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Roller coaster: kinetic energy 
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#1
Sep2507, 07:20 PM

P: 150

A roller coaster car may be approximated by a block of mass m. The car, which starts from rest, is released at a height h above the ground and slides along a frictionless track. The car encounters a loop of radius R, as shown. Assume that the initial height h is great enough so that the car never loses contact with the track.
http://session.masteringphysics.com/...3/MPE_ug_2.jpg so, i know kinetic energy = .5m(v^2) and centripetal force in circle is m(v^2)/R so that if i play around with the equations i can get KE = 0.5m(gR) ... but how do i take into account the height if i have to give my answer in terms of m, g, h, and R? Anyone out there who can solve this thing? 


#2
Sep2507, 07:53 PM

P: 150

Find an expression for the kinetic energy of the car at the top of the loop.
Express the kinetic energy in terms of m, g, h, and R. forgot to add that what's above is the problem! 


#3
Sep2507, 07:56 PM

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Just use conservation of energy... I don't think you need to deal with centripetal motion or anything.



#4
Sep2507, 08:21 PM

P: 150

Roller coaster: kinetic energy
i can't work just on that. what do you mean by 'just use conservation of energy'. i need to express my answer in terms of those variables i listed above.



#5
Sep2507, 08:40 PM

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#6
Sep2507, 08:43 PM

P: 150

The energy of the coaster at the beginning is potential energy which is just mgh.



#7
Sep2507, 08:52 PM

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#8
Sep2507, 09:20 PM

P: 150

thanks! i got it ... now what if i want to find the minimum initial height h at which the car can be released that still allows the car to stay in contact with the track at the top of the loop? how would i approach this one?



#9
Sep2507, 09:48 PM

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#10
Sep2507, 09:56 PM

P: 150

well acceleration is V^2/R . and so min velocity would be v = gR ...



#11
Sep2507, 09:57 PM

P: 150

sorry, v = (gr)^(1/2)



#12
Sep2507, 10:01 PM

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#13
Sep2507, 10:10 PM

P: 150

mgh... sorry i'm not getting it



#14
Sep2507, 10:17 PM

P: 150

i set mghmg2R = 0.5(mv^2) and plugged in what i got for v ... so i ended up with h=3R but i think i'm off by some multiplicative factor ???
the ans should be in terms of R by the way... 


#15
Sep2507, 10:22 PM

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#16
Sep2507, 10:25 PM

P: 150

ah, stupid calc. error. thanks lots learningphysics. you made my day haha



#17
Sep2507, 10:27 PM

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#18
Apr310, 05:30 PM

P: 2

Thats very simple and straight forward. use the conservation of energy law, and solve for the unkwon K=kinetic energy at the top of the loop. NB: th energy at initial position is equal to the energy at final position = top of the loop. initial kinetic energy = 0, So u will left only with final unknown kinetic energy K. Min Velocity, v=gR^0.5



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