= −
= = = when term
D K vmgD mg v vKBetween :termv v
dvm mg K vdt
0 ≤ ≤
= − η(1 )
η−
= −
with solution for start at rest
[culture]K tm
termv v e
review
slide 4Physics 1401 - L 6 Frank Sciulli
Centripetal Force
l Must always be a force to hold an object in circular motion
l This force supplies the centripetal acceleration!
l Hey! What happened to centifugal force?
2
=vT mR
review
slide 5Physics 1401 - L 6 Frank Sciulli
Centrifugal Force is a FICTION! (Fake Force)
l Real life experiences that make clear … objects without force travel in a straight line at the velocity with which they started!
l We use “fake forces” to explain real sense because we are not recognizing acceleration!
review
slide 6Physics 1401 - L 6 Frank Sciulli
F=ma better than using “fake forces”
l We found tanθ=a/g … from Fx=mal But if postulated “fictional force” in direction
of a, this would “explain” the angle, but would not be correctu Same rationale holds for centrifugal forces
Accelerometer Problem
review
slide 7Physics 1401 - L 6 Frank Sciulli
Prob. 6-41 (unassigned)l What speed will m travel
at, so as to maintain circular motion of radius, r ?
l For given M and r, specific v works!
=
=
=
2
so
T MgvT mr
Mv rgm
v
T
T
Mg
slide 8Physics 1401 - L 6 Frank Sciulli
Conical Penduluml Ball rotating stably in
fixed circlel Rotate the ball, tension
in string supplies centripetal force
l Notice that circle is always below the hand
T
T
F mgvF mr
vrg
θ
θ
θ
=
=
=
2
2
cos
sin
tan
Note r = Lsinθ
sin tanv Lg θ θ=
slide 9Physics 1401 - L 6 Frank Sciulli
An Abnormal Normal Force
Go to the amusement park!
v
slide 10Physics 1401 - L 6 Frank Sciulli
Sample Problem 6-8l The ROTORl Rotates fast giving
rider speed tangential speed v at the outer wall
l Floor fallsl Rider stays upl Needed: friction at
the walll Given: R and µsl What must v be ? v
slide 11Physics 1401 - L 6 Frank Sciulli
Race cars on a track
Notel required force on car (tires)
from frictionl forces on people!l all turns are arcs of circles
R
slide 12Physics 1401 - L 6 Frank Sciulli
Sample Problem 6 - 9l Problem: driving in car on a circular, level track.l What is the static coefficient of friction required?
(so it won’t skid!)
x
2
2
ma
s
criticals s
criticals
N mgvf mR
f mv
g
Rg=
=
=
=
µ
µ
slide 13Physics 1401 - L 6 Frank Sciulli
Make life easier - Bankthe track!
l Elevate outer ring of track relative to inner ring
l Look at it from the front (next slide)R
higher
lower
slide 14Physics 1401 - L 6 Frank Sciulli
Car on banked track –circle center to right
l No friction...what speed (vc) is required to keep car from sliding!
l Lets work it out!
cN N
cc
vF mg F mR
v v RgRg
θ θ
θ θ
= =
= =
2
2
cos sin
tan tan
l What happens if v is q Bigger than vc?q Smaller than vc?
slide 15Physics 1401 - L 6 Frank Sciulli
Work and Energyl Highly useful concept (Newton missed it)u work & energy scalars, rather than vectors
l Work is performed whenever force is applied to an object with some component along or opposite the direction of displacement
l Work done=Force × distance moved in the direction of the force
l Energy of several general types:u kinetic: energy involved in motion (often recoverable)u potential: energy available by virtue of availability to
do work; recoverable in future as “kinetic”u dissipated energy: lost, converted to heat
l Work creates energy … energy convert between kinetic (motion) and potential (eg gravity)
slide 16Physics 1401 - L 6 Frank Sciulli
Quantities and Units
Quantity Unit
Displacement (x) Meters (m)
Time Seconds (s)
Velocity Meters/second (m/s)
Acceleration m/s/s (m/s2)
Mass Kilogram (kg)
Force Newton (N) = kg-m/s2
Work (Energy) Joule (j) = N-m
slide 17Physics 1401 - L 6 Frank Sciulli
Quantitative Definition of Work
l Man does work on system of bed and penquin
l Note that normal and gravitational do NO work in this case.
l Only the force component moving the system in the same direction as the displacement does work
Work done = displacementin same direction
W
W F
W F r
=
∆ = • ∆
ir r
r∆r
slide 18Physics 1401 - L 6 Frank Sciulli
Bead on a Wire with constant Force (and acceleration) – no friction
l Work is + or -, depending on whether force has component in the same direction as displacement or opposite to the displacement
l Positive work increases Kinetic Energy
x
x
Fmx x
Fm
x
a W F dv v dW F dW mv mvW K K
= =
= +
≡
= −
= −
2 20
2 21 102 2
0
2
≡ 212 Kinetic ene ( - new conr cept)gyK mv
slide 19Physics 1401 - L 6 Frank Sciulli
Work-Energy Theorem
Take in -direction and dependent on :Each increment in produces Add up all the work to get total work:
F x F xx W F x
W∆ ∆ = ∆
Work=change in Kin. EnergyGeneral Theorem is valid
so long as no energy dissipated
2 21 102 2
0
W mv mvW K K
= −
= −
slide 20Physics 1401 - L 6 Frank Sciulli
Consistent with what you know … get it easier!
Simpler way to get many of the answers got before (with grav force)
Note for any height y, then
2 21 102 2
2 20
Work done (by grav) = Chg K
2− = −
= −
mgy mv mvv v gy
slide 21Physics 1401 - L 6 Frank Sciulli
Conclusions
l Begun to discuss important topic of work and energy
l Next time, we use it for several casesl HW 2 solutions posted todayl Sample exam and solution for MT1 will be
posted todayl “General exam guide” posted at the
“Exam Specifics” web pageuWhat to expect on exam day is described
there … please read uWe will go over it quickly in the next lecture
