Topic: Engineering Mechanics
An elevator has a mass of 5000 kg. When the tension in the supporting cable is 60 kN, the acceleration of the elevator is nearly
- A. 8 m/s²
- B. 12 m/s²
- C. -2 m/s²
- D. 2 m/s²
Answer: D. 2 m/s²
Explanation: Applying Newton's second law and drawing a free body diagram for the elevator: Net Force = mass * acceleration. The upward force is the cable tension (T = 60000 N) and the downward force is the weight (mg = 5000 kg * 9.81 m/s²). The equation is T - mg = ma. Substituting the values gives 60000 - 49050 = 5000 * a. Solving for acceleration yields 10950 = 5000 * a, resulting in a = 2.19 m/s², which is approximately 2 m/s².