Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A spring is hanging down from the ceiling, and an object of mass $m$ is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up anddown, and the time $T$ required for one complete up-and-down oscillation is given by the equation $T=2 \pi \sqrt{m / k},$ where $k$ is known as the spring constant. What must be the dimension of $k$ for this equation to be dimensionally correct?

$K=\frac{M}{T^{2}}$

Physics 101 Mechanics

Chapter 1

Introduction and Mathematical Concepts

Physics Basics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Lectures

04:16

In mathematics, a proof is…

09:56

In mathematics, algebra is…

01:56

The time T required for on…

05:08

An 8-kg mass is attached t…

01:36

An object of unknown mass …

02:24

A mass oscillates at the e…

02:05

(II) An object of unknown …

02:30

The formula for the up-and…

The formula for the up and…

01:11

Mass-Spring System The fre…

00:48

Refer to the following:

08:14

A force of $3 \mathrm{N}$ …

01:22

refer to the following:

0:00

[T] A mass hanging from a …

01:41

A spring with spring const…

02:13

Show that the period of th…

25:07

A mass of $0.1 \mathrm{kg}…

05:50

A 2 -kg mass is attached t…

Mass-Spring System A mass …

04:45

Conservation of Energy can…

00:39

Spring-Mass System A mass …

Hello, students, and welcome back. So today we have a problem Where there is a Here's the ceiling and they're just bringing touched with the mess attached to that. All right, so there's our mess, all right. And the equation that's gonna show us where it's going to know how long it's gonna take for one oscillation, right? One, um, cycle of it going up and down is given by t this equal to two by times square root of em over K, where t is the period or the time that it takes 2 to 1 full oscillation to prize a dimension Wisconsin dimension. This constant m is mass and K is called the spring constant. All right, so we're trying to find the dimensions of key so that, uh, this equation makes sense. So they're mentions of time are just time. You know what in brackets? Because it's a dimension two pies. That is a dimension this constant that just makes this equation workout. So we're, uh, not gonna be using that for this problem. To find the dimensions of case, since it is to mention this mess because Dimension and kids what we're trying to find all right, So we can start to bring some underway here to solve four K. We're gonna square both sides to get rid of this square root sign We got t squared is equal T o mm Over K. And then we can, um what we can do is weaken. Want to play both sides by K and then divide both sides by t squared. I'm gonna do this 11 Steptoe kind of saves. I guess I can do it in two steps. Just, uh uh, we have time and space on the board here. So why not? So then what? What by both sides by K. All right. And, uh, they're solving for K right here. We're gonna all right it off to the right hand side here. We're gonna k is equal. Mm. Divided by t squared. All right. And there you have it. The order. The dimensions for Kay. Look, that was helpful. And good luck on the rest of your homework.

View More Answers From This Book

Find Another Textbook

University of Sheffield

University of Winnipeg

In mathematics, a proof is a sequence of statements given to explain how a c…

In mathematics, algebra is one of the broad parts of mathematics, together w…

04:27

Before attempting this problem, review Examples 7 and 8. Two curves on a hig…

02:40

A raindrop has a mass of $5.2 \times 10^{-7} \mathrm{kg}$ and is falling nea…

03:24

The drawing shows a plane diving toward the ground and then climbing back up…

02:07

At some airports there are speed ramps to help passengers get from one place…

03:48

The drawing shows a baggage carousel at an airport. Your suitcase has not sl…

04:32

A model rocket blasts off from the ground, rising straight upward with a con…

02:35

A football player, starting from rest at the line of scrimmage, accelerates …

07:27

ssm A cannon of mass $5.80 \times 10^{3} \mathrm{kg} \times 10^{3} \mathrm{k…

03:26

A centrifuge is a device in which a small container of material is rotated a…

03:34

mmh A stream of water strikes a stationary turbine blade horizon- tally, as …