An elevator cable breaks when a 925 kg elevator is 225 m...

An elevator cable breaks when a 925 kg elevator is 22.5 m above the top of a huge spring (k = 8.00×10^4 N/m) at the bottom of the shaft. a. Calculate the work done by gravity on the elevator before it hits the spring. b. Calculate the speed of the elevator just before striking the spring. c. Calculate the amount the spring compresses (note that here work is done by both the spring and gravity.)

Transcript

00:02 So in this problem we are given that an elevator breaks its cable from the top.

00:08 It has a mass m which is equal to 925 kg and it falls the distance of 22 .5 meters straight down a shaft onto a spring which has a spring constant of 8 into 10 to power 4 newton per meters.

00:29 So with this situation given we are first asked to find what is the work done by the gravity on.

00:35 This elevator.

00:37 So this work done by gravity becomes equal to force by due to gravity times the height h.

00:42 Let's call this height as h.

00:45 So gravity acts the force of gravity or the weight force acts on the body through this force through the distance h and that's the amount of work done because they're both in the same direction.

00:55 This displacement is downwards and the force due to gravity is also downwards.

01:01 First due to gravity is simply the mass times gravity or the weight force times h and you will raise realize that this is also the potential energy formula.

01:09 So work turn to gravity is basically potential energy.

01:13 If you do work against gravity, you gain potential energy.

01:17 Or if you let the gravity do work, then you're losing potential energy in that same fashion.

01:23 So this becomes equal to 925 times 9 .81, which we take as acceleration to gravity times 22 .5.

01:30 And this gives you that the work done is 204 kilojoules.

01:38 So that's part one.

01:40 Then we are asked to find what will be the speed of this elevator just before it hits the spring.

01:49 So basically when it is just here, it has reached down but not hit the spring yet, just a little distance from the spring.

01:55 What will be the speed be at this point? so for that, we say that in the usual case, we'll say the potential energy is equal to kinetic energy.

02:06 Potential energy is what we have calculated...

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