Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 37

A spring with spring constant \(k=340 \mathrm{N} / \mathrm{m}\) is used to weigh a 6.7-kg fish. How far does the spring stretch?

Short Answer

Expert verified
The spring stretches 0.193 m or 19.3 cm.

Step by step solution

01

Understand Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its extension. This can be expressed as: \( F = kx \), where \( F \) is the force, \( k \) is the spring constant, and \( x \) is the extension of the spring.
02

Find the weight of the fish

The weight of the fish is the force of gravity on it. This is found by multiplying the mass of the fish by the acceleration due to gravity (approximately 9.8 m/s²). Hence, the weight \( F \) of the fish is \( F = m \cdot g = 6.7 \, kg \cdot 9.8 \, m/s² = 65.66 \, N \).
03

Calculate the extension of the spring

With Hooke's law, we equate this weight to the force exerted by the spring when stretched. We can then solve for the extension \( x \). Rearranging Hooke's law gives \( x = F / k \). Substituting the given values gives \( x = 65.66 \, N / 340 \, N/m = 0.193 m \). Hence, the spring stretches 0.193 meters (or 19.3 cm).

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

You're assessing the Engineered Material Arresting System (EMAS) at New York's JFK airport. The system consists of a 132 -m-long bed of crushable cement blocks, designed to stop aircraft from sliding off the runway in emergencies. The EMAS can exert a 300 -kN force on a 55 -Mg jetliner that hits the system at \(36 \mathrm{m} / \mathrm{s} .\) Can it stop the plane before it plows through all the blocks?

Show that the units of acceleration can be written as N/kg. Why does it make sense to give \(g\) as \(9.8 \mathrm{N} / \mathrm{kg}\) when talking about mass and weight?

We often use the term "inertia" to describe human sluggishness. How is this usage related to the meaning of "inertia" in physics?

A mass \(M\) hangs from a uniform rope of length \(L\) and mass \(m\) Find an expression for the rope tension as a function of the distance \(y\) measured downward from the top of the rope.

A biologist is studying the growth of rats on the Space Station. To determine a rat's mass, she puts it in a \(320-\mathrm{g}\) cage, attaches a spring scale, and pulls so that the scale reads \(0.46 \mathrm{N}\). If rat and cage accelerate at \(0.40 \mathrm{m} / \mathrm{s}^{2}\), what's the rat's mass?
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Radiation

Read Explanation

Electric Charge Field and Potential

Read Explanation

Force

Read Explanation

Fluids

Read Explanation

Thermodynamics

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