Modified from the AP College BoardEngineers are tasked with designing a new solar system themed roller coaster ride. The track starts at Point P, at thetop of a sphere with radius R (representing Jupiter). The track goes down to ground level, then to Point Q, the top ofa sphere of radius r (representing Neptune) and then back to the ground level.Ignore air resistance, and assume friction between the cart and the track is negligibleJupiterRadius RNeptuneradius r Using conservation of energy, derive an expression for the velocity of the cart when it is at the top of the Neptunesphere in terms of R, r and physical constants as needed.Question 2 (2.5 points)1) ListenDraw a clearly labeled free-body diagram of the cart at the top of Neptune (at Point Q). Engineer A says that the problem is the difference in height between the two spheres, and he suggests they decreasethe height of the first sphere (Jupiter) relative to the height of the second sphere (Neptune).Engineer B says the problem is the small radius of curvature of the track as the cart goes over the top of Neptune,and he suggests that they increase the radius of the sphere that represents Neptune.Explain how your answers to Questions 1 and 3 support each engineer's reasoning. The design engineers are concerned about the safety of the coaster. If the normal force becomes less than zero, thecart will lose contact with the track and become a projectile (not good for the occupants!).Derive an expression for the maximum safe speed for the cart at point Q.

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Using conservation of energy, derive an expression for the velocity of the cart when it is at the top of the Neptune sphere in terms of R, r and physical constants as needed.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 64P

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