A sample of an unknown material appears to weigh 295 N in air and 165 N when immersed in alcohol of specific gravity 0.700.

(a) What is the volume of the material?
___________m^3

(b) What is the density of the material?
____________ kg/m3

I am getting the wrong answer. Can you please check my work? My answer is off by a multiple of ten.

This is what I have so far. My answer is wrong, it is off by a multiple of 10

295N-165N=130N

F=pVg
130N=(.700)V(9.8m/s^2)
V=18.93

F=mg
295N=m(9.8)
m=30.10kg

pV=m
p(18.93)=30.10
p=1.59kg/m^3

You have to divide the volume by 1000

Oh, dear! It looks like someone needs a little help from the Clown Bot! Let's see if we can figure this out together, shall we?

To solve this problem, we need to use Archimedes' principle. The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Given:
Weight of the object in air = 295 N
Weight of the object in alcohol = 165 N
Specific gravity of alcohol = 0.700

(a) To find the volume of the material, we first need to find the weight of the alcohol displaced by the object.
Weight of the displaced alcohol = Weight in air - Weight in alcohol
Weight of the displaced alcohol = 295 N - 165 N = 130 N

Now, we can use the equation: Weight of displaced fluid = density of fluid × volume of fluid × gravitational acceleration

Density of alcohol = Specific gravity × density of water
Density of water = 1000 kg/m^3 (approximately)

Therefore, density of alcohol = 0.700 × 1000 kg/m^3 = 700 kg/m^3

Plugging in the values, we have:
Weight of displaced alcohol = 700 kg/m^3 × volume of alcohol × 9.8 m/s^2

Solving for the volume of alcohol:
Volume of alcohol = Weight of displaced alcohol / (density of alcohol × gravitational acceleration)
Volume of alcohol = 130 N / (700 kg/m^3 × 9.8 m/s^2)

(Bear with me while I calculate this...)

*drumroll please*

(cue the circus music)

Voila! The volume of the material is approximately _______ m^3.

(b) To find the density of the material, we can use the equation:
Density of the material = Mass of the material / Volume of the material

To find the mass of the material, we need to use the weight of the material and the acceleration due to gravity. Given that Weight = Mass × Gravity, we can rearrange the equation to find Mass:
Mass = Weight / Gravity

So, the Mass of the material = 295 N / 9.8 m/s^2

Finally, we can calculate the density of the material:
Density of the material = Mass of the material / Volume of the material

And now, drumroll once again, please!

The density of the mysterious material is approximately _______ kg/m^3.

Remember, if your answer is off by a multiple of ten, it's usually a unit conversion error. So double-check your units and calculations. If you're still stuck, feel free to ask for more clown-tastic assistance!

Let's work through the problem step by step.

(a) The weight of the material in air is given as 295 N, and the weight when immersed in alcohol is 165 N. To find the volume of the material, we can use Archimedes' principle, which states that the weight loss of an object immersed in a fluid is equal to the weight of the displaced fluid.

The weight loss of the material is given by:
Weight in air - Weight in alcohol = 295 N - 165 N = 130 N

To find the volume, we need to convert the weight loss to mass by dividing by the acceleration due to gravity (g). The average value for g is approximately 9.8 m/s^2. So, the mass of the material can be calculated as:
Mass = Weight loss / g = 130 N / 9.8 m/s^2

Let's calculate the mass first:
130 N / 9.8 m/s^2 = 13.27 kg

Next, we need to determine the density of the alcohol. The specific gravity of alcohol is given as 0.700, which means it is 0.7 times as dense as water. The density of water is approximately 1000 kg/m^3. So, the density of the alcohol can be calculated as:
Density of alcohol = Specific gravity x Density of water = 0.700 x 1000 kg/m^3 = 700 kg/m^3

Now, we can find the volume using the formula:
Volume = Mass / Density = 13.27 kg / 700 kg/m^3

Let's calculate the volume:
Volume = 0.01896 m^3

Therefore, the volume of the material is approximately 0.01896 m^3.

(b) To find the density of the material, we can use the formula:
Density = Mass / Volume = 13.27 kg / 0.01896 m^3

Let's calculate the density:
Density = 699.372 kg/m^3

Therefore, the density of the material is approximately 699.372 kg/m^3.

Please verify if these calculations match your answer.

To find the volume and density of the unknown material, we can use the concept of buoyancy.

(a) To find the volume of the material, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

In this case, we need to consider the weight of the material in air and when submerged in alcohol. The weight in air is given as 295 N, which is equal to the weight of the material. The weight when immersed in alcohol is given as 165 N.

The buoyant force when immersed in alcohol can be calculated as the difference between the weight in air and the weight in alcohol:
Buoyant force = Weight in air - Weight in alcohol
Buoyant force = 295 N - 165 N
Buoyant force = 130 N

Now, the buoyant force is equal to the weight of the alcohol displaced by the material. The weight of the displaced alcohol can be calculated using its density and volume:
Weight of displaced alcohol = Density of alcohol * Volume of displaced alcohol

The specific gravity of the alcohol is given as 0.700, which is the ratio of the density of alcohol to the density of water. Since the density of water is 1000 kg/m^3, we can calculate the density of alcohol as follows:
Density of alcohol = Specific gravity * Density of water
Density of alcohol = 0.700 * 1000 kg/m^3
Density of alcohol = 700 kg/m^3

Now, we know the density of alcohol and the weight of the displaced alcohol (which is equal to the buoyant force). We can rearrange the equation for the weight of displaced alcohol to solve for the volume:
Volume of displaced alcohol = Weight of displaced alcohol / Density of alcohol
Volume of displaced alcohol = 130 N / 700 kg/m^3
Volume of displaced alcohol ≈ 0.186 m^3

Since the volume of the material is equal to the volume of the displaced alcohol, the volume of the material is also approximately 0.186 m^3.

(b) The density of the material can be calculated using the formula:
Density = Mass / Volume

We know the volume of the material is approximately 0.186 m^3. To find the mass, we can use the weight in air and divide it by the acceleration due to gravity (g ≈ 9.8 m/s^2) to get the mass:
Mass = Weight in air / g
Mass = 295 N / 9.8 m/s^2
Mass ≈ 30 kg

Now, we can calculate the density using the mass and volume:
Density = Mass / Volume
Density = 30 kg / 0.186 m^3
Density ≈ 161 kg/m^3

So, the density of the material is approximately 161 kg/m^3.

If your answer is off by a multiple of ten, it suggests that there might have been an error in the conversion of units. Double-check your calculations and make sure you're using the correct units consistently throughout the calculations.