Draw a before-and-after pictorial representation for the problem. Identify the k

Question

Draw a before-and-after pictorial representation for the problem. Identify the key information and list the known and unknown. + Draw free-body diagrams to visualize forces. Draw as many as you need. + Distinguish conservative and nonconservative forces. Determine We and Wnc during the whole motion. Are they zero or nonzero? Why? + Apply energy conservation theorem and solve problem Box your results + At the end of your solution, write one or two sentences reflecting on your results: do they make sense and why? Problem A 100g ball is tied to a string so that the center of mass hangs 50 cm below the point where the string is tied to a support rod. The ball is pulled aside to a 60° angle with vertical and released. As the string approaches vertical, it encounters a peg D cm below the support rod. The string then bends around the peg. What is the smallest value of D for which the ball will move in a circle wrapping the string around the peg? Use energy conservation to solve this.

Explanation / Answer

Velocity at the bottom portion,

v = sqrt(2g h(1-cos 60 degree))

= sqrt(2*9.8*0.50*(1-0.5))

= 2.2136 m/s

For completion of circle, velocity at bottom = sqrt(4gr)

2.2136^2 = 4gr

r = 2.2136^2/(4*9.8) = 0.125 m =12.5cm

D = 50-12.5 cm = 37.5 cm answer

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