Final answer:
To calculate the tension in an elevator's cable, the mass of the elevator, its acceleration, and gravity are important factors. The sum of the force of gravity and the force needed for acceleration gives the tension during ascent, while the weight of the elevator equals tension at constant velocity. For deceleration, the force required to slow down is subtracted from the elevator's weight.
Step-by-step explanation:
Understanding Elevator Physics
When calculating the tension in the cable of an elevator, we consider the mass of the elevator, its acceleration, and gravity. To solve for the tension when an elevator accelerates upward:
- Calculate the force of gravity (weight) using Fg = m * g, where m is mass and g is the acceleration due to gravity.
- Calculate the net force required for acceleration using F = m * a, where a is the acceleration.
- The total tension is the sum T = Fg + F.
In case (a), the elevator with a mass of 1700 kg accelerates at 1.20 m/s², so the tension is greater than the weight of the elevator.
For case (b), when the elevator moves at a constant velocity, the net force is zero as there is no acceleration, and the tension equals the weight of the elevator.
To find the tension during deceleration in case (c), you subtract the force required for deceleration from the weight.
Lastly, to determine how high the elevator has moved and its final velocity, you use kinematic equations.