AP Free Response Question
2004 Form B - B1
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A designer is working on a new roller coaster, and she begins by making a scale model. On this model, a car of total mass 0.50 kg moves with negligible friction along the track shown in the figure below.
The car is given an initial speed v
_{o}
= 1.5 m/s at the top of the first hill of height 2.0 m. Point A is located at a height of 1.9 m at the top of the second hill, the upper part of which is a circular arc of radius 0.95 m.
(a) Calculate the speed of the car at point A.
(b) On the figure of the car below, draw and label vectors to represent the forces on the car at point A.
(c) Calculate the magnitude of the force of the track on the car at point A.
(d) In order to stop the car at point A, some friction must be introduced. Calculate the work that must be done by the friction force in order to stop the car at point A.
(e) Explain how to modify the track design to cause the car to lose contact with the track at point A before descending down the track. Justify your answer.
Topic Formulas
Description
Published Formula
centripetal acceleration
elastic potential energy
friction
gravitational potential energy
Hooke's Law
kinetic energy
Newton's 2nd Law
Newton's Law of Universal Gravitation
period of a simple pendulum
period of a spring
potential energy
power
power
work
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