Tricky density and bouyancy question

In summary, to find the density of the metal, you can calculate its mass by using its weight in air and the gravitational acceleration, and then use the formula p=M/V to find its density. To find the density of the unknown liquid, you can use the upthrust principle, where the weight of the liquid displaced is proportional to the upthrust it produces. By calculating the upthrust in both water and the unknown liquid, you can find the volume and then use the formula p=M/V to find the density. It is important to use the correct units for weight and mass in order to get the correct density value.
  • #1
jlin94
4
0

Homework Statement




1. A piece of metal weighs 53.1 N in air, 36.6 N
in water, and 41.7 N in an unknown liquid.
Find the density of the metal.
Answer in units of kg/m3

2 Find the density of the unknown liquid.
Answer in units of kg/m3
2. Homework Equations [/b]

p= M/V

W= mg


The Attempt at a Solution


i have no clue how to do now?
how do i find teh density of the metal and liquid w/out volume?

thanks alot, really appreciate it!
 
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  • #2
Hint: You should know the density of water
 
  • #3
so is this what i should do:

W=mg
m= W/g
m = 36.6/9.8
m = 3.73 kg

then put this in

p= m/v
1000 = m/v
v = m/1000
v = 3.73/1000
v= 0.00373 meter cubed

then mass density of metal is

p = m/v
p = 3.73/0.00373
p = 1001.25 kg/mcubed

how should i find the density of unknown liquid
 
  • #4
The upthrust is proportional to the weight of the liquid displaced. The block is completely submerged so the volume is the same for water and for the liquid.
You can calculate the upthrust in each case.
The upthrust in water is volume of water times density. That allows you to calculate the volume.

This volume produces the other value of upthrust so you can then work out the density because you know everything else you need. (weight of liquid displaced and volume)

You just need to be careful to use weight and mass where appropriate in order to come out with the right value for density.
Logical step by step and believe it will work.
Hint: As a quick reality check, the amount of upthrust from the unknown liquid is less but not a huge amount less so the density answer you get should be similar in proportion to that of water.
 
  • #5


I would first clarify the question and ask for more information. The homework statement is missing important information such as the volume of the metal and the unknown liquid. Without this information, it is impossible to accurately calculate the density of either substance.

Assuming that the volume of the metal is known, we can use the formula p=M/V to calculate its density. The mass of the metal is given as 53.1 N, but we need to convert this to kilograms (kg) by dividing it by the acceleration due to gravity (g=9.8 m/s^2). This gives us a mass of approximately 5.42 kg. We can then divide this by the volume of the metal to get the density in kg/m^3.

For the density of the unknown liquid, we would need to know its mass and volume. However, we can make some assumptions and use the principle of buoyancy to estimate its density. Since the metal weighs more in the unknown liquid compared to water, we can assume that the density of the liquid is greater than that of water (1000 kg/m^3). We can use the formula W=mg to calculate the mass of the liquid, where W is the weight of the metal in the liquid (41.7 N) and g is the acceleration due to gravity (9.8 m/s^2). This gives us a mass of approximately 4.25 kg.

Without knowing the volume of the liquid, we cannot accurately determine its density. However, we can estimate a range of possible densities based on the assumption that the liquid is more dense than water. For example, if we assume a volume of 1 liter (1000 cm^3), the density of the liquid would be approximately 4.25 kg/1000 cm^3 = 4.25 g/cm^3. This is much greater than the density of water, so we can assume that the actual volume of the liquid is less than 1 liter, and therefore the density is greater than 4.25 g/cm^3.

In summary, without knowing the volume of the metal and the unknown liquid, we cannot accurately calculate their densities. However, we can make some assumptions and use the principle of buoyancy to estimate a range of possible densities for the liquid. It is important to always provide all necessary information when solving problems in science, as missing information can lead to inaccurate or impossible solutions.
 

What is density?

Density is a measure of how much mass is contained in a given volume of a substance. It is usually expressed in units of grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3).

How is density calculated?

Density is calculated by dividing the mass of an object by its volume. The equation for density is: density = mass / volume.

What is the relationship between density and buoyancy?

The density of an object determines whether it will float or sink in a fluid. If the density of the object is greater than the density of the fluid, it will sink. If the density of the object is less than the density of the fluid, it will float.

How does temperature affect density?

As temperature increases, the density of most substances decreases. This is because the particles in a substance spread out and take up more space when heated, resulting in a lower density. However, this is not always the case as some substances have a higher density when they are heated.

What is the difference between density and specific gravity?

Density and specific gravity are related but not the same. Density is a measure of the mass of a substance per unit volume, while specific gravity compares the density of a substance to the density of water. Specific gravity has no units and is often expressed as a ratio.

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