At the scene of an elevator accident, an investigator is gathering evidence. At

Question

At the scene of an elevator accident, an investigator is gathering evidence. At some point the cable broke and a one metric ton elevator with 8 passengers of average mass 70 kg each started to descend. Immediately after the cable snaps, the safety measure begins, which creates a friction force of 15,000 N to slow down the elevator. If the final velocity of the elevator was deduced to be 4 m/s, approximately how many stories did the elevator fall. (Note: Each floor is 4 m in height, one metric ton = 1000 kg.)

I Have the answers , I just have no idea how to solve the problem. Please show as much detail as possible in work. ty

[answer ~11 floors]

Explanation / Answer

We can use kinematics and the knowledge of forces to solve this. First, we know that:
Vf2 - Vo2 = 2ax

We know the two velocities, and we can find the acceleration:

We know that the friction force acts up, and the gravitational force acts down, and that their difference is the total force:

mg - Ffr = Fnet --> where m = 1 metric ton (1000 kg) + (8 * 70 kg) = 1560 kg

(9.81 m/s/s * 1560 kg) - 15,000 N = Fnet

Fnet = 303.6 N --> we divide by m to find acceleration

a = (303.6 N) / (1560 kg)

a = .1946 m/s/s

Pluggin back in to the kinematic, we have:

(4 m/s)2 - (0 m/s)2 = 2(.1946 m/s/s)x

16 = (.38923 m/s/s) x

x = 41.107 m

Dividing by the number of meters per floor, we get:

41.107m / ( 4 m / floor) = 10.277 floors, which we can round to 11 floors, since it won't be at 4 m/s by 10 floors.

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