Collectible coins are sometimes plated with gold to enhance their beauty and value. Consider a commemorative quarter-dollar advertised for sale at $4.98. It has a diameter of 24.1 mm and a thickness of 1.78 mm. and it is completely covered with a layer of pure gold 0.180 µm thick. The volume of the plating is equal to the thickness of the layer multiplied by the area to which it is applied. The patterns on the faces of the coin and the grooves on its edge have a negligible effect on its area. Assume the price of gold is $25.0 per gram, (a) Find the cost of the gold added to the coin, (b) Does the cost of the gold significantly enhance the value of the coin? Explain your answer.
(a)
The cost of gold added to the coin.
Answer to Problem 1.54AP
The cost of gold added to the coin is
Explanation of Solution
Given info: The thickness of the coin is
Write the expression for total surface area of the coin,
Here,
Formula to calculate the area of curved surface of the coin is,
Here,
Formula to calculate the area of faces of the coin is,
Substitute
Substitute
Thus, the total surface area is
Write the expression for volume of the gold plating,
Here,
Substitute
Thus, the volume of gold plating is
Formula to calculate the mass of the gold used for plating is,
The density of the gold is
Substitute
Thus, the mass of gold plating on the coin is
Write the expression to calculate the cost of gold added to the coin,
Substitute
Conclusion:
Therefore, the cost of gold added to the coin is
(b)
The percentage the cost of the gold significantly enhance the value of the coin.
Answer to Problem 1.54AP
The cost of gold significantly enhances the value of the cost of coin by
Explanation of Solution
Given info: The thickness of the coin is
From the part (a), the cost of gold added to the coin is
The value of the coin is quarter dollar
Write the expression for enhance value,
Substitute
Conclusion:
Therefore, the cost of gold significantly enhances the value of the cost of coin by
Want to see more full solutions like this?
Chapter 1 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Additional Science Textbook Solutions
Biology: Life on Earth (11th Edition)
General, Organic, and Biological Chemistry - 4th edition
Fundamentals Of Thermodynamics
Organic Chemistry
- In a scene from The Avengers (the first one) Black Widow is boosted directly upwards by Captain America, where she then grabs on to a Chitauri speeder that is 15.0 feet above her and hangs on. She is in the air for 1.04 s. A) With what initial velocity was Black Widow launched? 1 m = 3.28 ft B) What was Black Widow’s velocity just before she grabbed the speeder? Assume upwards is the positive direction.arrow_forwardIn Dark Souls 3 you can kill the Ancient Wyvern by dropping on its head from above it. Let’s say you jump off the ledge with an initial velocity of 3.86 mph and spend 1.72 s in the air before hitting the wyvern’s head. Assume the gravity is the same as that of Earth and upwards is the positive direction. Also, 1 mile = 1609 m. A) How high up is the the ledge you jumped from as measured from the wyvern’s head? B) What is your velocity when you hit the wyvern?arrow_forwardA) If Yoshi flings himself downwards at 9.76 miles per hour to hit an enemy 10.5 m below him, how fast is Yoshi traveling when he hits the enemy? 1 mile = 1609 marrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage Learning