2. Another amusement park ride that seems to defy gravity is a rollercoaster when it goes through a loop. Let's study the moment when the coaster is upside down at the exact top of the loop. Assume the loop of this coaster is circular and has a radius of 8.0 meters. a) Draw a free body diagram for a rider at the moment she is upside down. You may ignore any horizontal forces you might think of - we only want to understand the vertical behavior. Careful! There are only 2 vertical forces but this is still a strange situation. Rollercoasters are designed to go fast enough that they don't "just barely" make it through the top of the loop: you still feel a normal force while upside down, though it is usually smaller than your full weight. In other words, you don't lose contact with your seat. Assume that this particular rollercoaster is designed so that at the top of the loop, n = 0.6mg. b) Using this assumption, write down Newton's Second Law based on your diagram and then solve it for the speed of the coaster at the top of the loop. Note that again the mass must cancel, because we want people of all different sizes not to fall out of the rollercoaster.
2. Another amusement park ride that seems to defy gravity is a rollercoaster when it goes through a loop. Let's study the moment when the coaster is upside down at the exact top of the loop. Assume the loop of this coaster is circular and has a radius of 8.0 meters. a) Draw a free body diagram for a rider at the moment she is upside down. You may ignore any horizontal forces you might think of - we only want to understand the vertical behavior. Careful! There are only 2 vertical forces but this is still a strange situation. Rollercoasters are designed to go fast enough that they don't "just barely" make it through the top of the loop: you still feel a normal force while upside down, though it is usually smaller than your full weight. In other words, you don't lose contact with your seat. Assume that this particular rollercoaster is designed so that at the top of the loop, n = 0.6mg. b) Using this assumption, write down Newton's Second Law based on your diagram and then solve it for the speed of the coaster at the top of the loop. Note that again the mass must cancel, because we want people of all different sizes not to fall out of the rollercoaster.
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Transcribed Image Text:2. Another amusement park ride that seems to defy gravity is a rollercoaster when it goes through a loop.
Let's study the moment when the coaster is upside down at the exact top of the loop. Assume the loop of
this coaster is circular and has a radius of 8.0 meters.
a) Draw a free body diagram for a rider at the moment she is upside down. You may ignore any horizontal
forces you might think of - we only want to understand the vertical behavior. Careful! There are only 2
vertical forces but this is still a strange situation.
Rollercoasters are designed to go fast enough that they don't "just barely" make it through the top of the
loop: you still feel a normal force while upside down, though it is usually smaller than your full weight. In
other words, you don't lose contact with your seat. Assume that this particular rollercoaster is designed so
that at the top of the loop, n = 0.6mg.
b) Using this assumption, write down Newton's Second Law based on your diagram and then solve it for
the speed of the coaster at the top of the loop. Note that again the mass must cancel, because we want
people of all different sizes not to fall out of the rollercoaster.
Expert Solution
Introduction:
We are at the top of loop in roller coaster ride. We draw free body diagram. We experience centrifugal force at the top which prevents us from falling downwards. We then apply 2nd law of motion and find speed of roller coaster.
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