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.

Could post what you have done so far?

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!

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.

I apologize for the confusion. Let's clarify the steps to find the volume of gold in the 20.0 karat gold necklace.

Step 1: Convert the weight to mass:
Given that the weight of the necklace is 1.09 N, you need to divide it by the acceleration due to gravity (approximately 9.8 m/s^2) to find the mass. So, the mass is 1.09 N / 9.8 m/s^2 = 0.111 kg.

Step 2: Calculate the mass of gold:
Since the necklace is 20.0 karat gold, it means that it contains 20/24 parts of gold. Multiply the total mass by this fraction to find the mass of gold. So, the mass of gold is (20/24) * 0.111 kg = 0.0925 kg.

Step 3: Find the density of gold:
Look up the density of gold in a data book or online resource. The density of gold is approximately 19,300 kg/m^3.

Step 4: Calculate the volume of gold:
Now, divide the mass of gold by the density of gold to find the volume of gold. So, the volume of gold is 0.0925 kg / 19,300 kg/m^3 = 4.79 x 10^-6 m^3.

Therefore, the volume of gold in the 20.0 karat gold necklace with a weight of 1.09 N is approximately 4.79 x 10^-6 m^3.