A 1000 kg elevator is supported by a cable. When the elevator is moving downward and decelerating at 2 m/s^2, taking g = 9.8 m/s^2, what is the tension in the cable?
Answer and explanation
Correct answer: A. 11800 N
- Step 1: Moving downward and decelerating means the acceleration vector points upward: a = +2 m/s^2 (upward).
- Step 2: Apply Newton's second law: T - mg = ma, so T = m*(g + a).
- Step 3: Substitute values: T = 1000 (9.8 + 2.0) = 1000 11.8 = 11800 N.
Answer
11800 N.
Why not the others: 7800 N assumes downward acceleration (downward acceleration subtracts ma); 9800 N is the equilibrium weight at constant speed; 2000 N is only the inertial force ma without gravity.
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