R R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.)

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A mass m = 88 kg slides on a frictionless track that has a drop, followed by
a loop-the-loop with radius R = 15.8 m and finally a flat straight section at
the same height as the center of the loop (15.8 m off the ground). Since
the mass would not make it around the loop if released from the height of
the top of the loop (do you know why?) it must be released above the top
of the loop-the-loop height. (Assume the mass never leaves the smooth
track at any point on its path.)
Transcribed Image Text:R R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.)
4) If the mass has just enough speed to make it around the loop without
leaving the track, what is its speed at the final flat level (15.8 m off the
ground)?
m/s
Submit
m
5) Now a spring with spring constant k = 16500 N/m is used on the final flat
surface to stop the mass. How far does the spring compress?
+
Submit
+
6) It turns out the engineers designing the loop-the-loop didn't really know
physics when they made the ride, the first drop was only as high as the
top of the loop-the-loop. To account for the mistake, they decided to give
the mass an initial velocity right at the beginning.
How fast do they need to push the mass at the beginning (now at a height
equal to the top of the loop-the-loop) to get the mass around the loop-
the-loop without falling off the track?
m/s Submit
+
Transcribed Image Text:4) If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (15.8 m off the ground)? m/s Submit m 5) Now a spring with spring constant k = 16500 N/m is used on the final flat surface to stop the mass. How far does the spring compress? + Submit + 6) It turns out the engineers designing the loop-the-loop didn't really know physics when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning. How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop- the-loop without falling off the track? m/s Submit +
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