# Conservation of Energy Question

• Arman777
In summary: There is the weight of the cab, the gravitational force, and the force of the spring. The spring is initially compressed, but it will eventually return to its natural length and exert the same force on the cab as before.
Arman777
Gold Member

Theres a pic.

## Homework Equations

##W_{friction}=W_{fr}=Δ(ME)##
##U_{spring}=U_s=\frac 1 2kx^2##

## The Attempt at a Solution

I found (a) using ##W_{fr}=Δ(ME)## which ##v=7,4 \frac m s##
For (b) I wrote;##\frac 1 2kx^2-\frac 1 2mv^2=W_{fr}##
##\frac 1 2kx^2-\frac 1 2mv^2=-F_{fr}x## (here x are the same and represents the comprassion distance)
I found ##\frac 1 2mv^2=48988J##
so ##75000x^2+4400x-48988=0##
I solved it but didnt came the answer where did I go wrong ?

Thanks

What did you get for an answer? And what is the right answer?

I found 77 cm answer says 90 cm

Sorry, it took me so long to get back. I was off doing something else. I got 0.78 m (or 78 cm) for my answer.

TomHart said:
Sorry, it took me so long to get back. I was off doing something else. I got 0.78 m (or 78 cm) for my answer.

then we get same results so there must be some roundings during the process...so I am correct I guess thank you

TomHart
I solved (c) but (d) is hard.Can someone help me ?

Arman777 said:
##\frac 1 2kx^2-\frac 1 2mv^2=-F_{fr}x## (here x are the same and represents the comprassion distance)
Did hitting the spring turn off gravity?

TomHart
haruspex said:
Did hitting the spring turn off gravity?
Yeah...you are right.I didnt see that

Arman777 said:
Yeah...you are right.I didnt see that
Me either.

haruspex said:
Did hitting the spring turn off gravity?

I found 0.93m when I did it.

I found also (c) correctly with an exact result.

Still having problem with (d)

Arman777 said:
I found 0.93m when I did it.
Hmm... I think I got .90m.
Arman777 said:
Still having problem with (d)
d) seems a bit strange to me. Haven't you already worked out all the distances moved in b) and c)? Should just be a matter of adding them up. It feels like it is hinting at a shortcut to get this answer without using the intermediate ones, but I don't think there is one.

haruspex said:
Hmm... I think I got .90m.

d) seems a bit strange to me. Haven't you already worked out all the distances moved in b) and c)? Should just be a matter of adding them up. It feels like it is hinting at a shortcut to get this answer without using the intermediate ones, but I don't think there is one.

0.93 is approxemetly 0.90 I don't mind so much.

The answer is 15m for (d).

(b) is 0.9m and (c) is 2.8m

haruspex said:
Hmm... I think I got .90m.

d) seems a bit strange to me. Haven't you already worked out all the distances moved in b) and c)? Should just be a matter of adding them up. It feels like it is hinting at a shortcut to get this answer without using the intermediate ones, but I don't think there is one.
Consider the initial position and the eventual final (resting) position of the cab. The total energy input and eventually dissipated is determined by these points...

I guess I see...Last energy of our system is 47628J And he took 2.8m+0.9m=3.7m till now.He will go up and down until loses all energy which is 47628J.

gneill said:
Consider the initial position and the eventual final (resting) position of the cab. The total energy input and eventually dissipated is determined by these points...
How silly of me.

Then ;
##mgd-0=F_{fr}D##

here D comes 14.8m ?? I it this the answer

What are you using for the value of d? Are you including the displacement of the elevator to reach the equilibrium point?

haruspex
TomHart said:
What are you using for the value of d? Are you including the displacement of the elevator to reach the equilibrium point?

d is in the given part.3.7 m.The block will stop there

Will it?
Disclaimer: I have been wrong so many times that I question my own judgment. :)

TomHart said:
Will it?
Disclaimer: I have been wrong so many times that I question my own judgment. :)

I think that way cause.That seems logical to me..lets wait for another opinion

Won't the spring end up compressed some because of the weight of the elevator when it finally comes to rest? The problem states that there is no friction when it comes to rest, so something has to be supporting the weight of the elevator.

Arman777
Arman777 said:
I think that way cause.That seems logical to me..lets wait for another opinion
Opinion is worth much less than calculation. What is the restoring force for a spring at its natural length? Will it hold up the cab?

Arman777
Yep I totally forget that.Ok thanks all of you

Arman777 said:
I think that way cause.That seems logical to me..lets wait for another opinion
Tom is right. Consider the forces on the cab when it has stopped.

## 1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transferred or transformed from one form to another.

## 2. Why is conservation of energy important?

Conservation of energy is important because it helps to sustain the balance and stability of our natural world. It also plays a crucial role in the functioning of our daily lives, from powering our homes and transportation to the growth and development of living organisms.

## 3. How is energy conserved?

Energy can be conserved through various methods such as reducing energy use, improving energy efficiency, and using renewable energy sources. It is also important to properly manage and maintain energy resources to ensure their sustainability.

## 4. What are some examples of energy conservation?

Some examples of energy conservation include turning off lights and electronics when not in use, using public transportation or carpooling instead of driving solo, using energy-efficient appliances, and using renewable energy sources such as solar and wind power.

## 5. What are the consequences of not conserving energy?

The consequences of not conserving energy can include depletion of natural resources, increased pollution and carbon emissions, and higher energy costs. It can also lead to negative impacts on the environment and human health, such as air and water pollution and climate change.

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