Ugh I'm so dumb and it makes me so mad. I should have considered your initial warning more. Okay, that makes perfect sense now. Thank you soooooo much for your help, it was much appreciated towards not only getting the correct answer, but fully understanding the problem at hand.
In the up direction of my FBD:
Force of friction = 17000
In the downward direction of my FBD:
Weight = m*g = 19600
Spring force = k*x = 10600
So, up - down:
17000-19600-10600=ma; a= -6.6 m/s^2 which is not right. This seems logical, but where did I go wrong?
Ah, that is the right answer. Thanks for pointing out my dumb mistake.
And now for part b, the acceleration:
I don't know how to approach this problem at all. Maybe,
Sum of the Forces = ma; where the sum of the forces would be 1/2kx^2-frictional force?
I don't know, I am stumped.
Ok, so using:
Initial Kinetic Energy + Potential Energy due to Gravity = Energy of the Spring + Energy of the Frictional Brake
.5*2000*42+2000*9.8*2 = .5*k*22+17000*2
I get k = 10600 N/m
Then plugging it back into:
Initial Kinetic Energy + Potential Energy due to Gravity = Energy of...
Yes, I copied it word for word.
Even if I use k = 9000 N/m, I still come out with the wrong velocity of 8.23.
If you know what you are doing, and sure you are right, that might be possible that the elevator stops before it reaches 2m, but the problem should still be valid if it is not...
So,
.5*m*v^2 = .5*k*x^2+f*x
.5*2000*16 = .5*k*4+17000*2
If that's correct, then k = -9000 N/m.
Plugging that back into my original of:
.5*2000*42+2000*9.8*2=.5*2000*v2+.5*(-9000)*12 - 17000(1).
I get v=8.76 m/s^2 which is still incorrect.
Homework Statement
In a "worst-case" design scenario, a 2000-kg elevator with broken cables is falling at 4.00 m/s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing 2.00 m as it does so. During the motion a safety...