Final answer:
The tension in the cable supporting an accelerating elevator is calculated using Newton's second law. For an elevator with a mass of 1950 kg and an upward acceleration of 1.95 m/s², the tension is 22912.5 N.
Step-by-step explanation:
To calculate the tension in the cable supporting an elevator during its acceleration, we need to use Newton's second law, which is F = ma, where F is the force, m is the mass, and a is the acceleration. The net force on the elevator is the tension in the cable minus the gravitational force (weight), so the tension T can be found using the equation T = mg + ma, where g is the acceleration due to gravity (9.8 m/s²).
Given the mass of the elevator m is 1950 kg and it accelerates upward at 1.95 m/s², the gravitational force (weight) is mg = 1950 kg × 9.8 m/s². The additional force due to acceleration is ma = 1950 kg × 1.95 m/s². Adding these together:
T = (1950 kg × 9.8 m/s²) + (1950 kg × 1.95 m/s²)
T = 19110 N + 3802.5 N
T = 22912.5 N
Therefore, the tension in the cable is 22912.5 N while the elevator accelerates upward.