ира3 Frac C2+25c2-25- C/c+5 . - 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

65.75 kg

Step 1: Calculate the angular velocity (ω). 10 revs in 3.5 s means the frequency (f) is 10 revs / 3.5 s = 20/7 Hz. ω = 2πf = 2π(20/7) rad/s = (40π/7) rad/s.

Step 2: Calculate the centripetal acceleration (ac). ac = ω²r = ((40π/7) rad/s)² * 0.6 m = (1600π²/49) m/s²

Step 3: Calculate the centripetal force (Fc). Fc = mac = (0.02 kg) * (1600π²/49) m/s² = (3200π²/49) N

Step 4: Determine the tension in the cord (T). Since the system is in equilibrium, the tension in the cord equals the centripetal force. T = Fc = (3200π²/49) N

Step 5: Calculate the mass of the hanging mass (mh). The tension in the cord is balanced by the weight of the hanging mass. T = mhg mh = T/g = (3200π²/49) N / (9.8 m/s²) = (3200π²/480.2) kg

Step 6: Round the final answer. mh ≈ 65.75 kg

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