1) One end of a string is attached to a center pivot, the other end to a 175 gra

Question

1) One end of a string is attached to a center pivot, the other end to a 175 gram object. The distance from the pivot to the center of of mass of the object is 12cm. The mass swings around the pivot 100 times each 60 seconds at constant speed. a) what is the speed of the mass? b) what is the tension is the string? (ignore the effects of gravity) 2) The same string as in problem 1 is not hung vertically (no rotation), supporting the 175 gram object against gravity (in equilibrium). a) what is the tension on the string? b) how much mass would have to be added to the 175 gram object to make the tension the same as in problem 1b?

Explanation / Answer

a) rotations pers sec = 1.67 ,so omega = 2*pi*1.67

v = r*omega = 0.12*1.67*2*pi m/s = 1.25 m/s

b) T = mv*v/r = 2.28 N

2nd part

a) T = mg = 1.715 N

b) M = 2.28/g = 0.233 kg = 233 grams

so mass to be added = 233-175 = 58 grams

(the answer are rounded to two decimal positon)

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