Solved: CP A thin-walled, hollow spherical shell of mass m

Chapter 10, Problem 76P

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QUESTION:

A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in Fig. P10.76. Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to \(h_{0}\) and R, and the work done by rolling friction is negligible. (a) What is the minimum height \(h_{0}\) for which this shell will make a complete loop-the-loop on the circular part of the track? (b) How hard does the track push on the shell at point B, which is at the same level as the center of the circle? (c) Suppose that the track had no friction and the shell was released from the same height \(h_{0}\) you found in part (a). Would it make a complete loop-the-loop? How do you know? (d) In part (c), how hard does the track push on the shell at point A, the top of the circle? How hard did it push on the shell in part (a)?

Equation Transcription:

Text Transcription:

h_0

h_0

h_0

h_0

Questions & Answers

QUESTION:

A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in Fig. P10.76. Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to \(h_{0}\) and R, and the work done by rolling friction is negligible. (a) What is the minimum height \(h_{0}\) for which this shell will make a complete loop-the-loop on the circular part of the track? (b) How hard does the track push on the shell at point B, which is at the same level as the center of the circle? (c) Suppose that the track had no friction and the shell was released from the same height \(h_{0}\) you found in part (a). Would it make a complete loop-the-loop? How do you know? (d) In part (c), how hard does the track push on the shell at point A, the top of the circle? How hard did it push on the shell in part (a)?

Equation Transcription:

Text Transcription:

h_0

h_0

h_0

h_0

ANSWER:

Solution 76P

  1.  The minimum starting height necessary for the shell to go around the loop without falling is

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