The uniform ball of radius ρ and mass m is gently placed in the bowl B with inner radius R and is released. The angle ϕ measures the position of the center of the ball at G with respect to a vertical line, and the angle θ measures the rotation of the ball with respect to a vertical line. Assume that the system lies in the vertical plane. Hint: In working the following problems, we recommend using the rϕ coordinate system shown.
Figure P7.59
Assuming that the ball rolls without slip, that it weighs 3 lb, is at the position ϕ = 40°, and is moving clockwise at 10 ft/s, determine the acceleration of the center of the ball at G and the normal and friction force between the ball and the bowl. Use R = 4 ft and ρ = 1.2 ft.
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