D = 8cm H=8cm - Gauthmath

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Question

A 20-g rotating object is set in horizontal motion as shown in the figure below.  The rotating object is connected to a hanging mass using a cord. The radius of the  motion is supposed to be 60 cm. What is the mass of the hanging mass if the time  it takes to complete 10 revs is 3.5 s?  Hanging massSHOW LESS0

Solution

The mass of the hanging mass is 0.197 kg.

Explanation: Step 1: The rotating object is in uniform circular motion. The centripetal force is provided by the tension in the cord. Step 2: The tension in the cord is equal to the weight of the hanging mass. Step 3: The centripetal force is given by: F = mv^2/r, where m is the mass of the rotating object, v is its speed, and r is the radius of the circular path. Step 4: The speed of the rotating object is given by: v = 2πr/T, where T is the period of the motion. Step 5: The period of the motion is the time it takes to complete one revolution. In this case, the period is 3.5 s/10 revs = 0.35 s/rev. Step 6: Substitute the values into the equation for centripetal force: F = (0.02 kg)(2π(0.6 m)/(0.35 s))^2/(0.6 m) = 1.93 N. Step 7: The weight of the hanging mass is equal to the tension in the cord, which is 1.93 N. Step 8: The mass of the hanging mass is given by: m = F/g = 1.93 N/9.8 m/s^2 = 0.197 kg.

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