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I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...
$$F=kx$$
$$k=\frac F x= \frac {50+50~N} {5+5~ cm}= \frac {100~N} {10~cm}= 10~N/{cm}$$
However, the answer is ##5~N/cm##, because the force on the spring is ##50~N##. I am having trouble understanding why the force isn't ##50~N## + ##50~N##. The diagram looks as though the spring is experiencing...
part d- ii and iii
ii) my answer is
300-140/300 *100
ke at y = 300
and spring energy at max compression is 140
iii) e is directly proportional to x^2
so it increases exponentially
is my explanation correct?
This was inspired by this:Dropping an extended Slinky -- Why does the bottom of the Slinky not fall?. There is that famous demonstration of dropping a slinky, and the bottom of the slinky does not move until the center of mass reaches the bottom. I was trying to figure out how hard are the...
A torque meter with a triangular slab extension is inserted into a corresponding triangular slot. The C-shaped arm features a V-shaped dent on which a roller is seated. This roller is held in compression by a spring. The roller's positions are labeled '0' for the initial state and '1' for the...
Is there a typo in this question? Supposing there was no friction, the block would fall until the force of the spring was equal to ##mg = 2 * 9.8 = 19.6##, taking the upward y direction as positive. Since ##F_{spring} = -200y## and ##19.6 = -200(-0.098)##, the block would fall 9.8 cm. It's not...
i'm copying from the book...
Hookes Law - F = -kx
W = Fdcos∅
since ∅ is 180°, W = -Fd = -Fx
W = ∫(-Fxdx)
now the book says, from Hookes Law equation "the force magnitude F is kx. Thus, substitution leads to W = ∫(-kxdx)"
why are they saying to substitute the magnitude of the force and not the...
Can someone explain that, when using the formula (Fs=1/2 kx^2) why do we use x=0.1m instead of 0.05m? Seems like a simple concept but why isn't it 0.05m (since 0.05m from equilibrium). Thanks.
Here is my attempt at the solution:
a) The apparatus may only experience acceleration ##a > g## while in contact with the spring. Since the spring exerts the greatest force when it is the most compressed, the apparatus will undergo the greatest acceleration at that point. So Newton's second...
I know that we can answer it using conservation of energy or using N's 2nd law.
Using N's 2nd Law:
##F = mv \frac {dv}{dx}##
##Fdx = mvdv##
For spring we have : ##F=-kx##
##(mg-kx)dx=mvdv##
We'll get same result using above equation.
My question:
Average spring force from 0 to x is ##-\frac...
Max speed occurs when all energy has been translated from spring into box.
E (Potential) = 1/2kx^2
E (Potential) = (1/2)(42 N/m)(0.280 m)^2 = 1.6464 N m
Ep = Ek =1/2mv^2
1.6464 N m= 1/2 (1.2 kg) v^2
v = 1.6565 m/s
In my physics lab we determined the spring constant of a steel spring. This turned out to be 20 N/m. However, when I search online, I can't see any uses of springs - I know springs can be used everywhere, but nobody seems to specify their spring constant. Anyone know of any applications?
I approach this by considering the four springs in parallel each with spring constant ##k## as one spring with four times the spring constant ##k' = 4k##. The car is dropped and at the moment its tyres touch the ground I assume that the spring is in its resting position. As the car continues to...
I am completely new to this subject and I am trying to find out how I read data off a displacement vs time graph to find the natural frequencies and mode shapes. Lecturer hasn't provided any materials on graphs, just looking for some help and where to go so I can understand it. Thank you
If I take a spring with clamps and I weight that system accurately. Then I compress the spring and clamp it thus giving it potential energy. If I now weigh the clamped spring I should see an increase in mass because of the added energy. Is this the case and something that could be proved in the...
Hello everyone,
I'm a new member, and you might see me around from now on. I'm now on a path to understanding the mathematics behind a complicated mechanical machine. My knowledge is basically what I learned during my school days and also during university courses, and for me, it was mostly...
We put object on weight ang get a mass. What would that mass be if we put a spring between object and weigt, so that the spring woul shrink to half its original size?
Source: A.P. French's Vibrations and Waves
I do not recognize the first equation, can someone explain how it came to be? The reasoning behind it.
How can force on a body attached to a spring at small displacement x be represented as
? I know recognize F = - kx (restoring force)
I realize...
My question is whether I've formed the integral for the work done correctly? It just seems a bit unwieldy to me...
If I call the extension of the spring ## x ##, I can see that ## z = \frac l 2 + x ## and ## z^2 = \left( \frac {l} {2} \right)^2 + y^2 ##. Combining them gives: $$ x = \sqrt {y^2...
Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems.
Have a wonderful day, again thank you for checking this post out!
There is some discussion currently and I was hoping to get some opinions here. The question is in regard to a Hook's law problem. The text gives the problem as seen below. The text says the answer is 50lb/in. Several people have tried from several different approaches. Factoring the "y" equation...
Determine the amount and type (tensile or compressive) of the spring force so that the resulting force is a vertical force. Also get the resultant force.
i find 60N (compressive)
and resultant forces is 10800
is that correct?
So here's what I did but it isn't right:
W = (Kf + Uf) - (Ki + Ui)
(2.6)(9.81)(0.45)(-0.01)=(1/2mvf^2 + 1/2kxf^2) - (1/2mvi^2 + 1/2kxi^2)
-0.1 = (1/2(2.6)(vf^2) + 1/2(855)(0.02^2)) - (1/2(855)(0.03^2))
1.3Vf^2 = 0.114
Vf^2 = 0.09
Vf = 0.3 m/s
The 7/8" Kinetic Recovery Rope like this yankum rope is the most common size used for Jeeps, Broncos, and other SUVs. I apologize for English units but that's how ropes are sold and marketed. I've talked to the biggest rope suppliers and they have no idea how to compute the rope's spring...
It's an explosion problem.
When two carts are pulled apart, the bigger one takes longer than the smaller one. So the velocity of the bigger one is small, and the velocity of the smaller one is large, and they are opposite each other. So the momentum before the explosion must be equal to the...
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!
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.