Calculating Tension in Elevator Cable

What is the tension in the cable of an elevator cab that weighs 27.0 kN when the cab's speed is (a) increasing at a rate of 1.07 m/s² and (b) decreasing at a rate of 1.07 m/s²?

Tension Calculation When Speed is Increasing

The tension in the cable when the cab's speed is increasing at a rate of 1.07 m/s² is 30,008.24 N. To calculate the tension in the cable when the cab's speed is increasing, we first need to determine the mass of the elevator cab. Using the weight of the cab, w = 27.0 kN, and the acceleration, a = 1.07 m/s², we can find the mass, m. Given: Weight of elevator cab, w = 27,000 N Acceleration, a = 1.07 m/s² We can calculate the mass, m: m = w/g m = 27,000 N / 9.81 m/s² m = 2,749.23 kg Next, we use the formula T = w + ma to find the tension in the cable: T = w + ma T = 27,000 N + 2,749.23 kg × 1.07 m/s² T = 30,008.24 N Therefore, when the cab's speed is increasing at a rate of 1.07 m/s², the tension in the cable is 30,008.24 N.

Tension Calculation When Speed is Decreasing

The tension in the cable when the cab's speed is decreasing at a rate of 1.07 m/s² is 23,991.76 N. To calculate the tension in the cable when the cab's speed is decreasing, we use a similar approach as above. The formula T = w - ma is used in this case. T = w - ma T = 27,000 N - 2,749.23 kg × 1.07 m/s² T = 23,991.76 N Therefore, when the cab's speed is decreasing at a rate of 1.07 m/s², the tension in the cable is 23,991.76 N. In conclusion, the tension in the cable is 30,008.24 N when the cab's speed is increasing at a rate of 1.07 m/s², and it is 23,991.76 N when the cab's speed is decreasing at a rate of 1.07 m/s².
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