Final answer:
Using Newton's second law of motion, the acceleration of the elevator is calculated to be -8.51 m/s². However, the negative acceleration indicates that the elevator cannot move upward as the force applied is insufficient to counteract gravity, pointing to a possible error in the problem as passengers are unlikely to weigh 800 kg each.
Step-by-step explanation:
The question asks us to find the acceleration of an elevator moving upward when a force is applied by the cable. To solve this, we will use Newton's second law of motion (F = ma), where F is the force applied, m is the mass of the object, and a is the acceleration. Given that the mass of the elevator is 10,000 kg and the combined mass of the passengers is 4,000 kg (5 passengers × 800 kg each), the total mass is 14,000 kg. The applied force by the cable is 18,000 N.
The net force acting on the elevator is given by subtracting the force of gravity (mg) from the applied force (F = ma). The force of gravity is calculated as the product of the total mass and acceleration due to gravity (g = 9.8 m/s²). Therefore, the force of gravity is Fg = 14,000 kg × 9.8 m/s² = 137,200 N.
The net force is the applied force minus the force of gravity: Net F = 18,000 N - 137,200 N = -119,200 N. We take the upward direction as positive, so the negative net force indicates that the actual upward force is less than the downward force of gravity. The acceleration is found by dividing the net force by the total mass: a = Net F / m = -119,200 N / 14,000 kg = -8.51 m/s². The negative sign indicates that the elevator actually can't accelerate upwards with the given parameters, suggesting there has been a mistake in the problem's figures or a misunderstanding of the question, as a typical passenger does not weigh 800 kg.