Rollercoasters are energy at work!
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Rollercoasters are energy at work!
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[post_date] => 2025-01-09 07:36:59
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
One of the most interesting and fun demonstrations of the conservation of energy can be found in amusement parks. Rollercoaster designers often utilize the principles of physics to ensure that a minimal amount of resources is pooled into the system, often by taking advantage of gravitational potential energy. This is fiscally beneficial for the owner of the park, as it is not necessary to propel the cart through the use of an engine.
An amusement park owner is developing one of these new rides. The coaster’s track begins with a 320kg cart starting from rest and rolling 34 meters down an incline. The cart then moves up a 21m tall ramp and eventually is stopped by a spring with a spring constant of 1325 N/m. Visitors will then exit the coaster and it will be manually returned to its starting position.
Assume that no energy is lost to heat or dissipated by friction or air resistance.
Figure 1. A rough diagram of the cart’s projected path.
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[question] => How fast will the cart be going when it reaches the top of the 21m tall ramp?
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[description] => Reason for the Correct Answer:
Use conservation of energy.
Gravitational potential energy is turning into kinetic energy.
mgh = ½ mv² or (320kg)(9.8m/s²)(34m-21m) = ½ (320kg)v² so v = 16m/s
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[each_answer] => A. 5.0 m/s
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[each_answer] => B. 12 m/s
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[each_answer] => C. 8.8 m/s
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[each_answer] => D. 16 m/s
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[question] => How could the ride be adjusted to decrease the amount the spring gets compressed?
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[answer] => 3
[description] => Reason for the Correct Answer:
In order to decrease the compression of the spring, the cart must reach it with less speed.
Think about what would cause the cart to have less kinetic energy when it reaches the spring.
Since increasing the height of the 21m tall ramp would increase the gravitational potential energy of the cart there, there would be less kinetic energy and less speed, which would cause less compression.
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[each_answer] => A. Make the 34m tall incline less steep
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[each_answer] => B. Decrease the spring constant
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[each_answer] => C. Make the 21m ramp taller
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[each_answer] => D. Make the 21m ramp more steep
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[question] => What was the total change in gravitational potential energy for the entire trip (from start to spring)?
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[answer] => 4
[description] => Reason for the Correct Answer:
Gravitational potential energy is given by the equation PE = mgh
The change in anything is the final amount – initial amount.
PE(final) – PE(initial) = (320kg)(9.8m/s²)(21m) – (320kg)(9.8m/s2)(34m) = -41,000J
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[each_answer] => A. 5,000 J
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[each_answer] => B. -23,000 J
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[each_answer] => C. 19,000 J
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[question] => While the spring is being compressed by the cart, what is happening to the kinetic energy of the cart, gravitational potential energy of the cart, and spring potential energy of the spring?
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[answer] => 1
[description] => Reason for the Correct Answer:
The cart is being slowed down by the spring.
The vertical height of the cart is not changing.
The spring is being compressed.
Since the cart is slowing, KE decreases, since the height does not change PE(gravity) stays constant, and since the spring is being compressed PE(spring) increases
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[each_answer] => A. KE decreases, PE(gravity) stays constant, and PE(spring) increases.
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[each_answer] => B. KE increases, PE(gravity) decreases, and PE(spring) stays constant.
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[each_answer] => C. KE stays constant, PE(gravity) stays constant, and PE(spring) decreases.
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[each_answer] => D. KE decreases, PE(gravity) decreases, and PE(spring) increases.
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[question] => How much will the spring be compressed once the ride stops?
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[answer] => 4
[description] => Reason for the Correct Answer:
Use conservation of energy
Use the velocity of the cart when it hits the spring, as calculated in question 1
Kinetic energy is turning into spring potential energy
½ mv² = ½ kx² or ½ (320kg)(16)² = ½ (1325N/m)x², so x = 7.9m
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[each_answer] => A. 9.3 meters
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[each_answer] => B. 5.2 meters
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[each_answer] => C. 6.1 meters
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[each_answer] => D. 7.9 meters
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[post_title] => Rollercoasters are energy at work!
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