What is the spring constant of a spring that stores25 Jof elastic potential energy when compressed by7.5 cm?

Short Answer

Expert verified

Spring constant is,k=8.9×103 N/m .

Step by step solution

01

Given

Elastic potential energyU=25 J

Compressed lengthx=7.5 cm=7.5×10−2 m .

02

To understand the concept 

The problem is based on the concept of elastic potential energy. It is energy stored as a result of applying a force to deform an elastic object. By using the concept of elastic potential energy, we can find the spring constant.

Formula:

U=12kx2

03

Calculate the spring constant of the spring 

Elastic potential energy can be written as

U=12kx2k=2Ux2

Substitute all the value in the above equation.

k=2×25 J(7.5×10−2 m)2k=8.9×103 N/m

Hence the spring constant is, k=8.9×103 N/m.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The spring in the muzzle of a child’s spring gun has a spring constant of 700 N/m. To shoot a ball from the gun, first, the spring is compressed and then the ball is placed on it. The gun’s trigger then releases the spring, which pushes the ball through the muzzle. The ball leaves the spring just as it leaves the outer end of the muzzle. When the gun is inclined upward by 30oto the horizontal, a 57 gball is shot to a maximum height of 1.83 mabove the gun’s muzzle. Assume air drag on the ball is negligible. (a) At what speed does the spring launch the ball? (b) Assuming that friction on the ball within the gun can be neglected, find the spring’s initial compression distance.

You drop a2.00 Kgbook to a friend who stands on the ground at distanceD=10.0 mbelow. If your friend’s outstretched hands are at distanced=1.50 mabove (fig.8-30), (a) how much workWgdoes the gravitational force do on the book as it drops to her hands? (b) What is the changeΔUin the gravitational potential energy of the book- Earth system during the drop? If the gravitational potential energy U of the system is taken to the zero at ground level, what is U (c) when the book is released and (d) when it reached her hands? Now take U to be 100 J at ground level and again find (e) Wg,(f) ΔU(g) U at the release point, and (h) U at her hands.

A 9.40 kgprojectile is fired vertically upward. Air drag decreases the mechanical energy of the projectile-Earth system by 68.0 kJduring the projectile’s ascent. How much higher would the projectile have gone were air drag negligible?

A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8 m. He begins to slide down the ice, with a negligible initial speed (Figure). Approximate the ice as being frictionless. At what height does the boy lose contact with the ice?

A volcanic ash flow is moving across horizontal ground when it encounters a10°upslope. The front of the flow then travels 920 mup the slope before stopping. Assume that the gases entrapped in the flow lift the flow and thus make the frictional force from the ground negligible; assume also that the mechanical energy of the front of the flow is conserved. What was the initial speed of the front of the flow?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free