Work required to stretch a spring. 76 cm is 1. ) W = J. m/s O 97. Identify the equation that describes the work done by a spring in displacement, which is W = 1 2 × k × x 2 where k is the force constant and x is the displacement. Find the work required to stretch the spring an additional 0. To stretch a certain spring by 2. 00 cm is 27. Hooke’s Law states that the force required to displace a spring x meters from equilibrium is given by F ( x )= kx, where k is a constant of proportionality. Question: When a certain spring is expanded 8 centimeters from its natural position and held fixed, the force necessary to hold it is 1600 dynes. Use Hooke's Law to determine the variable force in the spring problem. 1. 5 meter fro… 01:27 A spring exerts a force of $100 \mathrm{N}$ when it is stretched $0. Pleaseshow your work!) Here’s how to approach this question. 59 cm to 6. 16 IP The work required to stretch a certain spring from an elongation of 4. ) W = J Compute the work (in joules) required to compress a spring 12 cm more when it is already compressed 7 cm Suppose a force of 60 N is required to stretch and hold a spring 0. Mar 27, 2019 · The work required to stretch or compress a spring. They first tried using the force relation F=kx, but then realized that they needed to use the formula for work done on a spring, which is 0. 50 J of work. A spring that required a force of 300 N to be stretched 0. Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to the following heights. Use increasing limits of integration. 4. Physics. If 40 N is required to stretch a spring 4 m from its equilibrium position, find the amount of work required to stretch the spring this distance. beyond its natural length? ft-lb. This video shows how to calculate the work required to stretch a spring using Hooke's Law. Use increasing Calculus questions and answers. k N/m Record your numerical answer below assuming three significant figures. Assume? Hooke's law is obeyed. 07) 2 = 0. How much work is done in stretching the spring from 35 cm to 38 cm? Give your answer to three decimal places. Compute the work required to stretch a spring from equilibrium to 10 cm past equilibrium, assuming that the spring constant is k = 190 kg/s? W J. If the spring is stretched beyond its elastic limit, the a. 25 meter. The work required to stretch the spring from the relaxed state x = 0 to the stretched length x = L is W 0. If you are given a problem in metric, be careful if you are given mass to stretch or compress the spring vertically because mass is not force. 00 O 1. Explore how force applied to a spring results in compression or elongation, and how this relationship is linear. The work required to stretch a spring is given as. (3p. 3 m beyond its rest length. 00 OOJ 0 2. ???W=\int^b_aF(x)\ dx??? where ???W??? is the work done, ???F(x)??? is the force equation, and ???[a,b]??? is the distance over which the spring is stretched or compressed. 6. An explanation would be nice. 2 m from the equilibrium position. Determine the spring constant, k, using the formula for work done to stretch a spring given by W = ( 1 2) k x 2, where W is the work done, k is the spring constant, and x is the distance stretched (in this case, 1 ft), with the given work done W as 10 ft-lb. 16K views 6 years ago Calculus Integrals. Six joules of work is required to stretch a spring 0. It is important to note that this calculation assumes that the spring constant remains constant throughout the stretching process. Oct 15, 2016 · Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. Assume that 10 ftlb of work is required to stretch a spring 1 ft beyond itsnatural length. 4) 0. A spring that required 40 J of work to be stretched 0. 10 meter. There are 2 steps to solve this one. 00 cm greater than, less than, or equal to 31. is stretched 4. 2 m from its equilibrium position. Work to Stretch a Spring. 4 m from its equilibrium position? Assume Hooke's law is obeyed. How much work is done in stretching the spring from 35 cm to 38 cm? Question: Compute the work required to stretch a spring from equilibrium to 8 cm past equilibrium, assuming that the spring constant is k=140 kg/s2 (Use decimal notation. Find the work required to stretch the spring an additional 3 inches. …. Find the force constant of the further stretched through 0. View the full answer. So W = ∫ 160 x dx = 160 [x 2 /2] evaluated from x = 0 to x = 0. Choose units and enter the following: The calculator returns the work in newton meters (N*m) defines the force used to displace a spring as: . 2. Find the work required to stretch the spring an additional o. 59 cm. Question: Problem 4. 0 J . How much work is required to compress the spring 0. If the work required to stretch a spring 3 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 27 in. (Use decimal notation. Step 1. Give your answer to three decimal places. W=__J. The objective If the work required to stretch a spring 3 ft beyond its natural length is 12 ft-lb, how much work (in ft-lb) is needed to stretch it 9 in. Dec 28, 2014 · You are confusing force and work in the first step. How much work is required to stretch the spring 0. 2 cm? A spring has a spring constant of 40N/m . a. From Hooke's Law we have force used to displace a spring is F = - k*x where k -spring …. A graph showing force vs. b. Compute the work required to stretch the spring starting from a stretched total length of 6 m to a stretched total length of 9 m. Select a cart mass • In the data table below. What work is required to stretch the spring from x=0 to x=2 m ? ?! Here’s the best way to solve it. Mar 12, 2024 · The simplest oscillations occur when the restoring force is directly proportional to displacement. (Assume the unstretched position is zero) What work is required to stretch a spring of spring constant 40N/m from x=0. What is the natural length of the spring? Nov 16, 2022 · Example 1 A spring has a natural length of 20 cm. 267 J/cm * 5. 1 m from its equilibrium position b. Find step-by-step Calculus solutions and your answer to the following textbook question: Use Hooke’s Law to determine the variable force in the spring problem. beyond its natural length? ft−lb IP The work required to stretch a certain spring from an elongation of 4. 08 m. 78 times the work Question: Use Hooke's Law to determine the work done by the variable force in the spring problem. A linear spring is one with a linear relationship between force and displacement, meaning the force and displacement are directly proportional to each other. . Example 2: A spring is stretched 60 cm, and it takes a force of 40 Newtons to hold Step 1. preview answers. Work done = 0. Calculate its spring constant, k. It is given that the work required to stretch a spring 3 f t beyond its natural length is 12 f t - l b. Show transcribed image text. By the Hook's law the force required to stretch the spring for x x x meters is: F (x) = 12 x F(x)=12x F (x) = 12 x. 8 J? (b) Verify your answer to part (a) by calculating the Compute the work required to stretch a spring from equilibrium to 12 cm past equilibrium, assuming that the spring constant is k = 130kg/(s^2) There are 2 steps to solve this one. 59 cm to an elongation of 5. 1 m from its equilibrium position? where k is the spring constant. 10 m from its equilibrium position. Question: Six joules of work is required to stretch a spring 0. If Jennifer weighs 552 N, what is the magnitude of her momentum? 951 kg. What is the spring constant? (The answer is 20 lb/ft, but I don't know how to do it. When a certain spring is expanded 13 centimeters from its natural position and held fixed, the force necessary to hold it is 2600 dynes. 6 kgm/s 672 kgm/s 137 kg. (10 points) Compute the work required to stretch a spring from equilibrium to 8 cm past equilibrium, assuming that the spring constant is k = 160 kg/s². 100% (2 ratings) workdone in stretc Our expert help has broken down your problem into an easy-to-learn solution you can count on. 0 cm to 19. In the case where you are given a single length, you're probably just asked to solve for k. Compressing 4 cm more when it is already compressed 5 cm. (c)If the spring is then released, find the speed with which the mass passes through the Question: What work is required to stretch a spring of spring constant 40N/m from x=0. Question: 6) (10 pts) A spring that obeys Hooke's law has a spring constant 10 N/m and a natural length l=5 meters (m). If x=0 corresponds to when the springs are at their relaxed state, which image best represents the magnitude of the force applied to the springs as a function of the stretch distance. Computation 57 J of work is required to stretch an ideal spring from 1. How much work is needed to stretch it from 35 c 11,050 solutions. W = integral ergs. Mechanical work is force * displacement; incremental work dW = F cos θ dx = kx dx for a spring. org 9. Then W = 80 (0. 5kx^2. A spring that required 120 J of work to be stretched 0. Compute the work required to stretch a spring from 5 to 12 cm past equilibrium, assuming that the spring constant is k = 120 kg/s?. Problems with Detailed Solutions Problem 1 What is the magnitude of the force required to stretch a 20 cm-long spring, with a spring constant of 100 N/m, to a length of 21 cm? Feb 1, 2021 · the work required to stretch the spring is 8 J. Definitions. ) Here’s the best way to solve it. 25m. Suppose it takes a force of 10 N (in the negative direction) to compress a spring 0. What is the force constant of this spring?k = _______________ N/m. A spring that required 60 J of work to be stretched 0. 00 cm is 31. 76 cm = 1. Answer. How much additional work is required to stretch it to 3 cm from equilibrium? Here’s the best way to solve it. beyond its natural length? 3 ft-lb. Question: Use Hooke's Law to determine the work done by the variable force in the spring problem Five joules of work is required to stretch a spring 0. beyond its natural length? A stiff spring has a force law given by F = - kx 2. 00 cm is 25. A spring that required a force of 200 N to be stretched 0. So we can say that. 00 cm. (Assume the unstretched position is zero) Here’s the best way to solve it. Question: 5. Created by Sal Khan. How does the work required to stretch a spring 4 cm compare with the work required to stretch it 3 cm? (a) same amount of work (b) About 3 times the work (c) About 4 times the work (d) About 1. In terms of W0, how much work is required to extend the spring from the Sep 13, 2010 · Springs. 8 J of work to stretch this spring from an elongation of 4. Four joules of work is required to stretch a spring 0. Previous question. )A “stiff” spring has a force law given by F = -kx3. One end is then attached to a hook and the other end is pulled by a force that increases to 25. Question: A force F = 20x - x3 stretches a nonlinear spring by x. 536 J. Round your answer to the nearest hundredth if necessary. A nonlinear spring has a nonlinear relationship between force A spring required a force of 5. View the full answer Step 2. 00 cm greater than, less than, or equal to 25. 20 meter. Find the work W required to stretch the spring an additional 13 centimeters. Seven joules of work is required to stretch a spring 0. m/s Step 1. Question: To stretch a certain spring by 2. In this circumstance, the work to stretch the spring from 0 to 12 cm is also equal to the work for a composite path A spring required a force of 5. It requires 324 J to stretch the spring to 7 m. Unlock. Science. Here, F F is the restoring force, x x is the displacement from equilibrium or deformation, and k k is a constant related to the difficulty in deforming the system. This is called Hooke’s law force, or spring force: F = −kx. In summary, the individual is trying to calculate the work required to stretch a spring by 9 inches beyond its natural length, given that the work required to stretch it by 3 feet is 8 ft-lb. Question: Compute the work W required to stretch a spring from 9 cm to 13 cm past equilibrium, assuming that the spring constant is k = 110 kg/s2. Part A What is the force constant of this spring? k k = nothing N/m SubmitRequest Answer Part B. Set up the integral that gives the work done in stretching the spring 1. -Eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. The work required to stretch the spring can be calculated using Hooke's Law. A force of F = 20x−x3 N stretches a nonlinear spring by x meters. Solutions are written by subject matter experts or AI models, including those trained on Chegg's content and quality-checked by experts. 0 N, causing the spring to stretch to a length of 19. Part A Is the work required to increase the elongation of the spring from 5. 5 m from its equilibrium position. (b)Work required to stretch the spring to that initial position. Question: Predict/Calculate Problem 8. 00 cm to 6. 59 cm greater than, less than, or equal to 29. 2 m from its equilibrium position, a. Processing The calculator compute the work based on the spring constant (k) and the displacement (x). 5cm from its equilibrium position? Here’s the best way to solve it. Compute the work required to stretch a spring from 7 to 10 cm past equilibrium, assuming that the spring constant is k=120 kg/s2 (Use decimal notation. How much work is required to strech the spring 0. 0 J ? Explain. 3 m from its equilibrium position? c. A spring that required 80 J of work to be stretched 0. make a column for spring stretch. extension of the spring, x = 8 cm = 0. 39 Joules. What is the force constant of this spring? How much work was required to stretch the spring from 17. Calculate the work required to stretch the spring from 5 m to 8m. It takes 29. 0 kgm/s O 68. Dec 11, 2003 · Examples: Example 1: If the force to stretch a spring is given by F = (100 N/m)x, how much work does it take to stretch the spring 4 meters from rest? Solution: We have k = 100 N/m and x = 4 m. Question: (1 point) Compute the work required to stretch a spring from equilibrium to 12 cm past equilibrium, assuming that the spring constant is k = 200 kg/s? = W = J. Question: If the work required to stretch a spring 2 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 18 in. 1 m. Nov 16, 2022 · Example 1 A spring has a natural length of 20 cm. displacement for a linear spring will always be a straight line, with a constant slope. Our expert help has broken down your problem into an easy-to-learn solution you can count on. Assume Hooke's law is obeyed. We have given that. Find the work required to stretch the spring an additional 3 Suppose a force of 30 N is required to stretch and hold a spring 0. A spring that required a force of 50 N to be stretched 0. (a) What work is required to stretch it from x =O to x = 2? (b) What is its potential energy V at x = 2, if V (0) = 5? (c) What is k = dF/dx for a small additional Given, It is the work required to stretch a spring 3ft beyond its natural length is 6 ft-lb. Find: (a)The initial potential energy of the spring. Physics questions and answers. Compute the work required to stretch a spring from 5 to 11 cm past equilibrium, assuming that the spring constant is k = 140 kg/s2. 4 m from its equilibrium position? d. 0 cm long when it is lying on a table. Step 3. Calculate the work required to stretch the following springs 1. 0J ? Explain. 00 cm from its equilibrium position requires 7. Provide your answer below: w. This video shows how to calculate the Discover the phenomena of springs and Hooke's Law. A 40 N force is required to stretch (and hold the spring) to a length of 30 cm. Sep 12, 2022 · Notice that the work required to stretch the spring from 0 to 12 cm is four times that required to stretch it from 0 to 6 cm, because that work depends on the square of the amount of stretch from equilibrium, \(\frac{1}{2}\)kx 2. Transcribed image text: Our expert help has broken down your problem into an easy-to-learn solution you can count on. Compute the work required to stretch a spring from equilibrium to 6 cm past equilibrium, assuming that the spring constant is k = 120 kg/s?. 2 cm. Question: Calculate the work required to stretch the following springs 0. 0J . A spring with a spring constant k = 50N/m has an unstretched lengthof 20cm. Using Hooke's Law to determine the work done by the variable force, find the constant of Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. According to Newton's third law, if a spring is stretched or compressed using force F, as a reaction the spring also react by a force - F. Calculus questions and answers. See full list on khanacademy. 8) O 2 10 pts Question 14 Jennifer is walking at 1. Calculus. There are 3 steps to solve this one. Starting with Spring Stretch 1. The work required to stretch the spring is calculated as; Therefore, the work required to stretch the spring is 8 J. record the distance the spring is stretched before launch. 8 m beyond its rest length to 3. 22 m/s. Explanation: Given; spring constant, k = 2500 N/m. In Exercises 3–6, compute the work (in joules) required to stretch or compress a spring as indicated, assuming a spring constant of k = 800 N/m. ) W=Compute the work (in joules) required to compress a spring 4 cm more when it is already compressed 10 cm, assuming that the spring constant is k=140 N/m. Mar 13, 2023 · Question: A spring requires 5 Joules to stretch the spring from 8 cm to 12 cm, and an additional 4 Joules to stretch the spring from 12 cm to 14 cm. 00 J of work. Now we want to find out what work is needed to stretch the spring to a length of 6 6 6 m. A spring has a natural length of 4 m. Since spring's natural length was 4 4 4 m then the value of x x x is: x = 6 − 4 = 2 x=6-4=2 x = 6 − 4 = 2 Calculus questions and answers. 6) O 0. What is the work required to stretch the spring? O 4. Calculate the work required to stretch the spring from 7 m to 11 m. 25 m from its equilibrium position. Uncover the concept of restorative force and how it counteracts applied force, keeping our spring in equilibrium. 1 / 4. Suppose the work required to stretch a spring from its natural length to 3ft beyond its natural length is 18ft-lbs. Since you are stretching 0. Remember to include a ""if necessary. Click Save All Answers to save all answers. Question: Question A spring has a natural length of 1 m. Expert-verified. 00 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. Assuming the spring obeys Hooke's law, find the spring constant k. the work done by a spring in x displacement is W = 1/2 k x^2here K Question: If the work required to stretch a spring 3ft beyond its natural length is 15ft−lb, how much work is needed to stretch it 9 in. Example: The Work Required to Stretch or Compress a Spring. W = ∫ a b k x d x. A light spring obeys Hooke's Law. Here’s the best way to solve it. 0 N to compressit 0. Therefore, the extra work required to stretch the spring an additional 5. 70 cm from its equilibrium position requires 7. How many lbs of force does it take to hold a spring 4ft beyond its natural length? (A) 4 (D) 8 (C) 16 (B) 36 (E) 1 ve and Submit to save and submit. Work is measured in joules, so your given quantity is work. 2 \mathrm{m}$ beyond its natural length. W = 12 f t − l b a = 0 b = 1 f t. Find the work required to stretch the spring to a lengthof 30 cm. 5 meters from equilibrium position, and work is the integral of the force used over the distance moved, we have that Calculus questions and answers. Eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. F = − k x. 5 m from their equilibrium positions. The work required to stretch the spring from the relaxed state x = 0 to the stretched length x = l is W0. How much work is required to stretch the spring 3. Question: A spring with a spring constant k = 50N/m has an unstretched lengthof 20cm. 5 meter from its natural length. Nine joules of work is required to stretch a spring 0. Recall Hooke's Law: The force required to maintain a spring stretched x units beyond its natural length is proportional to x. If the work required to stretch a spring 4 feet beyond its natural length is 10 foot-pounds, how much work is needed to stretch it 10 inches beyond its natural length? Your answer must include the correct units. Question: A force of F=20x−x3 N stretches a nonlinear spring by x meters. (4 points) A spring requires 2 J of work to be stretched 0. How much work is done to stretch the spring 0. 4 m from its equilibrium position. A horizontal frictionless spring/mass system with a spring constant of k = 100 N/m is stretch 15. Example 2: A spring is stretched 60 cm, and it takes a force of 40 Newtons to hold A spring with a spring constant of 2500 N/m. To calculate the work done when we stretch or compress an elastic spring, we’ll use the formula. Question: Compute the work required to stretch a spring from 4 to 12 cm past equilibrium, assuming that the spring constant is k=190 kg/s2 (Use decimal notation. A spring is 17. Question: Eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. 1 m from its equilibrium position. Find the work W required to stretch the spring an additional 8 centimeters. (a) Is the amount of work required to increase the elongation of the spring from 5. Question: Use Hooke's Law to determine the work done by the variable force in the spring problem. The work required to stretch a certain spring from an elongation of 4. (You may enter lbf or lb*ft for ft-lb. Start by setting up the integral for the work required to stretch the spring a given distance beyond its natural length for the case where work is given. 5 meter from its nAtural length find the work required to stretch the spring an additional 0. 07 m. 20 m to 0. 30 meter. Therefore, Work = (1/2)kx 2 = (1/2) (100 N/m) (4 m) 2 = 800 Joules. What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches? There are 2 steps to solve this one. Use Hooke’s Law to determine the variable force in the spring problem. Use Hooke's Law to determine the work done by the variable force in the spring problem Six joules of work is required to stretch spring 0. 6 m from their equilibrium positions. 4 m? 04 O 0. Calculate work done. Question: To stretch a certain spring by 3. It requires 180 J of work to stretch the spring to 10 m. Nov 11, 2009 · This gives us a total work of 0. W =. more. 0 cm from its equilibrium position. Calculate the work required to stretch the following springs 0. W = J. 00 cm to an elongation of 5. The negative sign on the force gets cancelled by θ being 180 degrees between force and displacement. Question: If the work required to stretch a spring 1 ft beyond its natural length is 6 ft-lb, how much work is needed to stretch it 3 in. Sep 24, 2022 · The work required to stretch a spring by a displacement x from equilibrium is W = kx 2 /2. Aug 21, 2014 · Generally, you will need to solve for k, that's why 2 different lengths are provided. Jun 18, 2019 · 20 J work is required to stretch a spring through 0. From the given information of the spring, find the spring constant. 5 m from the equilibrium position? Question: Part 2: Spring Shot! Your goal is to find the relationship between the amount of work that was required to stretch the spring and the resulting velocity. Question: As a section of an exercise routine to build their pectoral muscles, a woman stretches a spring which has a spring constant k=665N/m a. So f (x) = kx, where k is the spring constant. 000 3. four joules of work is required to stretch a spring 0. zp gt in vw ur dx eg qn hu ux