What is Spring force: Definition and 119 Discussions
Hooke's law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660.
Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.
Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.
On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, the galvanometer, and the balance wheel of the mechanical clock.
The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
In this general form, Hooke's law makes it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.
I am designing a small box with a lid. The box and its lid measure 100mm x 70mm x 25mm tall..
The lid is spring loaded by a suitably designed torsion spring. When the lid is closed it is latched in place horizontally. The latch mechanism consists of a fixed item in the lid and a moveable latch...
This is how I tried to do it. The force required to move B up the incline is $kx$ where x is elongation and k is spring constant. we know that spring force is greater than $mg(sin\theta+\mu cos\theta)$. And we can use work-energy theorem to figure out velocity.
$0.5*k*x^2=0.5*mv^2$ where...
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...
There is a trampoline drawn here and a graph of the spring force vs height.
I don't see why the spring force is decreasing at a decreasing rate with respect to height above trampoline.
F= kx = k * h/sin(theta), letting theta be between the horizontal and the spring.
Hi folks,
I have an interesting problem here from the real world, it's a design i am working on.
So I have an object that is pressed by an hydraulic press with 50kN, let's call it F_before. Then I drive in a jig to fixate it. But the part that holds the jig has a limited stiffness. Hence if I...
Summary:: Calculating the inclination angle
A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...
Its a very basic problem and my friend suggested a solution that we should equate mg and kx ie mg=kx and just plug in m=8 and x=0.16 but i think that we should equate the energies like mgx=1/2kx^2 ie because at the point where mg will be equal to kx the mass will still have a velocity hence it...
I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##.
After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation...
Consider a spring with one end attached to a wall and the other to a free mass, which is then stretched so some potential energy U. After it has been released and has de-stretched, the change of elastic potential energy is -U which equates to the negative of the work done by the spring force on...
Hello, do someone have time to help me out with an assignment?
My question
In the answer sheet they say:
What I do not understand is why m is withdrawn from both sides, since I don't see that those represent the same mass. When I did the assignment I thought m at the left side would be the...
Hi I'm new here and I've checked everywhere on google but I can't seem to find a website that'll tell me the spring force constant of items. Also what things would be in the range of a spring force constant of 163.427 N/m/
Homework Statement
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.30 N is applied. A 0.540-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and...
Suppose a spring of spring constant=K and Length=L is split into two parts L1 and L2, with spring constants K1 and K2 respectively.
Then,why is it such that the spring force F=K1*L1=K2*L2=K*L?
Please give an intuitive explanation of why the spring force doesn't change?
I will be thankful for...
Homework Statement
Homework EquationsThe Attempt at a Solution
Wspring = ∫-k*xdx
limits of integration are 12 and 0
So
[0 - .12^2/2]*172 = -1.24J of force
Getting 1.8/2 points for this anser
Homework Statement
I feel like my numbers are wrong so I just had a general question
what is a typical value for k (spring constant) for a rubber band
assuming in this case that k=F/x is an equation that works for rubber bands
because the number i got...idk it seems rather large
Homework...
Okay, so I am designing a new treadle hammer and I want to know how much force a spring will add to the force of the hammer.
Basically I have an 8 pound head that can either fall at the speed of gravity or be forced down by a 20lb extension spring.
The attached image is not my design and I...
The force constant of the spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 0.012m?
The formula for spring force is F =kx
When I do 550 x 0.012m I get 6.6 but I am supposed to round my answer four decimal...
Homework Statement
Show how you use calculus to find the time when the magnitude of the Spring Force reaches its maximum. Then, when you found that time show how you calculate the Spring force at that time as well.
m = 1.125kg
vi = .8 m/s
k = 2250 N/m
x = 0m
Homework Equations
Fs (t) = [-mvi...
Homework Statement
This is an attempt to solve a problem I asked about here https://www.physicsforums.com/threads/can-a-car-ever-sit-like-this.929453/
Homework Equations
F = kx spring force
The Attempt at a Solution
using the largest angle down it can get with the front spring compressed all...
Homework Statement
I'm having a hard time finding the reactions at the supports and the force exerted by the spring.
Given:
20 lbs
25 lbs
35 lbs
k = 200 lb/ft
lo = 2.5 ft
members are 4 ft longHomework Equations
ΣM
∑Fy = 0
∑Fx = 0
The Attempt at a Solution
I tried solving for the reactions...
Homework Statement
Two masses connected with a spring with contant k. The string streched by l . Find the max velocity of mass m!
M2 ___spring___ M1
M2--stretched by x2--____spring____--x1--M1
l = x1+ x2
2. Homework Equations
F = k.l
Mass1.x1 = mass2.x2
(x= displacement?)
a=w^2 x
v = wx
Ep +...
1. A hydraulic cylinder equipped with a helical coil compression spring(figure is attached). The oil pressure acts the spring and moves the boom from position 1 to position 2.
Maximum boom load in position 1 F1max= 16550N
Minimum boom load in position 2 F2min = 18550N
cylinder load...
I would like to ask about the sense of the restoring force in mechanical vibrations.
Comment 2 says that resultant force is opposite the motion but I have some hesitations about it because let's think the situation that mass is moving back upward to its equilibrium position. In this case the...
Homework Statement
Find the maximum compression in the spring, if the lower block is shifted to rightwards with acceleration of '##a##'. All the surfaces are smooth.
Homework Equations
$$\vec{F}=m\vec{a}$$
$$\vec{F}_{sp}=k\vec{x}$$
The Attempt at a Solution
FBD of the upper block:
From...
Homework Statement
An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high...
Hello there,
I'm working on a design project where I have come upon a mechanical problem that I'm having trouble with. Basically I'm making a kind of specialized stapler (at least I think that's a good translation...), and I want it to clamp the staplers using a mass accelerated by a spring...
Hello,
Following Hooke's law, the force applied by a string on an object attached to one of its ends is F = -kx
But here is my question : if we consider the equilibrium coordinate x=0 of a horizontal string, and the string is stretched until its end reaches a coordinate x1>0. By applying hooke's...
Homework Statement
A 5.3kg mass hangs vertically from a spring with spring constant 720N/m. The mass is lifted upward and released. Calculate the force and acceleration the mass when the spring is compressed by 0.36m.
Note: I already solved for acceleration and I got the correct answer-...
Evening all,
I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary:
The shock uses compressed air as the spring, the pressure is adjustable via an air valve.
The shock...
Evening all,
I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary:
The shock uses compressed air as the spring, the pressure is adjustable via an air valve.
The shock...
Homework Statement
Ok so here is the prompt: a 3kg object is fastened to a light spring over a pulley. The pulley is frictionless and its inertia may be neglected. The object is released from rest when the spring is unstretched. If the object drops 0.1 meters before stopping, find the spring...
Homework Statement
A pendulum, initially at equilibrium, is set into motion by a spring-loaded launcher (compressed a distance of 0.0150 m) which fires horizontally. If the mass of the pendulum bob is 0.340 kg and it rises to a maximum height 0.120 m (relative to equilibrium), what is the...
A novelty clock has a 0.0109 kg mass object bouncing on a spring that has a force constant of 1.34 N/m.
How many joules of kinetic energy does the object have at its maximum velocity if the object bounces 3.49 cm above and below its equilibrium position?
Homework Statement
The first theory shows a spring under an axial load where the Torque is given as WRcos(a)
The second theory shows a spring under axial Torque. T is given as Wsin(a)
Homework Equations
Given in links
The Attempt at a Solution
A torque T would be at full strength along...
A question on my lab is find the amount of "stopping force" required to stop the egg, by determining the size of the "crumple zone"
A brief description of the lab:
Build a container that will keep an egg from breaking as it is dropped from the third floor of the school, your container must...
I have a question that asks to find the velocity of the object attached to a horizontal spring when it is halfway to equilibrium. I am given the mass, how far the spring was stretched, and the velocity of the spring when it was released.
I am unsure of what it means by halfway to equilibrium...
Hello,
If we have a spring at rest and has a constant k=2 N/m (at its natural length with one end at origin (x=0) and the other end held stationary) is having a force applied on it. The force varies in same way as the the spring with function 2X. My question is how is it possible to start the...
Homework Statement
There is a block of 1kg (m1) resting frictionless on another block of 5kg (m2). m1 is connected by a horizontal spring to m2. m2 is resting on an inclined plane of 45°. Between m2 and the plane there is friction.
A force of 200N is applied on m2, pushing it upwards.
F=200N...
A block lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring
is at its relaxed length and the block is station ary at position x = 0 .Then an applied force with a constant magnitude of 3 N pulls the block in the positive direction of the x...
Hello Folks!
I want to find the maximum applicable force on a full suspension mountain bike and i will use this force on a FEA software structural analysis for a uni design project.
This bike has a rear suspension with 400 lbs/in spring rate.Also rear wheel vertical displacement(travel amount)...
I have a block with a certain mass attached to a spring. I pull it and then release. Spring pulls block back. When spring is back to its relaxed position, is the velocity of the block positive or negative? Exercise does provide k, mass and x, but that's not where the error is comming from...
Homework Statement
1.In a game a .12kg disk is shot across a frictionless surface . The spring is compressed by 6cm. The spring constant is 230 N/m. What is the magnitude of the spring force?
2. A piece of plastic is attached to a spring. The spring is compressed 2cm and the released. If the...
Matter can neither be created nor destroyed...but potential energy can be converted into a different kind of energy. Let's say we have a spring with a mass connected to it. This mass is a magnet, and the apparatus is inside a copper coil. It's a horizontal magnet with friction minimized at the...
Homework Statement
You've attached a bungee cord to a wagon and are using it to pull your little sister while you take her for a jaunt. The bungee's unstretched length is 1.3m and you happen to know that your little sister weighs 220N and the wagon weighs 75N. Crossing a street, you accelerate...
Homework Statement
A mass
(m = 1.35 kg),
originally at rest, sits on a frictionless surface. It is attached to one end of an unstretched spring
(k = 747 N/m),
the other end of which is fixed to a wall (see figure below). The mass is then pushed with a constant force to stretch the spring...
I have a heavy door that I am adding torsion springs too in order to make it easier for a human to open.
-The door weighs 460lbs.
-It is hinged on one side by two heavy duty hinges and uses a thrust bearing in each hinge with a friction coef. of .008
-the effective radius of the thrust bearing...
Homework Statement
Hi everyone, I am generalizing the following problem because I disagree with how the book solves the problem.
A square mass 'm' is attached to two springs with identical constants 'k', in a configuration such that the springs mount to the left/right sides of the...