Part A Problem 10.58 What mass should the counterweight have so that it will acc

Question

Part A Problem 10.58 What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator is to be accelerated upward by connecting it to a counterweight by means of a lght but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the Express your answer with the appropriate units pulley, but its mass is 831 m-31358.05 N m= 31358.05 |N pulley, but its mass is 831 kg and it is 1.80 m in diameter. Submit My Answers Give Up Incorrect, Try Again; 3 attempts remaining Enter your answer using dimensions of mass

Explanation / Answer

Here, acceleration = (2 * 6.75)/9 = 1.5   m/sec2

=> angular acceleration of pulley = (1.5/0.9)   =   1.67 rad/sec2

=>     (T1 - T2) * 0.9 =   (1/2 * 831 * 0.9 * 0.9) * 1.67

=>    T1 - T2 = 624.49

Also, T2 - 22500 = 3443.87

=> T2 = 25943.87 N

=> T1 = 26568.36 N

Also,    W * 1.5/9.8 = W - 26568.36

=>   W = 31369.87 N

Part A)    Mass of counterweight = 31369.87 N

Part B)   Tension in cable on counterweight side =    26568.36 N

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