Question

3. = -16 points Ball in a Bowl A 39 g ball with a radius of 21 mm rolls back and forth in a hemispherical bowl of radius 6 cm. (a) What is the period of the oscillation if the ball is solid? (b) What is the period of the oscillation if the ball is hollow? (c) What is the percent difference between the two?

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A 39 g ball with a radius of 21 mm rolls back and forth in a hemispherical bowl of radius 6 cm.

(a) What is the period of the oscillation if the ball is solid?


(b) What is the period of the oscillation if the ball is hollow?


(c) What is the percent difference between the two?

Answer 1

IR-r I t2 ł= I& - mg(R-r) sind - I do For small angle sinoro ► d'O + mg (R- OG dt? I ura the period W = mg (R-1) T= 20 mg where I = I am + m (Rar)?

@ For a solid sphere I = 3 m p 2 + m (R-r? I = 2(0.039)(0.0212+(0.039)(0.06-0.0202 I = 6.62x10 km² - T = 21 (6.62x105 IT = 0.4195) Y(0,039) (9.8)(0.06-0021) For hollow sphere I= 2 mr² + m(R-r? I= {(0.039)(0.020)2+(0.039)(0.06-0.021)2 I=7.08x10®kg me DE 217 1.08x10 -TE 0.4335) 10.03919.8)(0.06-002) @ Percentage dyference %D72-X 100 ta %D=3.23%