Final answer:
When the elevator cable breaks, the elevator is in free fall and experiences an acceleration due to gravity. The tension in the cable is zero as it is no longer supporting the elevator. The height the elevator was at and its final velocity can be calculated using equations for free fall.
Step-by-step explanation:
In this scenario, the elevator is in free fall after the cable breaks. During free fall, the only force acting on the elevator is gravity. This means that the tension in the cable is zero, as there is no longer a cable supporting the elevator. The elevator will experience a downward acceleration due to gravity, which can be calculated using the formula a = g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
To determine how high the elevator was before the cable broke, we can use the equation for displacement in free fall: h = (1/2)gt², where h is the height, g is the acceleration due to gravity, and t is the time of free fall. Since the elevator starts from rest, the initial velocity is zero. So, we can set up the equation h = (1/2)(9.8)(t²), where h is the initial height and t is the time of free fall. Solving for h, we can find the height.
The final velocity of the elevator when it lands on the shock absorber can be determined using the equation v = at, where a is the acceleration due to gravity and t is the time of free fall. In this case, the final velocity will be the same as the velocity of the elevator just before landing.