Final answer:
The acceleration of the elevator while braking is (D) 9.8 m/s² up, calculated by applying Newton's second law of motion to the net upward force after accounting for the weight of the elevator.
Step-by-step explanation:
The question involves calculating the acceleration of an elevator when the braking force is applied. With the weight of the elevator acting downward and the brake force acting upward, we use Newton's second law of motion (F = ma) to find the net force and hence the acceleration.
To solve for acceleration, we first find the net force by subtracting the weight of the elevator from the braking force: 100,000 N (upward force) - 50,000 N (downward weight) = 50,000 N net upward force. Then, we divide the net force by the mass of the elevator (which is the weight divided by the acceleration due to gravity, g = 9.8 m/s²). The mass is 50,000 N / 9.8 m/s² = 5102 kg. The acceleration (a) is the net force divided by the mass: 50,000 N / 5102 kg = 9.8 m/s² upwards.
Thus, the correct answer is (D) 9.8 m/s² up, as the elevator would accelerate upward with this acceleration due to the brake force being greater than its weight.