Physics, 17.09.2019 19:20 abelxoconda

Red gold is a gold‑copper alloy used to make jewelry. a piece of jewelry made of red gold weighs 7.24 g and has a volume of 0.436 cm3 . gold has a density of 19.3 g/cm^3 and copper has a density of 8.96 g/cm^3 . calculate the percentage by mass of each metal in the jewelry. assume the total volume of the jewelry is the sum of the volumes of the two metals it contains.

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Answer from: unicornturd

%cu = 13.95%

%au=86.05%

Explanation:

Since the total volume is the sum of both volumes (gold, copper) we can say:

$V_{T} = V_{AU} + V_{CU}$

We know that $V_{AU} = \frac{m_{AU}}{\rho_{AU}}$ and $V_{CU} = \frac{m_{CU}}{\rho_{CU}}$ . Replacing these values into our volume equation:

$V_{T} = \frac{m_{AU}}{\rho_{AU}} + \frac{m_{CU}}{\rho_{CU}}$

We also know that: $m_{T}=m_{AU}+m_{CU}$

Solving this equation system:

$\left \{ {{V_{T} = \frac{m_{AU}}{\rho_{AU}} + \frac{m_{CU}}{\rho_{CU}}} \atop {m_{T}=m_{AU}+m_{CU}}} \right.$

$m_{CU}=1.01g = 13.95%$

$m_{AU}=6.23g = 85.94%$

Answer from: gabypinskyb7364

Percentage by mass of Gold is about 86%

Percentage by mass of Copper is about 14%

$\texttt{ }$

Further explanation

Let's recall Density formula as follows:

$\boxed {\rho = m \div V}$

where:

ρ = density of object ( kg/m³ )

m = mass of object ( kg )

V = volume of object ( m³ )

Let us now tackle the problem!

$\texttt{ }$

Given:

total mass of jewelry = m = 7.24 g

total volume of jewelry = V = 0.436 cm³

density of gold = ρ_g = 19.3 g/cm³

density of copper = ρ_c = 8.96 g/cm³

Asked:

percentage by mass of gold = m_g = ?

percentage by mass of copper = m_c = ?

Solution:

$\texttt{Total Volume = Volume of Gold + Volume of Copper}$

V = V_g + V_c

$\frac{m}{ \rho} = \frac{m_g}{ \rho_g} + \frac{m_c}{\rho_c}$

$\frac{m_g + m_c}{ \rho} = \frac{m_g}{ \rho_g} + \frac{m_c}{\rho_c}$

$\frac{m_g}{\rho} + \frac{m_c}{\rho} = \frac{m_g}{ \rho_g} + \frac{m_c}{\rho_c}$

$\frac{m_g}{\rho} - \frac{m_g}{ \rho_g} = \frac{m_c}{\rho_c} - \frac{m_c}{\rho}$

$m_g ( \frac{1}{\rho} - \frac{1}{\rho_g}) = m_c ( \frac{1}{\rho_c} - \frac{1}{\rho})$

$m_g ( \frac{ \rho_g - \rho}{ \rho\ \rho_g} ) = m_c ( \frac{ \rho - \rho_c} { \rho\ \rho_c} )$

$\frac{m_g}{m_c} = \frac{\rho_g}{\rho_c}\ \frac{\rho - \rho_c}{ \rho_g - \rho}$

$\frac{m_g}{m_c} = \frac{19.3}{8.96}\ \frac{ \frac{7.24}{0.436} - 8.96}{ 19.3 - \frac{ 7.24}{0.436} }$

$\frac{m_g}{m_c} = 6.112$

$\boxed {m_g = 6.112 m_c}$

$\texttt{ }$

$\texttt{Percentage by mass of Gold} = \frac{m_g}{m_g + m_c} \times 100\%$

$\texttt{Percentage by mass of Gold} = \frac{6.112m_c}{6.112m_c + m_c} \times 100\%$

$\texttt{Percentage by mass of Gold} = \frac{6.112}{6.112 + 1} \times 100\%$

$\texttt{Percentage by mass of Gold} = \frac{6.112}{7.112} \times 100\%$

$\texttt{Percentage by mass of Gold} \approx 86 \%$

$\texttt{Percentage by mass of Copper} \approx 100\% - 86 \% \approx 14 \%$

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Learn moreVelocity of Runner : Kinetic Energy : Acceleration : The Speed of Car : Average Speed of Plane : Impulse : Gravity :

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Answer details

Grade: High School

Subject: Physics

Chapter: Physical Quantities

Red gold is a gold‑copper alloy used to make jewelry. a piece of jewelry made of red gold weighs 7.2

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

i need with 1.3.2 investigate cycling o2 and co2 apex

we need to see it

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Red gold is a gold‑copper alloy used to make jewelry. a piece of jewelry made of red gold weighs 7.2...