Physics College

For a particular nonlinear spring, the relationship betweem the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation F = k x^2 What is the amount of work done by stretching the spring a distace x0? A) kx0^3 B) (1/2)kx0 C) (1/2)kx0^3 D) (1/3)kx0^2 E) (1/3)kx0^3

Answers

Answer 1

To get the work, you have to integrate the force as a function of [tex]$x$[/tex] from zero displacement to Xo

[tex](Integral of) $\mathrm{k} \mathrm{x}^{\wedge} 2 \mathrm{dx}$ from 0 to $\mathrm{Xo}_{\mathrm{o}}=(1 / 3) \mathrm{k}\left(\mathrm{Xo}^{\wedge}\right)^{\wedge} 3$[/tex]

The work done by stretching the spring to the given distance is [tex]W=\frac{k x_0}{3}[/tex]

The given parameters:

- Applied force on the spring [tex]$=F$[/tex]

- Extension of the spring [tex]$=x_0$[/tex]

The work done by stretching the spring to the given distance is calculated as follows;

[tex]W=\frac{k x_0}{3}[/tex]

[tex]$$\begin{aligned}& W=\int_{x_a}^{x_b} F d x \\& W=\int_{x_a}^{x_b} k x^2 d x \\& W=k \int_{x_a}^{x_b} x^2 d x \\& W=k\left[\frac{x^3}{3}\right] \\& W=k\left[\frac{x_b-x_a}{3}\right] \\& W=k\left[\frac{x_0-0}{3}\right] \\& W=\frac{k x_0}{3}\end{aligned}[/tex]

Thus, the work done by stretching the spring to the given distance is

[tex]W=\frac{k x_0}{3}[/tex]

measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

To learn more about work done visit:

https://brainly.com/question/13662169

#SPJ4

Related Questions

Other Questions
A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?1. The domain is distance (d) and the range is time (t).2. The domain is time (t) and the range is distance (d).3. The domain is time (t) and the range is 80.4. The domain is 80 and the range is time (t). Place the biochemical name and enzymatic activity corresponding to each complex within the respiratory chain. Complex 1 Complex II Complex III Complex IV Answer Bank cytochrome bo, complex facilitates electron transfer from ubiquinol to cytochromec facilitates electron transfer from cytochrome o to 0, facilitates electron transfer from spyinate to ubiquinone succinate dehydrogeonse complex facilitates electron transfer from NADH to ubiquinone cytochrome oxidase NADH dehydrogenase complex . An engineer has calculated the list of subnet IDs, in consecutive order, for network172.30.0.0, assuming that the /22 mask is used throughout the network. Which of thefollowing are true? (Choose two answers.)a.Any two consecutive subnet IDs differ by a value of 22 in the third octet.b.Any two consecutive subnet IDs differ by a value of 16 in the fourth octet.c.The list contains 64 subnet IDs.d.The last subnet ID is 172.30.252.0 Which statement best describes the religious persecution of the 1500's and1600's?Only Jews were persecutedPersecution was widespread Jews persecuted Catholics Persecution ended in 1545 What makes a field forever unique? two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200). a company had net cash flows from operations of $143,000, cash flows from financing of $376,000, total cash flows of $569,000, and average total assets of $3,880,000. the cash flow on total assets ratio equals: In a group of 500 people determine how many are suspects in the following scenario.A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected. 30 people total in the office22 wearing a white button down shirts16 wearing black pants7 wearing a multicolored tieUsing the data, how many suspects are there? Suzanne Collins, author of The Hunger Games, often writes choppy sentences or phrases using a first-person narrator. What is the MOST likely reason for using this technique? a researcher conducted an experiment in whice he compared two methods of teaching if there were 10 people is also called procurement. a.purchasing management b.automation c.inventory management d.materials control e.quality control Find the volume, in mL, of an object whose density is 400 g/mL and has a mass of 600mg. Acme Manufacturing is considering a project that requires an investment in new equipment of $4,000,000, with an additional $200,000 in shipping and installation costs. Acme estimates that its accounts receivable and inventories need to increase by $800,000 to support the new project, some of which is financed by a $320,000 increase in spontaneous liabilities (AP and accruals).The total cost of acme's new equipment is _______ and consists of the price of the equipment plus the ____. In contrast, acme's initial investment outlay is ______. Dna has an important role in making proteins, the biomolecules that help determine our traits as well as take part in chemical reactions throughout our bodies. Can you correctly label the steps/parts involved in protein synthesis?. In general terms, the cloud refers to high-power, large-capacity physical _____ located in data centers, and each one typically hosts multiple _____. 1. Which equation describes the line withslope -4 and y-intercept 2?A y=-4x+2B y=-4x-2C y=4x-2D y = 4x + 2 when sending a group email how do you ensure that one or several recipients cannot see the names?