Transcript Circular Motion Webquest Project Physics 12

Physics 12
Webquest
Emma Chiasson
June 8, 2007
Physics 12
Mr.Greer
HELP!!!
• Cameron needs YOUR help! You see,
he was asked out on a date by a very
cute girl named Cassie. But that’s not
the problem. The problem is that she
asked him to go to the Theme Park of
Futuristic Thrills to try out a new ride
named The Widow Maker .
• But where’s the problem you ask?
• …well Cameron has been to this park before,
he’s even been on many of the rides, but
never The Widow Maker. The reason? His
Mom won’t let him! She says its too
dangerous and he’ll be sent flying and crash
to the ground. There is no way that Cameron
is going to cancel his date with Cassie
because his Mom said he wasn’t allowed.
But there is also no way his Mom will let him
out of the house if she knows he is going to
ride The Widow Maker. Cameron has tried
begging before but his mom never gives in.
He has been given no other choice… he is
going to have to get the facts.
Your Mission?
• To help Cameron get all the facts
surrounding The Widow Maker.
• If Cameron gets enough information, he
will be able to convince his Mom to let
him go on his date with Cassie!
• Good Luck!
THE WIDOW MAKER
•
•
•
•
Once the ride has started,
the riders find themselves
revolving around the central
motor, in a horizontal circle.
The top of the rider’s
head is facing the motor
in the middle so the rider
(head to toe) is paralell
with the ground.
All of the chains and
chairs are of equal
length and mass.
Part 2 of this ride has the
rider revolving around
the centre in a vertical
circle, similar to a ferris
wheel.
Note: Motor in middle is
actually very small.
Diagram is only general
idea.
Step 1:
• The rider stays in their seat while they are
rotating in both a horizontal and vertical
circle.
• Find out what causes this circular motion:
• http://www.physicsclassroom.com/mmedia/cir
cmot/ucm.html
• http://www.fortunecity.com/greenfield/eagles/1
80/circle.html
Step 2:
• What is the centripetal force?
• http://regentsprep.org/Regents/physics/
phys06/bcentrif/default.htm
• http://www.physics247.com/physicstutorial/boarder-centripetal-force.shtml
Step 3:
• Did I hear the word Centrifugal?
• http://regentsprep.org/Regents/physics/
phys06/bcentrif/centrif.htm
What Cameron has learned
so far…
• The idea behind The Widow Maker must be
uniform circular motion, since it is moving in a
circle at constant speed.
• As in moves in a circle it is always changing
direction, which means although it is at a
constant speed, the velocity is changing since
velocity is a vector.
• This means it is also accelerating, since the
change in a velocity is acceleration.
• Any acceleration is
caused by an
unbalanced force.
• We learned that this
unbalanced force is
called the centripetal
force. (NOT centrifugal!)
• Centripetal force is a
net force, which means
it is supplied.
• The force of gravity, the
normal force and the
tension (in this case the
chains) can supply the
centripetal force.
• You’ve introduced
Cameron to a few
formulas that might
help him get some
information he
needs:
• Fc=mv²/r
• Ac=v²/r
Fc=mv²/r ?
• What does this
formula mean?
• How can it help
Cameron?
• The Centripetal Force= the
product of the mass,
(chains+ chair+rider) and the
velocity of the swing
squared, divided by the
radius (length of the chains)
• Using this formula, Cameron
knows that if he can find out
the mass of the
chair+swing+his own mass,
the velocity of the ride and
the length of the chain, he
can calculate the centripetal
force.
Ac=v²/r
• This is the formula
for centripetal
acceleration
(acceleration
towards the centre.)
• Centripetal
Acceleration = the
velocity of the ride
squared, divided by
the radius (length of
the chain).
•http://www.phy.ntnu.edu.tw/oldjava/circul
arMotion/circular3D_e.html
What about when the ride
changes to a Vertical
Circle?
• http://www.pschweigerphysics.com/APf
orceexamples.html (scroll to vertical
circle)
Vertical Circles
• When the chair is on different points in the
vertical circle (bottom, side, top), the
centripetal force will be different.
• This is because we add up (net force) all the
forces in the direction of the acceleration.
• Ex: When its at the top, there is both tension
and gravity pulling it down, but on the bottom,
the tension is pulling up and the gravity is
pulling it down.
Please Mom, Pleeaasee!
• So Cameron found out a lot of information on Circular
Motion, Centripetal force and acceleration.
• He also found out the ways to calculate it.
• ….so he presented all that he found to his Mom…
..And guess what she
said….
• “Well that is all very nice Cameron, but I still
don’t know very much about The Widow
Maker. I still don’t want you on that ride! Do
you even know how fast its going? Will it
break? I am just not convinced it is safe, I’m
sorry.”
• Clearly Cameron was not impressed…he
needs to know more about The Widow Maker.
So Cameron Went to the
Park, just to look at the
Ride…
• He found out from
the attendant at The
Widow Maker that
the chains are 6.5
metres long.
• He also found out
that the mass of the
chains and chair
together are 90
kilograms.
• The attendant did
not know how fast
the ride went,
although Cameron
remarked that it
made 3 revolutions
in 10 seconds.
So…
• If : Fc=mv²/r
M=90kg+50kg=140kg
(+50kg to add Cameron’s
own weight as if he was
on the ride)
R=6.8m
• Well…Cameron cannot
find the centripetal force
now because the
attendant did not know
the velocity.
• Cameron did remark
that it made 3
revolutions in 10
seconds though…
• http://www.glenbroo
k.k12.il.us/GBSSCI/
PHYS/Class/circles/
u6l1e.html
Some Calculations
• Fc=4π²mr/T²
• Fc=mv²/r
=4π²(140kg)(6.8m)
• Fc=4π²mr/T²
(10s/3rev)²
• Using this new
formula, Cameron
=11 275.04N
can calculate both
• V=d/t = 2πr/T
the centripetal force
=2π(6.8m)/(10s/3rev)
and velocity.
=12.82m/s
• Now Cameron has plenty of information to tell
his Mom.
• The ride has a centripetal force of: 11 275.04N
• It has a velocity of: 12.82m/s
• Since the tension supplies the centripetal force
while the ride is in it’s horizontal loop, the chain
will not break as long as the chains are of
sufficient strength.
• It turns out the chains can support 15 000N of
force so Cameron can tell his Mom the chains
will not break, at least in the horizontal circle.
• As for in the vertical circle…
•
Fg=mg=140kg(9.8m/s²)
• You helped Cameron
=1372N
find out that if the
• Fun=Fc=T+ (-Fg)
chains were going to
T= Fc+ Fg
break anywhere, it
T=mv²/r + mg
would be at the bottom
T=140kg(12.82m/s) ²/6.8m
of the vertical circle.
+(140kg)(9.8m/s²)
• This will happen if the
T=3382.51N+1372N
the force of gravity is
greater than the tension T=4754.51N
in the chains.
• The tension is greater
• So it is the moment of
than the force of gravity
truth…Cameron must
on the person on the ride
see if The Widow Maker
and so Cameron now
could possibly snap on
knows with his weight he
him at the bottom of the
can safely ride The
circle.
Widow Maker without
worries that it will break
• So you’ve helped
Cameron finally
figure it out.
• The ride will be safe
for him to ride.
• “Please Mom…can I
please go out with
Cassie now?”
• ….
• “Well Cameron
you’ve really shown
me that The Widow
Maker is a safe ride.
Actually I wouldn’t
mind coming along
to try it out!”
….
…the chains
breaking wouldn’t
be a bad thing right
about now.
Congrats! You helped
Cameron learn all that he
needed to convince his Mom
to let him go on his date.
…He would thank you if he
wasn’t so busy trying to
convince his Mom not to go
on his date with him... Can
you help him with that? …I
would stick to the physics if I
were you.
Practice Questions:
• http://www.physics247.com/physicshomework-help/circular-motion.php
Bibliography
• http://www.physicsclassroom.com/mmedia/circmot/ucm.html
• http://www.fortunecity.com/greenfield/eagles/180/circle.html
• http://regentsprep.org/Regents/physics/phys06/bcentrif/default.h
tm
• http://www.physics247.com/physics-tutorial/boarder-centripetalforce.shtml
• http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.ht
m
• http://www.phy.ntnu.edu.tw/oldjava/circularMotion/circular3D_e.
html
• http://www.pschweigerphysics.com/APforceexamples.html
• pbskids.org/.../images/rollovers/mom_home.gif
• http://www.marshall.k12.wi.us/mhs/teachers/mirus/20002001/Phys1/P
hys1Tests/Phys1Test05010206.html