### Physics Magic Trick Experiment#### Apparatus DescriptionYour physics instructor is designing a magic trick for elementary school children and seeks your assistance. The setup involves a small ball and a cup placed on a board. Here’s how it works:- **Components**: A board of length \( \ell = 1.59 \, \text{m} \), a cup, and a support stick.- **Setup**: The ball is placed such that its center aligns with the upper lip of the cup. The cup is attached to the board.- **Mechanism**: When the support stick is removed, the board rotates around the hinged end, and gravity pulls the ball downward. The goal is for the ball to fall into the cup.#### Experiment DetailsThe critical factor is the angle \( \theta \) of the board:- A larger \( \theta \) gives the ball more time to drop into the cup. - If \( \theta \) is too large, the cup might be too far for the ball to reach.- At \( 90^\circ \), the board wouldn’t rotate, preventing the ball from falling into the cup.#### Questions**(a)** Determine the minimum angle \( \theta \) (in degrees) at which the support wouldn't allow the ball to immediately fall off the board. Input your result:\[ \theta \geq \_\_\_\_^\circ \]**(b)** If you provide the wrong angle suggesting the trick will work, calculate where the cup should be positioned \( r_c \) on the board. (Give the distance \( r_c \) from the hinged end of the board in meters):\[ r_c = \_\_\_\_ \, \text{m} \]By altering \( \theta \) and \( r_c \), this educational demonstration can enhance understanding of rotational dynamics and gravitational effects.

Given,Length of the board, l= 1.59 mConcept:We know the torque is defined as from the rotational…

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked 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 = 1.59 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 9, the more ti 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 th ball. For example, in the limiting case of 90°, the board would not fall at all!

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked 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 = 1.59 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 9, the more ti 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 th ball. For example, in the limiting case of 90°, the board would not fall at all!

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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