The "karat" is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of gold in a 20.0 karat gold necklace whose weight is 1.09 N?
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Physics - DrRuss, Friday, April 6, 2007 at 1:24am
The sequence here is..
The implication in the question is to find out how much of the weight is gold, so do this using the fraction given.
Convert the weight to mass using F=ma and I would use a=9.8 m s^-2 unless your question/text book has a different value.
Now convert the mass to volume using density=mass/volume. The density of gold you will need to get from a data book, wikipedia, or maybe it is in the question/text book.
Please clarify this explanation.
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Physics, still don't get it! - DrRuss, Monday, April 9, 2007 at 1:07am
Could post what you have done so far?
Physics, still don't get it! - Mary, Monday, April 9, 2007 at 2:22am
F = ma
F/a = m
20.0/ 9.81 = 2.0387
density = mass/volume
volume = mass / 19300
volume = 0.0001056
This answer is incorrect. I am confused!
Physics, still don't get it! - bobpursley, Monday, April 9, 2007 at 6:24am
in your
mass=weight/g you put 20 for weight, That is not correct, it was given as about one newton.
Correct that, then 20/24 of that mass is gold.
Take the mass of gold, divide by the density of gold (look it up), and you have volume of gold.
IS MY WORKING OUT NOW CORRECT?
F = ma
F/a = m
(20.0/24.0 x 1.09N)/ 9.81 = 0.0926
density = mass/volume
volume = 0.0926/ 19300
volume = 0.000004798
You need to write the units as well as the numbers. 0.0926 kg is the mass of the gold
Divide that by the density for the volume. You did that. The answer you gave is in cubic meters. It equals 4.8 cubic centimeters
.
Yes, your working out is now correct.
To find the volume of gold in a 20.0 karat gold necklace, you need to follow these steps:
1. Start by converting the weight of the necklace from Newtons to kilograms. Since weight is related to mass through the formula F = ma, where F is the weight, m is the mass, and a is the acceleration due to gravity (approximately 9.8 m/s^2), you can rearrange the formula to solve for mass: m = F/a.
So, m = 1.09 N / 9.8 m/s^2 = 0.111 kg (rounded to three decimal places).
2. Next, you need to calculate the mass of the gold in the necklace. 20.0 karat gold means that it contains 20 parts of gold out of a total of 24 parts. So, the mass of gold is 20/24 times the total mass of the necklace.
Mass of gold = (20/24) x 0.111 kg = 0.0926 kg (rounded to four decimal places).
3. Now comes the crucial step of finding the volume of gold. Use the formula density = mass/volume to calculate the volume. The density of gold is a constant that you can look up in a data book or online resource, but let's assume it's 19,300 kg/m^3.
density = mass/volume
Rearranging the formula to solve for volume: volume = mass/density
volume = 0.0926 kg / 19,300 kg/m^3 = 0.000004798 m^3
4. Finally, remember to convert the volume from cubic meters to a more practical unit like cubic centimeters. To do this, multiply the volume by 1,000,000 (since there are one million cubic centimeters in a cubic meter).
volume = 0.000004798 m^3 x 1,000,000 = 4.798 cubic centimeters
So, the volume of gold in the 20.0 karat gold necklace is approximately 4.798 cubic centimeters.