Pieter Kreyns
Title: Free Fall
Purpose: The purpose of this lab was to gather height and time data for a series of dropped balls and,
from this data, calculate final velocities and acceleration. By doing this, the constant acceleration of
gravity is disco
Conservative and Nonconservative Forces
Work done by gravity on a closed path is zero:
1
Conservative and Nonconservative Forces
Work done by friction on a closed path is not
zero:
2
Vacuum
Ball is dropped from rest at a height h and experiences only a gr
Math Review
Up to this point the trigonometry utilized in our course has involved
the basic sine and cosine function definitions applied to triangles.
Review of graphs of sine and cosine functions
1
range
amplitude=a
period =
2
Give a few examples of peri
Clicker
Anobjectofmassmoscillateson
averticalspringwithperiodT.If
themassisdoubled,howwould
theperiodchange?
A)
B)
C)
D)
Theperiodwoulddouble
Theperiodnotchange
TheperiodwouldincreasebyafactorofSQRT(2)
TheperiodwoulddecreasebyafactorofSQRT(2)
13
EnergyCon
RollingMotion
Ifaroundobjectrollswithoutslipping,thereisafixedrelationshipbetweenthe
translationalandrotationalspeeds:
r
r
1
RollingMotion
Rollingmotioniscombinationofpurerotationalandpuretranslationalmotion:
Clicker
Whilewaitingtocrosstheroadatractor
pas
The canoeist decides to move from 1 m from the left of the canoe to 1 m from the right end of the canoe
(or 5 m from the left end). Assume there is no surface drag between the canoe and the water, no current
and no wind, so that there are no external hori
ZeroTorqueandStaticEquilibrium
Ifthenettorqueiszero,itdoesntmatterwhichaxisweconsider
rotationtobearound;wearefreetochoosetheonethatmakes
ourcalculationseasiest.
1
How do we incorporate the plank into the problem?
Recall when an object has a
symmetric sha
Newtons Law of Universal Gravitation
Newtons insight:
The force accelerating an apple
downward is the same force that
keeps the Moon in its orbit.
Hence, Universal Gravitation.
Nothing yet. How
about you Newton?
MechanicalUniverse3:2524:50
8.TheAppleandth
pointwherethetorqueismeasured
Magnitude Form
r = level arm
Rotational Form
pointofforceapplication
Newtons2nd Lawfor
arotatingbody
1
Substituting
Angular
acceleration
Solveforaccelerationa
Substituting
TensionTinthe
linear2nd law
equation
2
Ifthepulleyhas
ConservationofAngularMomentum
Ifthenetexternaltorqueonasystemiszero,theangularmomentumisconserved.
Themostinterestingconsequencesoccurinsystemsthatareabletochangeshape:
So where did the additional energy come from ?
Work=CentripetalForcexChangeinR
1
Click
The Cavendish experiment allows us to measure
the universal gravitation constant:
Mm
F G 2
R
Even though the gravitational force is very small, the mirror allows
measurement of tiny deflections.
Measuring G also allowed the mass of the Earth to be calcula
Lets say you were able to build a tunnel through
the center of the Earth to the opposite side. If
you were to jump in, you would accelerate
toward the center. However your acceleration
decrease as your distance to center decreases.
1
Let consider a very f
The net force acting on an object is the
rate of change of its momentum:
TheGeneralformofNewtons2nd law
Ifthenetforceiszero,thetotalmomentumdoes
notchange:Newtons1st Law
Conservation of Linear Momentum
Internal VersusExternal Forces:
Internalforcesactbetw
Just as the Work Done to an object transforms Energy,
the Impulse to an object can transfer momentum
Impulseisavector,inthesamedirectionastheaverageforce.
1
eggdemonstration
2
3
4
Momentumallowsustocharacterize
collisionsintotwocategories.
Elastic
Inelast
From a boat in the English Channel, you slowly approach the White
Cliffs of Dover. You want to know how far you are from the base of the
cliff. Then suddenly you see a rock break off from the top and hit the
water in 3.2 seconds. From your location in the
Adding Velocity Vectors: Relative Motion
Define a coordinate system and determine
the vector components
Y
PT + TG = PG
T
PT = 2meters
P
.
G
TG = 0.5meters
X
Table
Lets assume the displacements occurred
simultaneously within a 2 second period.
We then rewr
MU
Newtons Laws
1:40-21:40
http:/www.learner.org/resources/series42.html
6. Newton's Laws
1
2
Newtons Laws of Motion
First Law or Law of Inertia
A body at rest remains at rest and a body in motion continues to move at
constant velocity along a straight li
Whenanobjectisinmotiononasurface,therewill
bearesistancetothemotion.Frictional Relationship.
Frictionisproportionaltothenormalforce.
k=k N
s s N
W
F= fs
fssN
N
NoSlippage
F>fk
W
fk=kN
N
Slippage
1
2
F denotesfieldforce
Fdenotescontactforce
Fij istheforcee
F denotes field force
F denotes contact force
Fij is the force exerted by
object i on object j
F A FBA+FEA
FAE
A
FEA
FBE
FEB
B
Earth
FEB
FBE
F denotes field force
F denotes contact force
FEA
F A FBA+FEA
Fij is the force exerted by
object i on object j
FEA
Newtons Second Law
1
Utilizing Newtons second law to the two masses yields the following relations:
T m1a
m2 g T m2 a
m1m2
T m1a
m1 m2
Solve for a
m2
a
m1 m2
g
g
2
Inwhichcasedoesblockm1 experiencealarger acceleration?Incase(1)thereisa
m2 masshanging
An object of mass m
moves from point A to
point B
yB-yA=h
y
yB
yA
B
A
xA
xB
x
Completelyindependentofthepath
Theonlythingthatmattersisthedifferenceinheight
Whenever the work that is done by a force is independent of its path-it's only determined by the st
Once tension is define in a segment of a taut massless
rope, tension is define everywhere on the rope.
This also applies in a pulley system if static friction in
pulley axles can be neglected.
Pulley simply redirects the tension.
Assumingmasslessropeisgen
Newtons Second Law:
1
A force action on a body gives it an acceleration which is in the direction
of the force and has a magnitude given by mass times acceleration
F is the net force
This is the vector sum of all the forces acting on the object.
total
In physics, a force is said to do work if,
when acting on a body, there is a
displacement of the point of application in
the direction of the force.
Work
Force in the direction of displacement
Force at an angle to displacement
Positive, negative, and zer
isconstant
The work done is equal to the shaded area
between the force line and the x axis.
Work Done by a Varying Force
To use W = Fx cos , the force
must be constant, so the equation
cannot be used to calculate the
work done by a varying force.
Assume t
InelasticCollisions
0
Before
m1
m2
Whatisthefinalvelocity?
After
m1
m2
totalmomentumcannotchange
1
Before
m1
m2
Whatisthefinalvelocity?
After
m1
m2
Ballistic pendulum: the initial velocity v0 can be found using conservation of
mechanical energy after the
The force applied by a spring is also conservative
Spring Time
1
Total Energy of a spring in motion
Substitute for velocity and position
2
The force applied by a spring is also conservative
The potential energy curve for a spring:
A spring and block are o