A small block of mass 1.14 kg slides without friction on a horizontal table. Ini

Question

A small block of mass 1.14 kg slides without friction on a horizontal table. Initially it moves in a circle of radius R0 = 0.59 m with a speed 1.4 m/s. It is held in its path by a string that passes through a small hole at the center of the circle. The string is then pulled down a distance of 0.12 m.( R0 - Rf = 0.12 m. It is pulled so slowly that the object continues to move in a circle of continually decreasing radius. 1) What is the torque placed on the mass by the string? 2) What is the final speed of the block? 3) How much work was done by the force that pulled on the string?

Explanation / Answer

a) Touque = F*distance = mv2/r*r = 2.23 Nm

b) Conservation of momentum:

Initial momentum = I*angular vel = mr2*v/r = mvr = 0.94

Final momentum = mv'r' = 0.94

v' = 1.76 m/s

c) Initial energy 0.5Iomega2 = 1.1172 J

Final energy = 1.7656 J

WOrk done = 1.7656-1.1172 = 0.6484 J

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