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Can Tony Conquer the Third Hill on the Wooden Roller Coaster at PNE?

Tony decides to ride the wooden roller coaster at the PNE, but excitement turns to anxiety when the electrical system fails as he reaches the peak. With an initial kinetic energy (KE) of 2000J, Tony reaches the second hill before questioning if he can make it over the third. Through calculating the total energy transformations, including potential and kinetic energy, we find that Tony can indeed conquer the third hill. Discover the physics behind his thrilling journey and the calculations that lead to his triumphant ride.

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Can Tony Conquer the Third Hill on the Wooden Roller Coaster at PNE?

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  1. PNE Question Project Tony shao Alex McKenzie Austin Gardner

  2. Wooden Roller-coaster • Tony decides to ride the wooden roller coaster at the PNE. As his car reaches the top of the hill, the electrical system in the coaster crashes. After starting at the top of the first hill with an initial KE of 2000J, Tony makes it up the second hill. Is Tony able to make it over the third hill?

  3. TEi = 51450J PEi = 49450J KEi = 2000J Graph 11.547 m 30 degrees 34.61m H= 10m 55 degrees 30m 60 degrees H= 8m 30 degrees

  4. Solution • TEi = 51450 J TE = KE+PE+WEe • KEi= 2000 J Fg = Mg • PEi = 44450 J Fg = (175)(9.8) • M = 1751 Fg = 1715 N • M = 0.07 171Sin(30) = Fn • Fg = 1715 N 857.5 = Fn • Fn = 857.5 N Ff = mfN W = Ffd • Ff = 60.025 N Ff= (0.07)(85.7) • Ff = 60.025 N

  5. Solution • W1r = (60.025)(34.61) W3r = (60.025)(11.547) • TE = KE + PE +WFr TE = KE + PE + WEr • 51450 = KE + 0 + 2077.52 s WFr = 2770.6 + 693.1 • KE = 49372.5 51430 = WE + 0 + 3463.7 • KE = 47916.3 • W2r = (60.025)(11.547) • TE = WE + PE + WFrWfr = (60.025)(14.766) • WFr = 693.1 + 12077 TE = KE + PE + Wfr • 51450 = KE + PE + 2770.6 Wfr = 3463.7 + 586.2 • 45679.4 = WE + PE 51450 = 0 + PE + 4049.9

  6. Solution • PE = 47400.1 • Mgh = 47400.1 • 47400.1 J = (175)(9.8)h • H = 27.6 m • Yes, the cart can easily makes it over the third hill.

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