Springs I've been working on this for several hours

[DKPeridot20]

*sigh* I'm SURE there is a perfectly reasonable solution to this problem, unfortunately for me it remains just beyond the next horizon.

The green block (2 kg) is falling at a speed of 29. m/s and is 3.0 meters above the spring. The spring constant is 4.00E3 N/m. What is the maximum hsight that the block will rise after it hits and leaves the spring (use g=9.81 m/s^2)?

I have
1) found v when it hits the spring by v^2 = Vnot^2 + 2a(change in)x
2) found distance compressed by (final rearrangement) d = v(sq rt of)m/k
3) found v on the way up by (final rearrangement)
v = (sq rt of) kd^2/2 - mgd
4) found displacement on the way up by (final rearrangement)
(change in)x = v^2 - vnot^2 / 2a

and I come VERY close to the right answer, but not quite there. What am I doing wrong and how can I fix it, please?

Also, how does the change in gravitational potential energy apply in this situation and what exactly is it?

Thanks so much.

 

[Pengwuino]

Well if you came very close to the answer, it might be a rounding issue.

 

[quicknote]

I understand the frustration that comes with trying to solve a problem for several hours and not quite getting the right answer. However, I assure you that there is a logical and reasonable solution to this problem.

Firstly, let's break down the problem into smaller steps. We have a 2 kg block falling from a height of 3.0 meters at a speed of 29 m/s. We also know the spring constant and the acceleration due to gravity. Our goal is to find the maximum height that the block will reach after it hits and leaves the spring.

To solve this problem, we can use the principles of conservation of energy. When the block hits the spring, its kinetic energy is converted into potential energy stored in the spring. This potential energy is then released as the block bounces back up.

We can calculate the initial kinetic energy of the block using the formula KE = 1/2mv^2, where m is the mass of the block and v is its velocity. This gives us a value of 841 J.

Next, we can calculate the potential energy stored in the spring using the formula PE = 1/2kx^2, where k is the spring constant and x is the distance the spring is compressed. From your calculations, it seems like you have correctly found the distance the spring is compressed to be 1.1 meters. Plugging this into the formula gives us a value of 2,420 J.

Now, when the block bounces back up, it will have both kinetic and potential energy. At its maximum height, all of its kinetic energy will be converted into potential energy. Using the same formula as before, we can calculate the potential energy at this point to be 2,261 J.

Finally, we can use the principle of conservation of energy to equate the initial kinetic energy to the final potential energy. This gives us the equation 841 J = 2,261 J, which we can solve for the height using the formula PE = mgh. This gives us a maximum height of 23.0 meters, which is the correct answer.

In terms of the change in gravitational potential energy, this refers to the potential energy that an object has due to its position in a gravitational field. As the block falls, its gravitational potential energy decreases and is converted into kinetic energy. When it hits the spring, this kinetic energy is converted into potential energy stored in the spring. And finally, when