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At the equilibrium position all forces are equal to 0 (they balance). So, naturally we:
mg - kd = 0
d = mg/k
d = 0.356 m
This is the correct answer, I believe. But I want to solve it using the energy equations because I am really trying to understand energy's connection to the rest of...
I feel like I've gotten stuck on this. I know the work done is equal to the kinetic energy of block A, but I can't figure out how I would find the potential energy stored in the spring without using the spring constant in the equation. W = FA * dA + U
Hi group,
I heated a steel spring until red hot then plunged in water quenching it.
My understanding is that quenching so quickly would have an effect of the grain size such that I would expect it to be much more brittle as with small grain there is much less plastic deformation possible (as...
I am trying to model numerically the following system:
A rigid body mass is rotating freely around an axis (no rotational stiffness/damping) within a range, let's assume plus-minus 3 degrees for now.
Case A. The external forces on the mass are low and keep changing which results in the situation...
Two masses m and M are attached to a compressed spring. When the spring decompresses, the masses won't be pushed off the spring. What will happen to the masses and the entire system? By conservation of energy, the elastic potential energy of the spring will convert into kinetic energy, but which...
Hi Guys
I am looking for some guidance with regards to a Lagrangian problem I am trying to solve.
Please refer to the attached documents.
Please neglect all the forcing functions for the time being. I am currently just trying to simulate the problem using initial conditions only
I have...
Hello!
I was trying to find the equations of motion for a spring with uniform distribution of mass (uniform just in t=0, because after a while the distribution will be non-uniform).
I tried to attack this problem first in the discrete (non-continuous) way:
"Consider N springs with elastic...
Just to be clear, this isn't a homework problem. it is an example problem found on page 68 of the text "Matter and Interactions" 4th edition. The solution is given in the book, but I'm having difficulty following their reasoning.
according to the book the net force is not constant, therefore we...
Hey Guys,
I found this thread about the proper size dimension of a torsion spring for upholding a kickstand in the right position.
I have to develop a kickstand for my Omnium Cargo bike.
I have been thinking about using the same choice of spring type for my product, but I've also been...
Let's assume I have a ball moving at a constant velocity and it collides with a spring and the spring compresses n cm. If I know how much mass the ball has and the spring constant D, how would I calculate the Force? I mean since F = dp/dt I would have to know the time in which the stopping...
Let's say a mass is gently laid on top of a massless spring. The spring compresses.
There is a change in the height of the mass. Therefore, there is a change in the gravitational potential energy: a decrease.
The compressed spring now has potential energy (it has gained energy).
The change...
I have checked the program several times the program is running but the graphs I am getting is not what I was accepting soon one of the variables approaches zero I don't know why is it happening. The program I have made is below and it's in the FORTRAN language. If anyone knows Fortran can they...
I'm looking to find formulas to calculate the energy stored in a spring you would find in a clock. I have been having a hard time finding formulas that govern these types of springs. I have found formula in similar springs, such as the spiral-torsion spring found here but I believe this type...
My attempt at solving case B
I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this...
a)What is the total energy in the system?
Only energy acting on the system assuming the track is level and there is no potential energy of the carts, is the potential energy of the spring.
Comes out to 7.8125 using the potential energy of a spring equation.
b) What are their velocities if the...
I think I have all the pieces here, and am able to solve for a work through the air. But I have a power output, and don't know how to isolate it to find the distance.
I managed to isolate k to k=4pi^2/T^2 however I don't know If I did it correctly. I am trying to use K to find the mass of a bolt. I am stuck here, not sure If i need to find all three k's and then average them out?
We know linear spring force F = kx(t), k = spring constant, during any moment t of energy release.
displacement x(t) = ʃv(t)dt
the power p = F*V = kx(t)v(t)= kv(t)* ʃv(t)dt
My question:
Is there a mathematical function of special v(t) to make power p constant?
I am trying to understand the reaction of a steel coil compression spring when pulsed. The spring I am interested in has the following physical characteristics:
k (spring constant in pounds per inch) = 2.88
d (wire diameter in inches) = .043
n (number of active coils) = 29
D (mean diameter of...
a) When the system is in motion for the first time, the force causing ##M## to move is contact force with ##m## so:
$$\Sigma F=M.a$$
$$N \sin \alpha=M.a$$
$$mg \cos \alpha \sin \alpha =M.a$$
$$a=\frac{mg \cos \alpha \sin \alpha}{M}$$
Is that correct?
b) Is acceleration of ##m## the same as...
I completely missed the collisions approach when I first tried to solve this and tried using the work-energy formula. I am wondering if this approach can be made to work? Here is my attempt:
So I let the work done on the ball be ##W_b## and work done on spring be ##W_s##. Then $$W_b=\Delta K =...
My attempt at a solution: Is my logic accurate/correct, and is my answer correct?
I consider the forces acting to be: Restoring forces in springs parallel, and Force of the current-carrying conductor in the Magnetic field. I imagine a vertical displacement of y upwards ( direction determined...
Hello everybody.
I'm trying to figure out how to calculate gas springs for specific doors not with hinge, but lifted up, like on the picture.
Do anybody experience with such type of mechanism?
Also I'm looking for helpful software, for gas spring calculation (different types). I found screens...
I'd just like to check my work. Establish coordinates ##(t, x^i)## with spatial origin at the centre of mass; let the two masses have positions$$x_1(t) = (-a - b \cos{\omega t},0,0), \quad x_2(t) = (a + b \cos{\omega t},0,0)$$The quadrupole moment tensor ##q_{\mu \nu}## is calculated...
Summary:: Doubt in a spring exercise
Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...
I do not understand how in part a, the units for K can be N/m. If Work is in joules which is kg*m^2/s^2 and we are diving by x^2 which is m^2, then m^2 should cancel out and we should be left with kg/s^2.
Kg/s^2 makes more sense because in part b when you find the work done you are multiplying...
I just would like to check if my corrections to each of the wrong options are right.
A) & B) elastic potential energy greatest at B, not at A or O, based upon Eq.1
D) Since dU/dt = 0 at O because O is at equilibrium where no change of spring length.
E) At A, dU/dt = -kx. At B, dU/dt = -kx = -kx...
Assuming zero spring mass and zero friction,
At the greatest value of x, the loss in gravitational potential energy should equal the loss in elastic potential energy.
so I did
(1/2)kx^2=mgx
to isolate x in the formula,
x=(2mg)/k
then I plugged in my values so:
(2*13.6*9.81)/8.8= 30.3218...
Hello!
So here what I did is first calculated the potential energy; $$ E_p = \frac{1}{2} * k * x^2 $$ E_p should be = 0,125 J Now i tried calculating the kinetic energy, I used this formula $$ E_k = \frac{mv^2}{2} $$ to get v I used this formula $$v = x *\sqrt{\frac{k}{m}} $$ v should be =...
Hi all,
I'm studying the compression spring design issue that occurred in a machine design application.
As illustrated below, spring is bouncing or oscillating after impact to a stopping surface (1 -> 2 -> 3 -> 4) and eventually stop after few bounces.
Ideal case for this application is to...
So first I made an equation representing the forces
Fnet=kx-12.8v
a=1/m(kx-12.8v).
Now I am not really sure how to get w from this. I could argue the mass is at its max amplitude when a=0, but that wouldn't help me find w. If I say x(t)=kx-12.8v, then 1/m would be w^2, but this isn't right...
Hi,
On a driving force graph ##y = displacement (m)## and ##x = time## where the external force start at t = 0 and the system is in equilibrium at x=0, it's easy to find the driving frequency.
$$F = \frac{\omega}{2\pi}, \omega = \frac{2\pi}{T}$$ and we can get ##T## easily with the steady...
The other day when I solved a spring mass damper system in Matlab, I was curious how in olden days would have people solved the equation. We all know the 2nd order differential equation of the system:
However if I know the time, damping coefficient, stiffness and mass, will I be able to find...
So first I found what b/2m is and got 0.287129. Then I found what the sqrt part of the equation was and got 1.128713. Then I added them together to find w. Then I divided by 2pi to find frequency and got 0.255, but the answer is 0.180.
Since its critically damped that means k/m=(b/2m)^2, which would mean w=ib/2m. So m=ib/w. My issue now is that I need to find work.
I could put w back into x(t) to get Ae^((-b/2m)t+phi). I guess I could make this Acos((-b/2m)t+phi)). But I am kinda lost at this point. Sure, I could find the...
Hi,
First of all I hope it doesn't bother if I ask too much question.I found the values of ##u1,u2## for 2 differents posistions ##(r1,r2
)## and I now have to determine the spring constant (k).I'm thinking about using$$
F= -kx
$$
with ##F = -\frac{du}{dr}## then
$$
U = \int -kr \cdot dr...
i attempted this problem by using conservation of energy,
mgh=1/2kx^2
mgD=1/2kD^2
2mg=kD
k=2mg/D
why is it wrong ? btw the correct answer used mg = kx which is mg/D
I honeslty don't quite know how to start. It seems like the Hooke's coefficent k is independent of the answer to this problem.
I would also appreciate any clue of expressing the condition when "balls will collide again". The fact that all balls can keep moving make this rather difficult.
It...
I am trying to design a small box with a hinged door/lid that opens with a torsion spring.
When closed, the door will latch onto a mechanism where the open button is, and when the button is pressed this mechanism will slide away, removing the latch out of the way so that the door can fly open...
If M is displaced by an amount + x from equilibrium.What happens to the two masses at the point of release for displacements of x and less?
Will they remain static because mass m provides whatever it takes to stop mass M from moving
till some x where m slips and M oscillates
or
Will they...
I'm having trouble with this problem, I think I solved it but I don't know if what I did is right...
At first when the velocity is 0 and the spring is at its natural length, there's just gravitational potential energy, so $$E_i=mgh$$
And then, when the mass is released and then reaches its...
I attempted using f = 1/(2pi x sqrt l/g)
For Earth I found the value of length to be 0.0276m.
Then I substituted the value in the equation, putting (1/3)g instead of g, to find the value of f in Mars. My answer is C. I am confused.
Please help me.