A mass on a frictionless table revolves around a hole in the table, through whic

Question

A mass on a frictionless table revolves around a hole in the table, through which a massless, non-stretching string passes, connecting the revolving mass to a hanging mass underneath the table. Refer to diagram 3 and answer the following: Determine the mass that the revolving object must have to keep a 50 kg hanging mass stationary if it revolves with a velocity of 23 m/s at a distance of 3 meters from the whole. Find the period of the revolution around the hole given the speed and radius in part a). Briefly describe, in words, the nature of the motion of the two objects if the string is cut.

Explanation / Answer

a) As hanging mass is in equilibrium

Tension in string T = 50*9.8 =490 N

For revolving mass,

T = mv^2/r

490*3/23^2 = m

m = 2.78 kg

b) period = 2 pi r / v = 6.28*3/23 = 0.819 s

c) When the string is cut, tension becomes zero, hanging mass falls down and revolving mass moves tangentially

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