Explain why the top of the loop cannot be the same height as (or higher than) the top of the first hill. Assume the roller coast
er and its surroundings are close to a closed system. Use what you know about energy transformations and the effects of friction within a closed system to write your answer.
Passage
Examine this diagram of a roller-coaster track. The very top of the first hill (point B) is higher than the very top of the loop (point D). After the cars reach point B, this roller coaster needs no additional energy to complete its trip.
Passage
Examine this diagram of a roller-coaster track. The very top of the first hill (point B) is higher than the very top of the loop (point D). After the cars reach point B, this roller coaster needs no additional energy to complete its trip.
2 answers:
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1. 168.1 Hz
To find the apparent frequency heard by the driver in the car, we can use the formula for the Doppler effect:
where
f is the original sound of the horn
v is the speed of sound
is the velocity of the observer (the driver and the car), which is positive if the observer is moving towards the source and negative if it is moving away
is the velocity of the sound source (the train), which is positive if the source is moving away from the observer and negative otherwise
In this problem we have, according to the sign convention used:
Substituting, we find:
2.
The speed of light can be calculated as
where
d is the distance travelled
t is the time taken
In this problem:
is the total distance travelled by the laser beam (twice the distance between the Earth and the Moon)
t = 2.60 s is the time taken
Substituting in the formula,