Chapter 15: Q. 18 (page 415)

A $1.0 k g$ block is attached to a spring with spring constant $16 N / m$ . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives its a speed of $40 c m / s$ .
What are
a. The amplitude of the subsequent oscillations?
b. The block's speed at the point where $x = \frac{1}{2} A$ ?

Short Answer

Expert verified

a) The amplitude of the subsequent oscillations is $A = 10.0 c m$

b) The block speed at the point when $x = \frac{1}{2} A$ is $v = 34.64 c m / s$

Step by step solution

Given data.

Given:

$m = 1.0 k g$
$k = 16 N / m$
$v (0) = 40 c m / s$
$x (0) = 0$

Required:

(a) A

(b) $v$ when $x = \frac{1}{2} A$

Simplification.

a) using conservation law and simplify to get that

$v = ω \sqrt{A^{2} - x^{2}} \Rightarrow A^{2} = {(\frac{v}{ω})}^{2} + x^{2} \Rightarrow (1)$

All is known except $ω$ which is given by

$ω^{2} = \frac{k}{m} \Rightarrow (2)$

substitution in $(2)$ to get that

$ω^{2} = \frac{16}{1} = 16 \Rightarrow ω = 4 r a d / s$

substitution in $(1)$ to get that

$A^{2} = {(\frac{0.4}{4})}^{2} \Rightarrow A = 0.1 m = 10.0 c m$

Using equation (1)

To get

$v = 4 \sqrt{{(10)}^{2} - {(5)}^{2}} = 34.64 c m / s$

Where :

$x = A / 2 = 10 / 2 = 5 c m$

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.

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.

Short Answer

Step by step solution

Given data.

Simplification.

Using equation (1)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Atoms and Radioactivity

Rotational Dynamics

Work Energy and Power

Modern Physics

Astrophysics

Study anywhere. Anytime. Across all devices.

A 1.0kgblock is attached to a spring with spring constant 16N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives its a speed of 40cm/s.What area. The amplitude of the subsequent oscillations?b. The block's speed at the point where x=12A?

Short Answer

Step by step solution

Given data.

Simplification.

Using equation (1)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Atoms and Radioactivity

Rotational Dynamics

Work Energy and Power

Modern Physics

Astrophysics

Study anywhere. Anytime. Across all devices.