**Problem Statement:**A spring that is compressed 13.5 cm from its equilibrium position stores 2.98 J of potential energy. Determine the spring constant \( k \).---**Answer:**\[ k = \]A field is provided for input, with the answer 22.1 displayed. The answer is marked as "Incorrect" in red below the input field.**Explanation:**The problem involves calculating the spring constant using the formula for potential energy stored in a spring:\[PE = \frac{1}{2} k x^2\]Where:- \( PE \) is the potential energy (2.98 J),- \( x \) is the compression distance from the equilibrium position (13.5 cm or 0.135 m),- \( k \) is the spring constant to be determined.Converting the given distance to meters and rearranging the formula:\[k = \frac{2 \times PE}{x^2}\]Substitute the given values to solve for \( k \).

Compression of spring(x)=0.135 menergy stored in spring(U)=2.98 J

Answered: A spring that is compressed 13.5 cm…

A spring that is compressed 13.5 cm from its equilibrium position stores 2.98 J of potential energy. Determine the spring constant k. k = 22.1 Incorrect

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: -kx³. The work required to stretch the 0 to the stretched length x = l is Wo. In terms of A "stiff"…

Q: On a frictionless horizontal surface, a block is pushed up against a 70,425 N/m spring and…

A: Given data: The spring constant k=70425 N/m The speed of the block when it released v=27 m/s The…

Q: ) A box of mass m= 38 kg which is sliding on a horizontal rough surface and momentarily comes to st…

A: We know that We have given that the mass of 38 kg block moving on a horizontal plane with the…

Q: 4. A spring has a spring constant, k = 10000 N/m. How much potential energy is stored in the spring…

A: Given data, Spring constant k=10000 N/m Change in length x=1 cm=0.01 m

Q: The coefficient of kinetic friction between a suitcase and the floor is 0.272. If the suitcase has a…

Q: 9. How much work must be done to extend a spring by 1.50 cm from its relaxed length if its spring…

A: Work: Work done on an object is defined as the scalar product of the force vector and the…

Q: A 4.0 kg-block attached to a 20 N/m-spring constant spring moves on a frictionless horizontal…

A: Given data: Mass (m) = 4.0 kg Spring constant (k) = 20 N/m Amplitude (A) = 3 m Required: The…

Q: 10 cm Untit hill The 2. A0.12 kg marble is started on a frictionless marble track by compressing a…

A: Given Height of hill h = 10 cm =0.1 m Mass m = 0.12 kg Spring constant k = 490 N/m

Q: Calculate the potential energy of a 4.5 kg bowling ball that is on the ground. Assume that g = 9.8…

A: Given that:- Mass of the bowling ball=4.5Kg acceleration due to gravity is g=9.8m/s2 And as the ball…

Q: The 2kg collar is released from rest at A and slides down the inclined fixed rod in the vertical…

Q: 18. Consider a particle of mass m is freely drawn from the"h "height. The three different positions…

A: Energy lost by P. E = Energy gain by K. E

Q: A mass is hanging on a vertical spring and is orginally in equilibrium with the weight balanced by…

Q: Dot. What is the scalar product Ã· BifÃ = x₁ + yĵ and B = yî − xj? A. 2xy B. x² - y² o c. ryi-yry O…

A: Given data: Two vectors A = x i + y j and B = y i - x j Required: The scalar product of vector A…

Q: How much work is required to compress a spring of constant k from x1 to x2 (x2>x1)? A. ½ k…

A: Option D is the right answer 1/2 k(x2^2 - x1^2)

Q: As part of your daily workout, you lie on your back and push with your feet against a platform…

A: Given Data, Work Done(W)=81.0 J Compressed distance (x)=0.210 m

Q: 1. Refer and use figure 1 and 2. Calculate the magnitude of force needed to displace the block by…

A: The given graph is :

Q: A floating ice block is pushed through a displacement á = (27.0 m )î – (22.0 : j along a straight…

A: Given data: Displacement d→ = 27.0mi^ -22.0mj^ Force F→ = 178Ni^ -152Nj^ Required: Work done

Q: 1. The force required to extend a spring to .05 meters from equilibrium is 2 N. a. Find the spring…

A: Given data, force (F)=2N Spring extension (x)=0.05m

Q: On a frictionless horizontal surface, a 4.23 kg block is pushed up against a 6,768 N/m spring and…

A: Write the given values with the suitable variables. m=4.23 kgk=6768 N/mx=0.27 m Here, m, k, and x…

Q: 32. A ______________ force is a force that does zero work on a closed path. a. Non-conservative b.…

A: Work done by conservative force is independent of path and depends only on end points so its 0 in…

Q: 15. Object falls from height 1500 m. Find the velocity by time reach ground. Ans. 170 m/s 31. Spring…

Q: Compare the initial potential energy of the spring to the maximum gravitational potential energy of…

Q: A 4 kg ball falls from height of 29. What willbe potential energy of the ball after 1 second? Use g…

Q: A particle of mass m = 10 g moves in a dimension subjected to a force associated with a potential…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: What is the potential energy of a 15 kg dumbbell sitting on a weight bench 0.65 m above the floor?…

A: Given that, Mass of a dumbbell, m = 15 kg It is placed on a bench 0.65 m above the floor. We need to…

Q: 1. Draw a situation where a force is doing zero work. Explain why the force is doing no work,…

A: To explain a situation where work done by a force is zero.

Q: Two carts connected by 0.50 m spring hit a wall, compressing the spring to 0.75 m. If the spring…

Q: 1. A particle moves in one dimension and is subject to a conservative force, whose potential energy…

A: For equilibrium points we have to calculate force from the potential energy and equate it with zero…

Q: Force (N) SF-2 The force required to stretch (elongate) a spring is shown in the graph to the right.…

Q: 3. A force of 5.0 N is used to stretch a block attached to a spring from its resting position to a…

Q: Determine the velocity of a cart that is accelerated from rest by a 30.0 N force for 20.0 m. The…

A: Given data: Initial velocity (Vi) = 0 m/s Force (F) = 30.0 N Displacement (d) = 20.0 m Mass (m) =…

Q: art B alculate the work done by the force due to gravity. Value HÅ Part C Submit Request Answer…

Q: Which of the following is NOT an example of potential energy? a. A running woman b. An incredibly…

A: Required : Which is not an example of potential energy.

Q: A 225g cart compresses a horizontal 650J/m² spring 3.2cm and is released from rest. The cart travels…

Q: On a frictionless horizontal surface, a 6.84 kg block is pushed up against a 55,404 N/m spring. The…

A: rite the given values with the suitable variables. m=6.84 kgk=55404 N/mu=25.2 m/s Here, m, k, and u…

Q: QUESTION 9 The rate of change of work done is called : O Potential energy ,and SI unit is joule O…

A: The answer is given below

Q: A 1.77 kg book slides 1.25 m along a level surface. The coefficient of kinetic friction between book…

A: Kinetic frictional force is,

Q: 5. Spiderman uses his spider webs to save a runaway train moving about 60kph. His web stretches a…

A: Given that The speed of the train is (v) = 60kph as we know that 1kph = 0.278m/s…

Q: The Potential energy stored in a car Shock Absorber which is compressed by 20 cm is 50 J. The Spring…

A: Potential energy stored in a spring is given by: PE = (1/2)*k*x^2 k = spring constant = ? PE = 50 J…

Q: 2. The potential energy function associated with a force acting on a system is U = 3x3 – 5x. a) What…

A: (a) The potential energy function associated with a force acting on a system is given U = 3x3 – 5x.…

Q: It takes 1.81 J of work to compress a spring 13.1 cm. What is the force constant of the spring in…

Q: If it requires 6.0J of work to stretch a particular spring by 2.0 cm from its equilibrium length,…

Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

**Problem Statement:**

A spring that is compressed 13.5 cm from its equilibrium position stores 2.98 J of potential energy. Determine the spring constant \( k \).

---

**Answer:**

\[ k = \]

A field is provided for input, with the answer 22.1 displayed. The answer is marked as "Incorrect" in red below the input field.

**Explanation:**

The problem involves calculating the spring constant using the formula for potential energy stored in a spring:

\[
PE = \frac{1}{2} k x^2
\]

Where:
- \( PE \) is the potential energy (2.98 J),
- \( x \) is the compression distance from the equilibrium position (13.5 cm or 0.135 m),
- \( k \) is the spring constant to be determined.

Converting the given distance to meters and rearranging the formula:
\[
k = \frac{2 \times PE}{x^2}
\]

Substitute the given values to solve for \( k \).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Answer

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

1. Which of the following is NOT an example of potential energy? a. A running woman b. An incredibly compressed spring G. A tightly stretched rubber band d. An apple dangling off a branch 2. A ball drops from a height h. What more do we need to calculate initial potential energy? a. Elasticity of the Ball b. Mass c. Final Velocity d. Horizontal Displacement
The force on a particle is directed along an x axis and given by F = Fo(x/xo - 1) where x is in meters and F is in Newtons. If Fo= 1.4 N and xo = 2.3 m, find the work done by the force in moving the particle from x = 0 to x = 2x0 m. Number i Units
2. An object has 560 J of potential energy and 890 J of mechanical energy. How much kinetic energy does the object have?. ME = REHPE 560 560 330J= PE olog ertev 3. A slingshot rubber band with a spring constant of 850 N/m was stretched 0.33 m. A 0.4 kg rock was fired from the slingshot after it was released. a. Find the spring potential energy. PE =)2 kx? Z(850X.33) b. What is the kinetic energy of the stone once it was released? PEERE c. What is the velocity of the stone as soon as the slingshot was released?
4. Suppose you fire a mass m straight vertically upwards from a spring that is known to have been compressed a distance x from its equilibrium position, and the mass reaches a maximum height of h above its launch point. Using the conservation of energy, derive an expression for the spring constant k of the spring.
Solve using conservation of E. A 25 g ball, resting on a spring, compresses it 8.0 cm and is then launched up, reaching a height of 1.2m. Find k. Correct answer: 98 N/m
The figure below shows a force versus position graph for a spring/block system. If Fs=160N and the block is released at x = 12 cm (not shown on figure) how much work is done on the block by the spring as the block goes from x = + 8.0 cm to x = + 5.0 cm. HInt: Determine k from the graph. Don't forget to convert from cm.
Work and energy
need help with A-f
10. If the net work done on a particle is zero, which of the following statements must be true? A. The velocity is decreased B. The velocity is unchanged C. The speed is unchanged D. The velocity is zero 11. The work required to accelerate an object on a frictionless surface from a speed v to a speed 2v is A. equal to the work required to accel erate the object from v = 0 to v B. twice the work required to accelerate the object from v = 0 to v C. three times the work required to accelerate the object from v = 0 to V D. four times the work required to ac celerate the object from 2v to 3v E. not known without knowledge of the acceleration 12. A certain truck has twice the mass of a car. Both are moving at the same speed. If the kinetic energy of the truck is K, what is the kinetic energy of the car? A. K/4 B. K/2 C. 0.71K D. K E. 2K
7. A force of 180 N stretches a spring 0.050 m beyond its unstretched length. a. What is the spring constant of this spring? b. What magnitude of force is needed to stretch the spring 0.012 m beyond its unstretched length? C. How much work must be done to stretch the spring 0.012 m beyond its unstretched length? d. What magnitude of force is needed to compress the spring 0.025 m? e. How much work must be done to compress the spring 0.025 m?
The spring constant of a spring is 100 N/m. A force of 10 N stretches the spring by 10 cm. How much potential energy is stored in the spring? а. О.3] b. 0.2J c. 0.4J d. 0.5J
The force on a particle is directed along an x axis and given by F = Fo(x/xo - 1) where x is in meters and F is in Newtons. If Fo= 1.5 N and Xo = 5.8 m, find the work done by the force in moving the particle from x = 0 to x = 2x0 m. Number i Units