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Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked you, his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end - Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.89 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 0, the more time the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of the ball. For example, in the limiting case of 90°, the board would not fall at all! (a) Your instructor wishes to know the minimum angle 0 (in degrees) at which the support would fail to immediately fall out from under the ball. 0 > (b) For that angle, if you were to mistakenly tell your instructor that the trick would succeed, at what position r along the board would he mount the cup? (Give your answer, in m, measured from the hinged end of the board.) m

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked you, his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end - Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.89 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 0, the more time the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of the ball. For example, in the limiting case of 90°, the board would not fall at all! (a) Your instructor wishes to know the minimum angle 0 (in degrees) at which the support would fail to immediately fall out from under the ball. 0 > (b) For that angle, if you were to mistakenly tell your instructor that the trick would succeed, at what position r along the board would he mount the cup? (Give your answer, in m, measured from the hinged end of the board.) m

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter14: Static Equilibrium, Elasticity, And Fracture
Section: Chapter Questions
Problem 13PQ
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Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked you, his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end - Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.89 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 0, the more time the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of the ball. For example, in the limiting case of 90°, the board would not fall at all! (a) Your instructor wishes to know the minimum angle 0 (in degrees) at which the support would fail to immediately fall out from under the ball. 0 > (b) For that angle, if you were to mistakenly tell your instructor that the trick would succeed, at what position r along the board would he mount the cup? (Give your answer, in m, measured from the hinged end of the board.) m
Transcribed Image Text:Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked you, his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end - Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.89 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 0, the more time the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of the ball. For example, in the limiting case of 90°, the board would not fall at all! (a) Your instructor wishes to know the minimum angle 0 (in degrees) at which the support would fail to immediately fall out from under the ball. 0 > (b) For that angle, if you were to mistakenly tell your instructor that the trick would succeed, at what position r along the board would he mount the cup? (Give your answer, in m, measured from the hinged end of the board.) m
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