Spring Definition and 999 Threads

Is this even solvable? I don't know where to begin.

Why when we differentiate ## E = \frac {1}{2}mv^2 + \frac {1}{2}kx^2 ## with respect to time the answer is ## \frac {dE}{dt} = mva + kxv ##? I though it would be ##\frac {dE}{dt} = ma + kv ##. Many thanks!

For part (f) Solution is I don't understand why the bit highlighted in yellow is true. Would anybody be kind enough to help.

Can someone help me evaluate an idea that I have? I'm investigating the idea of placing a very progressive pull spring and a digressive shock on a rocker to control the timing and rotation of an axle. I could be way off, but here's the scenario in my head. Both shock and spring are being...

I have successfully completed parts A, and B, however, I am confused on Part C. Here was my attempt and the answer key's attempt: My attempt: Since I correctly knew the speed after the collision, and the gravitational potential energy after the collision if I set h=0 at when it was at rest...

a) Elastic potential energy stored in the compressed spring is written by, where k =400N/m, compressed spring distance x = 0.5m $$ U_g = \frac {1}{2}kx^2$$ $$ U_g = 50J$$ b) When block C is compressed, it has stored spring PE and when it is released, the block accelerates to the right, where it...

How do we have linear spring direction (mostly a spherical spring) to have pull/push force evenly across some points within a range? Or is it possible to create spring material with anomaly property capable of performing so?

It is to my understanding that if the spring was compressed 10cm, it is due to the Work of the Weight Force of the stone. So: Work done on the spring by the stone = m.g.x = 7.84 J The work done on the spring will be stored as potential energy of the spring, so: Us = W Us = (1/2).k.x² k =...

Hi everyone, I'm an electrical engineer working on making a linear model for a power take-off system. I've gotten inertial, friction, and hydraulic/electric components done, but what is really confusing me is the gas system; I haven't taken ANY thermodynamics. To simplify it, it is modeled as a...

Could anyone help me with some info on compression helical springs. First I would like to know if this type of spring would even have any appreciable histeresis when new, and if so does it does it grow with repeted use and age. I would also like to know if there is any relationship beteen the...

Hi It is about a DNA strand on which there are always two segments, the segment ##A##, which is folded and has the length ##l_A## and the unfolded segment ##B##, which has ##l_B+\lambda##. Here is a section of the DNA There is now, as shown in the picture, a force ##F## pulling on the...

I tried just using the formula for kinetic energy but that was apparently the wrong answer. The answer key says it's (1/6)mv². I don't understand how they got that answer. Could someone explain?

Note: wording is ambiguous so I assumed spring started from equilibrium, in which case it stretches as we go downslope. Final height (at lower point on slope) is 0. Distance along slope = Distance the spring stretches = d= ##s_f## = ##2/cos{\theta}## =2.13 Height change = h = ##2 tan{\theta}##...

I take a wire of metal X which has a diameter d. Let the total length of it be L and I roll it around a cylinder with diameter D to create a spring. Is it possible to predict the spring constant of this system (and relate it to the elastic constants of the metal)? Has anybody seen/heard/know a...

Basically the air works like a spring, it always tries to get back to its resting state. And it's like Hooke's law, the more it deforms the more elastic potential energy it has. That's why the faster you are, the air resistance is greater. Thinking in this way, I imagine that in fluid mechanics...

I am trying to solve this and get the equations of motion using the Lagrangian method. I could do all the steps but the equations (especially the third one) seems..weird. What am I doing wrong? Sorry if the equations aren't in their simplest form, they are pulled straight from Wolfram...

For the second force with the spring, I know the spring force will exert a force back on my hand, for example, but I'm confused whether the applied force is transmitted unchanged to the block or whether it will decrease because of the opposite spring force. What happens to the block when the...

I have calculated the acceleration of truck B from v=u+at as 5ms/s. The force applied to truck B is therefore 5x10=50N. I am unsure whether this question is poorly worded, but I feel a reasonable assumption is that the force applied to truck A would be the same as truck B, without knowing its...

I don't understand the difference between part c and d. After compressing the spring, the elevator bounds back and moves before coming to rest in both cases. What is the difference? Thank you.

Ki + Ui = Kf + Uf 1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so 1/2)kx^2 = F∆d. The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.

Hi , Can someone tell me wether my answer is corrrect or false ?

tried writing the x position as x = Acos(wt) (ignoring the phase) so that d2x / dt2 = -w2x Substituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass

m=6.00Kg K=145N/m a=1.80m/s Fp=Fs ma=-kx (6)(1.8)=-(145)x x=-0.0745m I’m just wondering why I see some people make Fs=kx instead of -kx? isn’t the force of a spring a vector?

Summary: I am confused in when to use 1/2 e squared k we studied in class that normally, the extension of the spring is directly proportional to the tension applied and we did this question : what is the work that has to be done for a spring to have an extension of length e as the area of the...

I don't understand the question. If it want the mass to stop and reverse its direction, then does that not means ##vo## can be anything? (obviously not 0 since it will make the system not moving at all).

Trying to derive the length of a spring hanging under its own weight. I was trying to approach it like a series of small springs free length ##l## connected in series, in hope to use a limit as ##l \to 0 ## to get the final result, but either I'm bungling it, or it just doesn't work. I'm...

yooo. Some help on the following problem would be much appreciated. I don't get how to solve the two equations I obtained for the COIs A and phi. calculated: ##\omega == 7rad/s## and ##\gamma = 0.396s^-1## for part C we have two initial conditions: at t = 0 > ##0 = Acos(\phi)## at t = 1s >...

What I've done so far is find the spring force through ##F_s = -kx## ##F_s = -111*16.7## ## = -1853.7N## My conclusion was that since this is the spring force, the tension force must be just the negative of that so ##1853.7N## because the net force has to balance out, but I am horribly...

I don't understand what I have done wrong in part (c) I have the initial velocity for the second part of the motion and have the final velocity zero and then the net work done is W_mg + W_Fs and the actual answer for x is 2.37m Could I get some help/tips please, thanks in advance. Here is my...

(a) By setting up a coordinate system with the x-axis pointing to the right and the y-axis pointing downward we have ##\begin{cases}-kx_{eq}+T_1+F_{s}=0\\ -RF_{s}+rT_1=0\\ r_p (T_2-T_1)=0\\ -T_2+mg=0\end{cases}\Rightarrow x_{eq}=\frac{mg}{k}\left(1+\frac{r}{R}\right)## which coincides with the...

Given the pendulum setup below: Details: ##m## is the mass of the bob ## r ## is the instantaneous length of the spring ## \theta ## is the angle the bob makes w.r.t vertical ## I ## is the bobs mass moment of inertia about pivot ## l_o## is the free length of the spring. ##k## is the spring...

A longer pendulum swings slower. So changing the length l of the pendulum changes the period T, which affects the timekeeping accuracy. But the problem is talking about the body on the spring, not the string. So the second formula cannot be applied here directly and I don't know how to progress...

How can I find the maximum bending moment and maximum deflection for a spring? It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner. that's all, thank you very much.

I'm reading an article about the order-chaos-order sequence of a spring pendulum [Ref 1], as I'm reading it I'm trying to reproduce the graphs and results through Mathematica. However, I am new to this software. I will list below some of the most important equations mentioned in the paper. "In...

i would like to get some help and to understand why my answer is incorrect , here is how i did the first and second part. about the first part i did it right but i don't understand what I am doing wrong in the second part i tried -k and i get -23.997 and i also try +k and i get 23.997 but they...

Summary: How to express ωₙ in terms of only mass (m) and stiffness (k)? I tried doing it with F=kx but it is out of my ability to simplify it to only m and k. Here is my approach:

I was doing the exercise as follows: I am not sure if you agree with me, but i disagree with the solution given. I was expecting that the kinect energy of the mass ##m## (##T_2##) should be $$T_2 = \frac{m((\dot q+lcos(\theta)\dot \theta)^2 + (lsin(\theta) \dot \theta)^2)}{2}$$ I could be...

In question 1, the spring constant from the two formulas was not the same. When we used the first formula, we got that the spring constant was 7.83 N / m. The second formula we got that the spring constant was 8,03 N / m. In questions 2 and 3 I do not know and am unsure about how to answer...

Please, i need help

i would like to understand why my answer is incorrect and how i need to solve this problem

i would like to understand why my answer is incorrect i don't know what I am doing wrong i would like for some help

My wife just lifted a stack of dinner plates in a cupboard and found about a thousand carpenter ants in a 3" ball. The plates were on a dishtowel that served as a cupboard liner and the ants were under the dishtowel. There was zero detritus, zero rot, zero poop, zero sawdust, no eggs, no...

Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force. The weight is simple enough ##12* 9.8=117.6N##...

Hi everyone, Any alternatives you know for metal spring? The idea is to find a replacement for a metal spring that has the same efficiency in bouncing an object that's hung by the spring. Any input of a kind would be valuable. TIA

Ei = 1/2 K (x)^ 2 K = .0152N/m x = .0375 m Ei = 1.06x10^-5 Ef= 1/2mv2 + mgh m = .164kg, v is unknown, h is .0375sin(8.3)=.00541, Ef set equal to Ei 1.06x10^-5=1/2(.164kg)(v^2)+ (.164kg)(9.8)(.00541) v = .3254m/s I have gotten this answer multiple times but it is not correct. I am going...

I'm building a power hammer for a buddy's forge and am working through the design phase. We are going to use a 1200lb leaf spring to actuate the upper anvil. Pretty much got the mechanical design down, but having some issues with the selection of motor and control. The leaf spring we selected...

A backpack is attached to a spring scale which is attached to the ceiling of an elevator. The elevator is moving downwards with an acceleration of 3.8 m/s^2. The scale reads 60 N (Fscale). What is the mass of the backpack? The solution to this problem says that Fscale - w (weight) = Fnet. This...

EDIT for clarity: I solved the question, just asking for if the explanations make sense and if the mechanical energy is considered to be conserved before and after the collision due to reasons listed below the photo. I hope this image is readable (grr, scanner is janky). I'm guessing the...

Here's what it looks like at my place: