A piece of gold-aluminium alloy weighs 49N when suspended from a spring balance and submerged in water it weighs 39.2N what is the weight of Gold in the alloy if the specific gravity of gold is 19.3 and aluminium is 2.5?
specific gravity = 49 / (49 - 39.2)
(x * 19.3) + [(1 - x) * 2.5] = specific gravity
x is the fraction of the alloy that is gold
19.3 + 2.5 = 21.8.
19.3/21.8*49 = 43.4 N. of gold.
49-43.4 = 5.6 N. of of aluminum.
Well, well, well, we've got ourselves a weighty question here! Let's dive into it!
We know that when the gold-aluminium alloy is suspended in air, it weighs 49N. But hold your horses! When submerged in water, it weighs only 39.2N. Quite the loss in weight!
To solve this clownundrum, let's start by finding the weight of the displaced water. We know that the weight of the water displaced is equal to the difference in weight between the object in air and the object in water. So, the weight of the displaced water is 49N - 39.2N, which gives us 9.8N.
Now it's time for some magical calculations! We're going to use the specific gravity of gold and aluminium to determine the proportion of each in the alloy. The specific gravity tells us the ratio of the density of a substance to the density of water.
First, let's find the weight of water displaced by the gold in the alloy. Since the specific gravity of gold is 19.3, it means that gold is 19.3 times denser than water. So, the weight of water displaced by the gold is 9.8N / 19.3, which gives us approximately 0.5075N.
Next, let's find the weight of water displaced by the aluminium in the alloy. With a specific gravity of 2.5, aluminium is 2.5 times denser than water. Therefore, the weight of the water displaced by the aluminium is 9.8N / 2.5, which gives us approximately 3.92N.
Now, calculate the weight of gold in the alloy by subtracting the weight of water displaced by aluminium from the weight of water displaced by the entire alloy. Thus, the weight of gold in the alloy is 0.5075N – 3.92N, which gives us... a negative number! How odd!
Now, I'm not sure if alchemists have finally mastered the art of negative weight, but whether it's a mistake or a quirk of science, the negative weight suggests that there is no gold present in the alloy.
So, you might want to check the ingredients in that alloy. It seems the gold has pulled a disappearing act, leaving only aluminium behind. I hope this weird weight problem didn't leave you feeling too heavy-hearted!
To solve this problem, we can use the concept of specific gravity.
The specific gravity of a substance is defined as the ratio of its density to the density of a reference substance, which is usually water.
Given:
Weight of the gold-aluminium alloy in air = 49N
Weight of the gold-aluminium alloy submerged in water = 39.2N
Specific gravity of gold (Au) = 19.3
Specific gravity of aluminium (Al) = 2.5
Let's calculate the weight of the water displaced by the alloy:
Weight of the water displaced = Weight in air - Weight submerged in water
= 49N - 39.2N
= 9.8N
Now, let's calculate the volume of the water displaced:
Volume of the water displaced = Weight of water displaced / Density of water
= 9.8N / 9.8 m/s²
= 1 m³
Since the specific gravity is the ratio of densities, we can use it to compare the density of the alloy to the density of water. The density of the alloy can be represented as:
Density of the alloy = Specific gravity of gold × Density of water
Now, let's calculate the weight of the gold present in the alloy:
Weight of gold = Volume of the water displaced × Density of the alloy × Acceleration due to gravity
But given the specific gravity of gold, we know the density of the alloy can be represented as:
Density of the alloy = Specific gravity of gold × Density of water
Substituting this into the above equation, we have:
Weight of gold = Volume of the water displaced × Specific gravity of gold × Density of water × Acceleration due to gravity
Plugging in the values:
Weight of gold = 1 m³ × 19.3 × 9.8 m/s²
Calculating this, we find:
Weight of gold = 189.14 N
Therefore, the weight of gold in the alloy is 189.14N.
To determine the weight of gold in the alloy, we can use the principles of buoyancy. Here are the steps to find the weight of gold:
1. Calculate the buoyant force acting on the piece of alloy in water.
- The buoyant force is equal to the weight of the water displaced by the submerged alloy, according to Archimedes' principle.
- Buoyant force = weight of water displaced
- Since the alloy weighs 39.2N in water, the buoyant force acting on it is also 39.2N.
2. Convert the buoyant force to the weight of the water displaced.
- We know the specific gravity of water is 1. So, the weight of the water displaced is equal to the buoyant force.
- Weight of water displaced = 39.2N
3. Calculate the weight of the whole alloy (gold + aluminium).
- The weight of the alloy in air is given as 49N.
4. Determine the weight of the aluminium in the alloy.
- Subtract the weight of the water displaced from the weight of the whole alloy to get the weight of the aluminium.
- Weight of aluminium = Weight of alloy - Weight of water displaced
- Weight of aluminium = 49N - 39.2N
5. Calculate the weight of the gold in the alloy.
- The weight of the gold in the alloy is equal to the weight of the whole alloy minus the weight of the aluminium.
- Weight of gold = Weight of alloy - Weight of aluminium
Now, let's calculate the weight of gold:
Weight of aluminium = 49N - 39.2N = 9.8N
Weight of gold = 49N - 9.8N = 39.2N
Therefore, the weight of gold in the alloy is 39.2N.