This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here are the calculations for the tension in the elevator cable under the given conditions. Given: Mass of elevator, m = 500 Kg Acceleration due to gravity, g = 9.8 m/s^2 Acceleration of elevator, a = 2 m/s^2 The forces acting on the elevator are the tension T (upwards) and its weight mg (downwards). According to Newton's second law, the net force F = ma. Taking the upward direction as positive: F = T - mg So, T - mg = ma. Rearranging for tension: T = mg + ma i) Stationary When the elevator is stationary, its acceleration a = 0 m/s^2. Step 1: Substitute the values into the tension formula. T = mg + m(0) T = mg Step 2: Calculate the tension. T = (500 Kg)(9.8 m/s^2) T = 4900 N The tension in the cable when the elevator is stationary is 4900 N. ii) Ascending with an acceleration of 2 m/s^2 When the elevator is ascending, the acceleration a = +2 m/s^2 (positive because it's upwards). Step 1: Substitute the values into the tension formula. T = mg + ma T = m(g+a) Step 2: Calculate the tension. T = 500 Kg (9.8 m/s^2 + 2 m/s^2) T = 500 Kg (11.8 m/s^2) T = 5900 N The tension in the cable when the elevator is ascending is 5900 N. iii) Descending with the same acceleration (2 m/s^2) When the elevator is descending, the acceleration a = -2 m/s^2 (negative because it's downwards). Step 1: Substitute the values into the tension formula. T = mg + ma T = m(g+a) Step 2: Calculate the tension. T = 500 Kg (9.8 m/s^2 + (-2 m/s^2)) T = 500 Kg (9.8 m/s^2 - 2 m/s^2) T = 500 Kg (7.8 m/s^2) T = 3900 N The tension in the cable when the elevator is descending is 3900 N.