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Physics 12 Webquest Emma Chiasson June 8, 2007 Physics 12 Mr.Greer

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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?

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…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.

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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!

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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.

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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.htmlhttp://www.physicsclassroom.com/mmedia/cir cmot/ucm.html http://www.fortunecity.com/greenfield/eagles/ 180/circle.htmlhttp://www.fortunecity.com/greenfield/eagles/ 180/circle.html

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Step 2: What is the centripetal force? http://regentsprep.org/Regents/physics/ phys06/bcentrif/default.htmhttp://regentsprep.org/Regents/physics/ phys06/bcentrif/default.htm http://www.physics247.com/physics- tutorial/boarder-centripetal-force.shtmlhttp://www.physics247.com/physics- tutorial/boarder-centripetal-force.shtml

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Step 3: Did I hear the word Centrifugal? http://regentsprep.org/Regents/physics/ phys06/bcentrif/centrif.htmhttp://regentsprep.org/Regents/physics/ phys06/bcentrif/centrif.htm

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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.

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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: F c =mv²/r A c =v²/r

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F c =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.

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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

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What about when the ride changes to a Vertical Circle? http://www.pschweigerphysics.com/APf orceexamples.html (scroll to vertical circle)http://www.pschweigerphysics.com/APf orceexamples.html

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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.

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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…

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..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.

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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.

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So… If : F c =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

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Some Calculations F c =mv²/r F c =4π²mr/T² Using this new formula, Cameron can calculate both the centripetal force and velocity. F c =4π²mr/T² =4π²(140kg)(6.8m) (10s/3rev)² =11 275.04N V=d/t = 2πr/T =2π(6.8m)/(10s/3rev) =12.82m/s

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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…

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You helped Cameron find out that if the chains were going to break anywhere, it would be at the bottom of the vertical circle. This will happen if the the force of gravity is greater than the tension in the chains. So it is the moment of truth…Cameron must see if The Widow Maker could possibly snap on him at the bottom of the circle. F g =mg=140kg(9.8m/s²) =1372N F un =F c =T+ (-F g ) T= F c + F g T=mv²/r + mg T=140kg(12.82m/s) ²/6.8m +(140kg)(9.8m/s²) T=3382.51N+1372N T=4754.51N The tension is greater than the force of gravity on the person on the ride and so Cameron now knows with his weight he can safely ride The Widow Maker without worries that it will break

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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?” ….

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“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!”

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…. …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.

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Practice Questions: http://www.physics247.com/physics- homework-help/circular-motion.php

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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 tmhttp://regentsprep.org/Regents/physics/phys06/bcentrif/default.h tm http://www.physics247.com/physics-tutorial/boarder-centripetal- force.shtmlhttp://www.physics247.com/physics-tutorial/boarder-centripetal- force.shtml http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.ht mhttp://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.ht m http://www.phy.ntnu.edu.tw/oldjava/circularMotion/circular3D_e. htmlhttp://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.htmlhttp://www.marshall.k12.wi.us/mhs/teachers/mirus/20002001/Phys1/P hys1Tests/Phys1Test05010206.html

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