ProblemSet7

# ProblemSet7 - rounded corner is arbitrarily small. Track C...

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Problem Set 7 Physics 1116 : Due Friday, 10/15/2010 Please write the names of any classmates with whom you discussed the homework problems at the top of your problem set 6. Consider a ﬁxed vertical hoop of radius R attached to the ground. One end of a massless spring of spring constant k and natural (relaxed) length x 0 is attached to the bottom of the hoop; the other end of the spring is attached to a mass m . The spring is oriented horizontally and then compressed to nearly zero length, and then let go, pushing the mass around the hoop. What is the minimum value of the spring’s natural length x 0 such that the mass would remain in contact with the hoop at all times? 7. A particle of mass m is released with zero velocity at the top of three diﬀerent frictionless tracks. Each track drops a vertical distance d , and is also a horizontal length d . Track A is a straight line. Track B is an “L” shaped track, where the

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Unformatted text preview: rounded corner is arbitrarily small. Track C is a quarter circle of radius d . Find the time it takes for the mass to go from the top to the end of each of the three tracks. Hint : R π/ 2 (sin θ )-1 / 2 dθ ≈ 2 . 62206. 8. Extra Credit Question Please work on this question by yourself! Iceman (the X-Man, not Val Kilmer’s character from Top Gun) is able to slide without friction inside a hemispherical bowl of radius R . The bottom of the bowl is ﬂat and sits on the ground, and the bottom of the bowl has a coeﬃcient of friction of μ = 1 with the ground. Iceman drops into the top of the bowl from rest ( v (0) = 0), and then begins sliding around inside the bowl. Assuming that Iceman has a mass m and the bowl has a mass M , what is the maximum ratio of m/M such that the bowl never moves relative to the ground? R M = 1 M m...
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## This note was uploaded on 11/03/2010 for the course PHYS 1116 taught by Professor Elser, v during the Spring '05 term at Cornell.

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ProblemSet7 - rounded corner is arbitrarily small. Track C...

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