Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 75

The U.S. quarter has a mass of 5.67 \(\mathrm{g}\) and is approximately 1.55 \(\mathrm{mm}\) thick. (a) How many quarters would have to be stacked to reach 575 \(\mathrm{ft}\) , the height of the Washington Monument? (b) How much would this stack weigh? (c) How much money would this stack contain? (d) The U.S. National Debt Clock showed the outstanding public debt to be \(\$ 16,213,166,914,811\) on October \(28,2012 .\) How many stacks like the one described would be necessary to pay off this debt?

Short Answer

Expert verified
In summary, \(113,039\) quarters are needed to reach the height of the Washington Monument, with the stack weighing approximately \(640.81 kg\) and containing $28,259.75. To pay off the U.S. national debt at that time, approximately \(573,448,261\) stacks of quarters would be necessary.

Step by step solution

01

(a) Finding the number of quarters

First, we need to convert the height of the Washington Monument from feet to millimeters. There are 1 foot = 304.8 millimeters, so: \(575 ft * 304.8 \frac{mm}{ft} = 175260 mm\) Now, we will divide this height by the thickness of a U.S. quarter (1.55mm) to find the number of quarters needed: \(\frac{175260 mm}{1.55 \frac{mm}{quarter}} = 113039 \text{ quarters}\) So, approximately 113,039 quarters would need to be stacked to reach the height of the Washington Monument.
02

(b) Finding the weight of the stack

We have to multiply the mass of a single quarter (5.67g) by the number of quarters in the stack (113,039) to find the total weight of the stack: \(5.67 \frac{g}{quarter} * 113039 \text{ quarters} = 640810.13g\) To make it more understandable, we can convert the weight to kilograms by dividing by 1000: \(\frac{640810.13g}{1000} = 640.81 kg\) So, the stack of quarters would weigh approximately 640.81 kilograms.
03

(c) Finding the total amount of money in the stack

To find the total amount of money in the stack of quarters, we need to multiply the number of quarters (113,039) by the value of a single U.S. quarter (0.25 dollars or 25 cents): \(113039 \text{ quarters} * 0.25 \frac{dollars}{quarter} = 28259.75 dollars\) So, the stack of quarters would contain $28,259.75.
04

(d) Finding the number of stacks needed to pay off the U.S. national debt

To find the number of stacks needed to pay off the U.S. national debt, we would divide the national debt amount (\(16,213,166,914,811) by the total amount of money in a single stack of quarters (\)28,259.75): \(\frac{16213166914811 dollars}{28259.75 \frac{dollars}{stack}} = 573448260.23 \text{ stacks}\) Since we cannot have a partial stack, we will round up to the nearest whole number: \(573,448,261 \text{ stacks}\) Therefore, approximately 573,448,261 stacks of quarters would be necessary to pay off the U.S. national debt at that given time.

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

For each of the following processes, does the potential energy of the object(s) increase or decrease? (a) The distance between two oppositely charged particles is increased. (b) Water is pumped from ground level to the reservoir of a water tower 30 \(\mathrm{m}\) above the ground. (c) The bond in a chlorine molecule, \(\mathrm{Cl}_{2},\) is broken to form two chlorine atoms.

In the year \(2013,\) an estimated amount of 36 billion metrictons ( 1 metric ton \(=1000 \mathrm{kg}\) ) of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) was emitted worldwide due to fossil fuel combustion and cement production. Express this mass of \(\mathrm{CO}_{2}\) in grams without exponential notation, using an appropriate metric prefix.

(a) A sample of tetrachloroethylene, a liquid used in dry cleaning that is being phased out because of its potential to cause cancer, has a mass of 40.55 \(\mathrm{g}\) and a volume of 25.0 \(\mathrm{mL}\) at \(25^{\circ} \mathrm{C}\) . What is its density at this temperature? Will tetrachloroethylene float on water? (Materials that are less dense than water will float.) (b) Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is a gas at room temperature and pressure. However, carbon dioxide can be put under pressure to become a usupercritical fluid" that is a much safer dry-cleaning agent than tetrachlorosthvlene, At a certain pressure, the density of super critical \(\mathrm{CO}_{2}\) is 0.469 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the mass of a 25.0 \(\mathrm{-mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

Carry out the following operations and express the answers with the appropriate number of significant figures. $$ \begin{array}{ll}{\text { (a) } 14.3505+2.65} & {\text { (b) } 952.7-140.7389} \\\ {\text { (c) }\left(3.29 \times 10^{4}\right)(0.2501)} & {\text { (d) } 0.0588 / 0.677}\end{array} $$

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) 25 \(\mathrm{ps}\) (b) \(374.2 \mathrm{mg},\) (c) 77 \(\mathrm{K}\) , (d) \(100,000 \mathrm{km}^{2},\) (e) 1.06\(\mu \mathrm{m}\) ,(f) \(16 \mathrm{nm}^{2},(\mathrm{g})-78^{\circ} \mathrm{C},(\mathbf{h}) 2.56 \mathrm{g} / \mathrm{cm}^{3},(\mathrm{i}) 28 \mathrm{cm}^{3} \cdot[\) Section 1.5\(]\)
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

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