Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 905

A 5 meter long wire is fixed to the ceiling. A weight of \(10 \mathrm{~kg}\) is hung at the lower end and is 1 meter above the four. The wire was elongated by \(1 \mathrm{~mm}\). What is the stored in the wire due to stretching ? (A) Zero (B) \(0.05\) Joule (C) 100 Joule (D) 500 Joule

Short Answer

Expert verified
(B) \(0.05\) Joule

Step by step solution

01

Calculate the force exerted by the weight

With the given mass, we can find the force this mass exerts on the wire due to gravity. The force can be calculated using the formula: \(F = mg\) where m is the mass (10 kg) and g is the acceleration due to gravity (approximated as \(9.81 \mathrm{~m/s^2}\)). \(F = (10\mathrm{~kg})(9.81 \mathrm{~m/s^2})\) \(F = 98.1 \mathrm{~N}\) (Newtons) Step 2: Calculate the spring constant (k)
02

Calculate the spring constant (k)

Using Hooke's law, we have the force and elongation relation as: \(F = kx\) We can rewrite this equation for the spring constant (k) as: \(k = \frac{F}{x}\) where x is the elongation (1 mm, or 0.001 m). We plug in the force and elongation values to find k. \(k = \frac{98.1 \mathrm{~N}}{0.001 \mathrm{~m}}\) \(k = 98100 \mathrm{~N/m}\) Step 3: Calculate the potential energy stored in the wire
03

Calculate the potential energy stored in the wire

We can now use the formula for the potential energy of a stretched wire: \(U = \frac{1}{2}kx^2\) and plug in the spring constant (k) and elongation (x) from previous steps: \(U = \frac{1}{2}(98100 \mathrm{~N/m})(0.001 \mathrm{~m})^2\) \(U = \frac{1}{2}(98100 \mathrm{~N/m})(0.000001 \mathrm{~m^2})\) \(U = 0.04905 \mathrm{~J}\) The stored potential energy in the wire is approximately 0.04905 Joules. We can round it to 0.05 Joules. Therefore, the correct answer is: (B) \(0.05\) Joule

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.

Start your free trial

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 temperature at which the vapour pressure of a liquid becomes equals of the external pressure is its. (A) Melting point (B) sublimation point (C) Critical temperature (D) Boiling point

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: The concept of surface tension is held only for liquids. Reason: Surface tension does not hold for gases. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: Tiny drops of liquid resist deforming forces better than bigger drops. Reason: Excess pressure inside a drop is directly proportional to surface tension. (A) a (B) \(b\) (C) (D) d

A beaker is completely filled with water at \(4^{\circ} \mathrm{C}\) It will overflow if (A) Heated above \(4^{\circ} \mathrm{C}\) (B) Cooled below \(4^{\circ} \mathrm{C}\) (C) Both heated and cooled above and below \(4^{\circ} \mathrm{C}\) respectively (D) None of these

A body floats in water with one-third of its volume above the surface of water. It is placed in oil it floats with half of: Its volume above the surface of the oil. The specific gravity of the oil is. (A) \((5 / 3)\) (B) \((4 / 3)\) (C) \((3 / 2)\) (D) 1
See all solutions

Recommended explanations on English Textbooks

Single Paragraph Essay

Read Explanation

Multiple Choice Questions

Read Explanation

Phonetics

Read Explanation

Summary Text

Read Explanation

English Language Study

Read Explanation

5 Paragraph Essay

Read Explanation
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