Hello. My teacher gave us a worksheet today she tried to explain it but I still don't understand it can someone help me please?
1) A jar is filled with mercury and has a volume of 500.mL. What is the mass of mercury in the jar? Show your work for credit.
2) GE's light bulb division ordered 100.kg of tungsten for the filaments. If the tungsten comes in a cube what is the volume of the cube? What is the length of each side?Show your work for credit.
3) A graduated cylinder has 25.0mL of water in it before an aluminum cube with the mass of 10.0g is added to it. What is the new level of water in the cylinder?Show your work for credit.
4) There are two cubes (one gold and one copper) with the same volume. The mass of the copper is 55.0g. What is the mass of the gold cube.Show your work for credit.
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Of course, I'm here to help you understand these questions and show you the steps to solve them. Let's go through each question one by one:
1) To find the mass of mercury in the jar, we need to know the density of mercury. The density of a substance is the mass of the substance per unit volume. In this case, we'll need the density of mercury, which is approximately 13.6 grams per milliliter (g/mL).
Now, we can multiply the volume of the jar by the density of mercury to find the mass. The volume of the jar is given as 500 mL. So the calculation would be:
Mass = Volume x Density
Mass = 500 mL x 13.6 g/mL
Mass = 6800 grams
Therefore, the mass of mercury in the jar is 6800 grams.
2) We are given that the light bulb division ordered 100 kg of tungsten, and we need to find the volume of the cube and the length of each side.
First, we need to convert the mass from kilograms to grams. Since there are 1000 grams in a kilogram, we multiply 100 kg by 1000 g/kg to find the mass in grams:
Mass = 100 kg x 1000 g/kg
Mass = 100,000 grams
Now, we need to find the volume of the cube. Since the density of tungsten is not given, we can't directly calculate the volume. However, if we assume that the density of tungsten is constant (which is a reasonable assumption for most solids), we can use the relationship:
Density = Mass / Volume
Since we have the mass (100,000 grams) and we want to find the volume, we can rearrange the equation:
Volume = Mass / Density
The density of tungsten is approximately 19.3 g/mL. Let's use this value to calculate the volume of the cube:
Volume = 100,000 grams / 19.3 g/mL
Volume ≈ 5181.34 mL
To find the length of each side of the cube, we need to find the cube root of the volume. Let's calculate it:
Length of each side = cube root of the volume
Length of each side = cube root of 5181.34 mL
Length of each side ≈ 17.6 mL
Therefore, the volume of the cube is approximately 5181.34 mL, and the length of each side is approximately 17.6 mL.
3) We are given that a graduated cylinder has 25.0 mL of water in it before adding an aluminum cube with a mass of 10.0 grams. We need to find the new level of water in the cylinder.
When the aluminum cube is added to the graduated cylinder, its volume displaces an equal volume of water. Therefore, the new level of water will be equal to the initial volume of water plus the volume of the aluminum cube.
However, the volume of the aluminum cube is not given. So we can use the same concept we used in question 2: assume the density is constant and calculate the volume from the mass.
The density of aluminum is approximately 2.7 g/mL. Let's calculate the volume of the aluminum cube first:
Volume = Mass / Density
Volume = 10.0 grams / 2.7 g/mL
Volume ≈ 3.70 mL
Now, we can find the new level of water by adding the initial level of water (25.0 mL) and the volume of the aluminum cube (3.70 mL):
New level of water = Initial level of water + Volume of aluminum cube
New level of water = 25.0 mL + 3.70 mL
New level of water ≈ 28.70 mL
Therefore, the new level of water in the cylinder is approximately 28.70 mL.
4) We are given that two cubes (one gold and one copper) have the same volume, and the mass of the copper cube is 55.0 grams. We need to find the mass of the gold cube.
Since the volumes of the two cubes are the same, their densities must be the same as well. The density of a substance is equal to its mass divided by its volume.
We can set up an equation using the density of each cube:
Density of gold = Mass of gold / Volume
Density of copper = Mass of copper / Volume
Since the volumes are the same, we can set the densities equal to each other:
Density of gold = Density of copper
Now, we can rearrange the equation to solve for the mass of gold:
Mass of gold = Density of gold x Volume
Mass of gold = Density of copper x Volume (since densities are equal)
Since the volume is the same for both cubes, we can directly substitute the values:
Mass of gold = 55.0 grams (mass of copper)
Therefore, the mass of the gold cube is also 55.0 grams.
I hope these explanations help you understand how to solve the given problems. If you have any further questions, feel free to ask!