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|#244 - If path 3 is taken, the mass converts GPE into KE at a faster …||10/27/2013 on which car enters first?||0|
|#170 - i am procrastinating solving this problem and this appears on … [+] (6 new replies)||10/27/2013 on which car enters first?||0|
#184 - quicksta (10/27/2013) [-]
The cars all reach the finish line at the same time.
Assuming that the entire scenario is a closed system, gravity is constant, friction is constant (or non-existent), and the cars are identical: all of the cars start at the same height and finish at the same height. Because of conservation of energy, we know that they all start with the same gravitational potential and end with the same kinetic energy. Since their energy conversion is the same, they take the same amount of time to reach the finish line, and each crosses the line at a different velocity.
An Engineering Student
#244 - wirelessfidelity (10/27/2013) [-]
If path 3 is taken, the mass converts GPE into KE at a faster rate than path 1.
so while it travels more distance, it's initial pickup in speed more than makes up for it. solving the euler-lagrange equation reveals that this path is a cycloid, and this path is of minimum time. it does not say different energy or speed. it just says the path will take the least time. likewise energy conservations describe nothing about time. it should be possible to consider energy conservation at each and every point and arrive at the same conclusion that path 1 is not the fast path.
A Physics student.
#213 - veettrees (10/27/2013) [-]
Just because they end with the same kinetic energy doesn't mean they have the same average velocity. If your answer were correct than pretty much any path between the two points would take the same time, which common sense would tell us is wrong. You need to do calculus to find the answer, which has been done by Newton and others (It's a cycloid). mathworld.wolfram.com/BrachistochroneProblem.html
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