(a) 18717 N
There are two forces acting on the elevator:
- The tension in the cable, T, upward
- The weight of the elevator+passenger, downward, which is given by
W = mg
where m=1700 kg is the mass and g=9.81 m/s^2 is the acceleration of gravity
According to Newton's second law, the resultant of these forces must be equal to the product between mass and acceleration:
T - mg = ma
where
a = 1.20 m/s^2 is the acceleration, also upward
Solving the equation for T, we find the tension in the cable:
(b) 16677 N
In this second part of the trip, the elevator continues at constant velocity. This means that the acceleration is zero:
a = 0
So Newton's second law becomes:
T - mg = ma = 0
Therefore, the tension in the cable will be equal to the weight of the elevator+passenger:
T = mg = (1700 kg)(9.81 m/s^2)=16677 N
(c) 15657 N
In this third part of the trip, the elevator has a deceleration of
a = -0.60 m/s^2
and we use a negative sign since the acceleration is now downward.
Therefore, Newton's second law is
T - mg = ma
And substituting all the data, we find the new tension in the cable:
(d) 19.35 m, 0 m/s
The distance covered by the elevator in part a) of the trip is
The final velocity reached in this part is
In the second part, the elevator moves at constant velocity of
so the distance covered is
The distance covered in the third part will be
While the final velocity is
and the total distance covered (so, the heigth of the elevator above the ground) is