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Case Study: How do we determine the energy

of a roller coaster?

A flume ride at Universal Studios Hollywood carries a boat filled with thrill-seekers
through scenes of life-like dinosaurs from the movie Jurassic Park. Near the end of the
ride the boat gently dips over the edge of a 33-m-long downhill track filled with rush-
ing water, and accelerates down the 51° slope before entering a pond of still water. The
boat glides about 15 m before coming to a near stop due to drag forces.
Kinetic energy is associated with motion. Conservative interactions within a system
give rise to potential energy; for example, the gravitational interaction between Earth
and the boat and riders can be described as gravitational potential energy of the
Earth–boat/rider system. Energy can be converted from one type into the other, but
total energy is always conserved.
That is certainly the case for our intrepid riders and their boat: Energy is neither
created nor destroyed; once the boat starts its descent, we can use the resulting rela-
tionship to determine the properties of its motion. After you learn the physics of the
conservation of energy and the relationship between work and energy, you’ll be able
to answer many questions about the science that underlies the Jurassic Park ride. For
example…
The speed of the boat at the top of the final drop is close to zero. Estimate the
speed of the boat at the bottom of the final drop. Ignore any nonconservative forces,
which are relatively small. Does the mass of the boat or the riders affect your answer?
Estimate the average drag force that the water in the pond exerts on the boat. Do
you think you yourself could exert a force of that magnitude?

By the end of these chapters, you should be able to apply conservation principles
and the work-energy theorem to real-world problems. For instance, another
amusement park wants to build a replica of this ride, but in order to slow down
the boats—and to save space!—it needs to replace the pond at the end of the ride
and consider whether they can use a horizontal spring. You will be able to help
them decide.

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Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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