A foam plastic of density of 0.58g/cm^3 is to be used as a life jacket.What volume of the plastic must be used if it is to keep 20percent by volume of an 80kg physics student above water in a lake if the average density of the student is 1.04g/cm^3
first calculate the buoyancy of 80% of a physics student.
Mass of student = 80 kg
density of student = 1040 kg/m^3
volume of student = 80/1040 = .0769 m^3
buoyancy of 80% of student = 1000 g .8 .0769
= 61.54 g Newtons
so we need a force of 80 g - 61.54 g Newtons up from the foam
that is 18.46 g Newtons up
Volume of plastic = v
weight of plastic = 580 g v
buoyancy of plastic = 1000 g v
up force from plastic = 420 g v Newtons
so
420 g v = 18.46 g
v = 18.46/420 = .044 m^3
Where does the 1000g come from?
Well, that's quite a puzzling question! Let me put on my thinking cap, or should I say, my clown wig?
To find the volume of foam plastic needed, we need to consider two things: the volume of the student and the required volume of foam plastic to keep them afloat.
First, let's find the volume of the student. We know that the average density of the student is 1.04 g/cm^3. Since density is defined as mass divided by volume, we can rearrange the formula to solve for volume. So, volume = mass/density.
The mass of the student is given as 80 kg, which is equivalent to 80,000 g. Plugging in these values, we get volume = 80,000 g / 1.04 g/cm^3 = 76,923 cm^3 (approximately).
Now, to find the volume of foam plastic needed to keep 20% of the student's volume above water, we multiply the volume of the student by 20% (or 0.2). So, volume of foam plastic = 76,923 cm^3 * 0.2 = 15,384.6 cm^3 (approximately).
Therefore, approximately 15,384.6 cm^3 of foam plastic must be used as a life jacket to keep the physics student afloat. Just remember, no clowns allowed on the life jacket!
To calculate the volume of foam plastic required for the life jacket, we need to determine the volume of the student that needs to be kept above water and then calculate the total volume of foam plastic.
Step 1: Calculate the volume of the student
Given that the student's density is 1.04g/cm^3, and the student's mass is 80kg, we can use the formula:
density = mass/volume
Rearranging the formula to solve for volume:
volume = mass/density
volume = 80kg / 1.04g/cm^3
Note: We need to convert the student's mass from kg to g to match the density unit.
volume = 80,000g / 1.04g/cm^3
volume ≈ 76,923.08 cm^3
Step 2: Calculate the volume of foam plastic needed to keep 20% by volume of the student above water
We know that the foam plastic has a density of 0.58g/cm^3, and we want it to keep 20% of the student's volume above water. So, we can calculate the volume of foam plastic as:
volume of foam plastic = (20/100) * volume of the student
volume of foam plastic = 0.2 * 76,923.08 cm^3
volume of foam plastic ≈ 15,384.62 cm^3
Therefore, approximately 15,384.62 cm^3 of foam plastic must be used to keep 20% of the student's volume above water.
To determine the volume of foam plastic required to keep 20% by volume of an 80kg physics student above water, we need to consider the average density of the student and the density of the foam plastic.
Given:
Density of foam plastic = 0.58 g/cm^3
Density of the student = 1.04 g/cm^3
Mass of the student = 80 kg
Percentage volume to be kept above water = 20%
To find the volume of foam plastic needed, we can follow these steps:
1. Calculate the volume of the student above water:
Mass of the student = Density * Volume
Volume of the student = Mass of the student / Density of the student
Given that the density of the student is 1.04 g/cm^3 and the mass of the student is 80 kg, we need to convert the mass of the student from kg to g:
Mass of the student in g = 80 kg * 1000 g/kg = 80000 g
Now, we can calculate the volume of the student above water:
Volume of the student above water = Mass of the student / Density of the student
Volume of the student above water = 80000 g / 1.04 g/cm^3
2. Calculate the total volume of the life jacket:
The total volume of the life jacket needed will be the volume of the student above water divided by the desired volume percentage of the foam plastic.
Total volume of the life jacket = Volume of the student above water / (Percentage volume of foam plastic / 100)
Total volume of the life jacket = (80000 g / 1.04 g/cm^3) / (20 / 100)
3. Calculate the volume of the foam plastic needed:
The volume of the foam plastic needed will be a percentage of the total volume of the life jacket, based on the density of the foam plastic.
Volume of the foam plastic needed = Total volume of the life jacket * (Density of the foam plastic / Density of the student)
Volume of the foam plastic needed = Total volume of the life jacket * (0.58 g/cm^3 / 1.04 g/cm^3)
Now you can plug in the values and perform the calculations to find the volume of the foam plastic needed to keep 20% by volume of the student above water.