A 2.25x10 4 N elevator is to be accelerated upward byconnecting it to a counterw

Question

A 2.25x104 N elevator is to be accelerated upward byconnecting it to a counterweight using a light (but strong!) cablepassing over a solid uniform disk-shaped pulley. There is noappreciable friction at the axle of the pulley, but its mass is 900kg and it is 1.50 m in diameter.

How heavy should the counterweight be so that it will acceleratethe elevator upward through 6.50 m in the first 3.50 s, startingfrom rest? Mass in kg = ?

Under these conditions, what is the tension in the cable onelevator side of the pulley? Tension in N = ?

Under these conditions, what is the tension in the cable on thecounterweight side of the pulley? Tension in N = ?

Explanation / Answer

Here,W = 2.25 * 104 N and g = 9.8 m/s2 mass : m = (W/g) = (2.25 *104/9.8) = 2.3 * 103 kg From the equations of motion we have : mass : m = (W/g) = (2.25 *104/9.8) = 2.3 * 103 kg From the equations of motion we have :                                                  S = ut + (1/2)at2 Here,S = 6.25 m, u = 0 m/s and t = 3.50 s                     a = (2S/t2)                         a = [(2 * 6.25)/(3.50)2]                         a = 1.02 m/s2 The weight of the counterweight is                        W = m * a = 2.3 * 103 * 1.02 = 2.34 *103 N The tension in the cable on elevator side of the pulley is2.25 * 104 N The tension in the cable on counterweight side of the pulleyis : 2.34 * 103 + 900 * 9.8                                                                                                                                                                             = 2.34 * 103 + 8820                                                                                                                                                             = 11160 N = 11.160 * 103 N. Hope this helps u! The weight of the counterweight is                        W = m * a = 2.3 * 103 * 1.02 = 2.34 *103 N The tension in the cable on elevator side of the pulley is2.25 * 104 N The tension in the cable on counterweight side of the pulleyis : 2.34 * 103 + 900 * 9.8                                                                                                                                                                             = 2.34 * 103 + 8820                                                                                                                                                             = 11160 N = 11.160 * 103 N. Hope this helps u!

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