THE PROBLEM An ice cube slides back and forth in a bowl. When viewed from the si

Question

THE PROBLEM An ice cube slides back and forth in a bowl. When viewed from the side, the height of the bowl is hcr2 where x is the horizontal position and c-0.002 cm1.The maximum speed of the ice cube is V-49 cm/s. At which values of x does the ice cube begin moving back toward the centre of the bowl? PAPER SOLUTION INTERPRET Identify all of the true statements. A. The ice cube has the same amount of potential energy at each turning point. B. Mechanical energy is conserved. C. The ice cube has negative kinetic energy in the left half of the bowl and positive kinetic energy in the right half. D. The ice cube has positive kinetic energy in the left half of the bowl and negative kinetic energy in the right half. E. Mechanical energy is not conserved because gravity is involved F. The ice cube has the same amount of kinetic energy at each turning point. G.None of the above. DEVELOP Derive an algebraic expression for the turning point at smaller x Derive an algebraic expression for the turning point at largerx

Explanation / Answer

Applying energy conservation,

PEi + KEi = PEf + KEf

0 + m v0^2 /2 = m g h + 0

h = v^2 / 2 g

and h = c x^2 = v^2 / 2 g

x = +- v / sqrt(2 g c)

x_left = - v / sqrt(2 g c)

x_right = + v / sqrt(2 g c)

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