Chapter 15: Q. 20 (page 416)

FIGURE EX $15.20$ is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant?

Short Answer

Expert verified

The spring constant is $k = 4.0 N / m$

Step by step solution

Given data.

From the graph:

x_{m a x} = A = 2 m K_{m a x} = 8.0 J

Required: spring constant $k$

Conservation law.

To get a spring constant we will use conservation law which tells that:

1. At max position the potential energy is maxed and kinetic energy is $0$ .

2. At equilibrium position the kinetic energy is max and potential energy is $0$ .

3. The max kinetic energy = The max potential energy.

According to these notes get that

$U_{m a x} = K_{m a x} \Rightarrow \frac{1}{2} k A^{2} = K_{m a x}$ $\Rightarrow (1)$

From $(1)$ we get that

$k = \frac{2 K_{m a x}}{A^{2}}$ $\Rightarrow (2)$ $\Rightarrow (2)$

Substitution in $(2)$ to get that

$k = \frac{2 \times 8}{{(2)}^{2}} = 4.0 N / m$

$U_{m a x} = K_{m a x} \Rightarrow \frac{1}{2} k A^{2} = K_{m a x}$

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!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

FIGURE EX $15.20$ is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant?

Short Answer

Step by step solution

Given data.

Conservation law.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Magnetism

Dynamics

Particle Model of Matter

Linear Momentum

Nuclear Physics

Study anywhere. Anytime. Across all devices.

FIGURE EX15.20 is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant?

Short Answer

Step by step solution

Given data.

Conservation law.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Magnetism

Dynamics

Particle Model of Matter

Linear Momentum

Nuclear Physics

Study anywhere. Anytime. Across all devices.

FIGURE EX $15.20$ is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant?