Hooke's law Definition and 257 Threads

I'm trying to understand the math behind Hooke's law and work done by a spring. I'm really looking for clarity. I am trying to understand why after integrating the equation I get three different results. I understand that each formula is specific to a problem but why does this work...

Homework Statement An unstrained horizontal spring has a length of 0.32 m and a spring constant of 220 N/m. Two small charged objects are attached to this spring, one at each end. the charges on the objects have equal magnitudes. Because of these charges, the spring stretches 0.020 m, relative...

Here is the question: I have posted a link there to this topic so the OP can see my work.

A force of 16,000lb compresses a string from its natural length of 13 inch to 8 inch. Find the work done to compress it to the first inch W=$$\int F dx$$ F=kx 16000=K(5) 3200=KW=$$\int F dx$$ W=$$\int_1^{13}\!\ 3200xdx$$ [1600x^2] from 1 to 13 w= 268800ftlb Am I right? I think the trick...

Hi, I know that for a massless spring the tension is T = kx, where k is a constant and x is the compression or elongation. What is the expression of the tension if the spring has a mass m? Thanks in advance.

Hello, I am self studying physics and am a bit confused with Hooke's law. Using the conservation of energy equation: (PE+KE)_i = (PE+KE)_f I don't see why the springs potential energy (½ kx^2) goes in the final part. Could someone please explain? EDIT: Also, (I'm a new user) can you...

Homework Statement An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should happen to break when the elevator is at a height h above the top of the spring, calculate the value of the spring constant k so that the passengers undergo an...

Homework Statement As shown in Figure A, a block of mass m is hanging from a spring attached to the ceiling. As shown in Figure B, two blocks of mass m/2 are hanging from two strings that are attached to a spring that has the same spring constant k. If the spring in Figure A is stretched a...

Calculus 2- Water pump problem Homework Statement The lower half of a sphere with radius 2m is filled with water. Find the work needed to pump the water to a point 1m above the centre of the sphere. Homework Equations The Attempt at a Solution I know you have to cut the problem...

Homework Statement A 46g rock is placed in a slingshot and the rubber band is stretched. The force of the rubber band on the rock is shown by the graph in the figure(Figure 1) . http://session.masteringphysics.com/problemAsset/1073689/4/10.P37.jpg a)Is the rubber band stretched to the...

Homework Statement F=kx What does k represent? Homework Equations The Attempt at a Solution k is the proportionality constant of restoring force over displacement. Or with respect to displacement?

Hi all, I am reading an online material on elastic force and Hooke's law on spring. The definition of the Hooke's law reads that the restoring force is linear proportional to the displacement of the spring with constant k. The restoring force is defined as the force bringing the object back...

Homework Statement A 50kg mass is attached to a spring and hung from an overhead beam. The Force on the spring when extended 2 meters from rest is 50N. The resting length of the spring is 1m. 1) Obtain the ODE to solve for the velocity as a function of position (NOT time) 2) Solve the...

Hi, For a linear spring one has Hooke's law: F = k x Is there an equivalent law for a spherical elastic balloon giving pressure inside as a function of radius? Thanks, John

Hello all, (Newbie here so I hope I'm posting this in the right section, if not please guide me to the correct one) I'm studying Hooke's Law in Physics and there is something I can't understand. The equation for the Simple Harmonic Motion of a spring is given by x'' + wx =0 the general...

Homework Statement Which one obeys Hooke’s Law and why? For the material(s) that did obey Hooke’s Law, calculate the spring constant, k. SHOW ALL WORK: listed variables, units, equations without substitutions, equations with substitutions, final answer with units! The Green line on the...

Hi guys - we did an experiment at college putting some weights on a spring for our Hooke's Law module. When I graph it I get a value for c, in the equation y=mx+c. Is this correct? Will c have a value? Thanks.

Homework Statement At a waterpark, sleds with riders are sent along a slippery, horizontal surface by the release of a large compressed spring. The spring with force constant and negligible mass rests on the frictionless horizontal surface. One end is in contact with a stationary wall. A...

There is a statement in my book i can't really understand. "To stretch a spring, we must do work. We apply equal and opposite forces to the ends of a spring and gradually increase the forces. We hold the left end stationary, so the force we apply at this end does no work.The force at the moving...

I did an experiment where I measured the stretch on a spring from its initial position when masses were added on the end of it, in increments of 50g. I plotted a graph of Force against length stretched and the graph does not go through the origin, or at least it is not linear for forces below...

Homework Statement A 1.01 kg mass is attached to a spring of force constant 9.5 N/cm and placed on a frictionless surface. By how much will the spring stretch if the mass moves along a circular path of radius 0.485 m at a rate of 2.14 revolutions per second? What i was thinking was using the...

Homework Statement A string of natural length 10 in. stretches 1.5 in. under a weight of 8-lb. Find the work done in stretching the spring from its natural length to a length of 14 in.Homework Equations \begin{equation} W= \int_a^b \, f(x)dx \end{equation} \begin{equation} f(x)=kx...

Homework Statement The problem is in the attachment Homework Equations F=-kx k1x1=k2x1 The Attempt at a Solution I got as my answer Keq= (k1k2)/(k1+k2) i just wanted to see if i had the right idea or no.

I understand the simplest application of the summation convention. x_{i}y_{i} I create a sum of terms such that in each term the subscripts are the same i.e. x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}+... But now when I look at understanding summation convention applied to the generalised Hooke's law...

Hooke's law describes a certain light spring of unstretched length 37.0 cm. When one end is attached to the top of a door frame and a 8.00-kg object is hung from the other end, the length of the spring is 40.5 cm. (a) Find its spring constant. (b) The load and the spring are taken down. Two...

Do you see where it says m(dv/dt)v = (d/dt)(.5mv^2) If it's an integration which I don't think it is then I would think it should be (d/dt)((mv^3)/3) because you're taking the two v's and adding an additional power. I don't think it is an integration because it says right there in the...

Homework Statement Hi I know for Hooke's Law F=-kx where -ve sign implies a restoring force back to equilibrium in the opposite direction of x. My question is: I have a mass being displaced attached to a spring - consider M2 and z2(t) and K2 in the link below...

I was just thinking, shouldn't hooke's law be represented with an exponential equation? I am thinking that in class, the springs we use for the hooke's law experiment are small, but if they were very large, then the higher coils would be sustaining much more weight than the lower coils, and...

This was on a practice test for an upcoming exam. You have persuaded your friend Astrid to attempt an illegal bungee jump from a Bridge. You will provide the bungee cord which has a total length of 40 m and a spring constant of k = 16 N/m. During the jump, Astrid will first fall freely for a...

Homework Statement Seven and one half foot pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional one-half inch Homework Equations W=kd W=∫f(x)dx The Attempt at a Solution 7.5=W ∫kxdx from...

Homework Statement Use Hooke's Law to determine the variable force in spring problem. Eighteen foot-pounds of work is required to stretch a spring 4 inches from it's natural length. Find the work required to stretch the spring an additional 3 inches. Homework Equations W=∫f(x)dx f=kd...

Hello all, I am currently working at a problem that is (seems) simple at calculations but I am puzzled by the word problems. The problems are: 1. A spring powered projectile launcher contains a spring with: k=300 N/m The spring is compressed by 15.0 cm. a. How much energy is...

Homework Statement A mass M = 0.454 kg moves with an initial speed v = 2.88 m/s on a level frictionless air track. The mass is initially a distance D = 0.250 m away from a spring with k = 876 N/m, which is mounted rigidly at one end of the air track. The mass compresses the spring a maximum...

Homework Statement I am currently doing some Hooke's Law problems. While I do not have any trouble with any exercise in particular, I do have trouble with the sign in the equation. Let's say I have a vertical spring and I attached a hanging mass m to it. The string will then stretch a distance...

Homework Statement 4 springs with a mass on each end are connected in series as below: | | | | m1 | | | | m2 | | | | m3 | | | | m4 All the masses are mass m, the length of each spring is 1, and the spring constant is k, find the extension of each spring...

Depending on how you fall, you can break a bone easily. The severity of the break depends on how much energy the bone absorbs in the accident, and to evaluate this let us treat the bone as an ideal spring. The maximum applied force of compression that one man’s thighbone can endure without...

Homework Statement A vertical ideal spring is mounted on the floor and has a spring constant of 132 N/m. A 0.80-kg block is placed on the spring in two different ways. (a) In one case, the block is placed on the spring and not released until it rests stationary on the spring in its equilibrium...

Are springs manufactured to obey Hooke's law, or do all springs just naturally obey this property?

Homework Statement A 2.70kg mass is pushed against a horizontal spring of force constant 25.0 N/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring. When the spring has been compressed enough to store 12.0 J of potential energy...

Homework Statement I'm given the mass of the object and acceleration (gravity), and I'm given the pull back distance of one test of the slingshot. I've found the k constant by finding force with f=ma, but I need to find the pull back distance using the same slingshot in order to propel the...

Homework Statement Assume the spring force of a bowstring acting on an arrow does not follow Hooke’s Law because the bow’s material becomes more rigid as it is drawn back. The string’s force as a function of the drawback distance in meters is: F(x) = -k1x -k2x|x| where positive x is along...

Homework Statement A student measures the force required to stretch a spring by various amounts and makes the graph shown in the figure, which plots this force as a function of the distance the spring has stretched. Part A) Does this spring obey Hooke's Law? Part B) What is the force...

A lift is used to lower miners 4000m into a mine. The lift is supported by many high strength steel strands of 3mm diameter each. The ultimate stress for the steel strands is 1200MPa and the allowable stress is 600MPa. The empty lift weighs 15kN. It has a capacity of 20 persons. The density of...

Homework Statement Whether or not the spring is vertical or not, assuming that the spring is ideal, is Fnet always equal to -kx? Is it incorrect to write the sum of the forces of a vertical spring as Fnet = -kx - mg? And does hooke's law account for the force of friction on a horizontal...

Homework Statement A 50g mass hangs at the end of a hookean spring. When a 20g more is added to the spring, it stretches 7.0cm more. Find the spring constant. The Attempt at a Solution Isn't it just mg = kx mg/x = k Shouldn't m = 70g instead of 20g? My key says m = 20g?

Homework Statement A 0.75 kg block is held at rest against a spring compressing it 27.0 cm. The spring constant is 735 N/m. The block is released and it begins to move toward a loop across a frictionless surface. How much kinetic energy does the block have when the spring is compressed 13.5...

Homework Statement is the hooke's constant same for compression as well as extension of all the materials and springs? Homework Equations Force = hooke's constant * extension [ to a limit] The Attempt at a Solution

Homework Statement A ball with mass 'm' is pushed against a spring (with a spring constant 'k') and causes a displacement 'x' on the spring. Once the force is released from, the ball is shot horizontally. What is the velocity 'v' horizontally? Homework Equations E(k) = 1/2 mv^2 E(s) =...

Homework Statement A small truck is equipped with a rear bumper that has a spring constant of 800,000 N/m. the bumper can be compressed up to 15cm without causing damage to the truck. What is the maximum velocity with which a solid 1000-kg car can collide with the bumper without causing damage...

A 2.0 kg mass and a 3.0 kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k=140N/m. A 15 N force is applied to the larger mass, as a shown (see picture). How much does the spring stretch from its equilibrium length? I've solved...