Your friend of mass 80 kg can just barely float in freshwater.Calculate her approximate volume.
For floating the buoyancy force F has to be equal to m•g
F = M•g = D•V•g, where D is the density of water.
Then m•g = D•V•g
V=m/D=80/1000 = 0.08 m^3
mkm
Why did the clown take measurements? Because she wanted to water-log her friend! But fear not, my friend, I'll still help you with the calculation. Assuming that the density of freshwater is approximately 1000 kg/m³, we can use the formula for density to find the volume. Let's get started:
Density = Mass / Volume
Rearranging the formula to solve for volume:
Volume = Mass / Density
Plugging in the given values:
Volume ≈ 80 kg / 1000 kg/m³
Volume ≈ 0.08 m³
So, your friend's approximate volume would be approximately 0.08 cubic meters. Just make sure she doesn't get too water-logged!
To calculate the approximate volume of your friend, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the displaced fluid.
Since your friend can just barely float in freshwater, the buoyant force on her must be equal to her weight. Therefore, the weight of the water displaced by her body is equal to her weight.
The density of fresh water is approximately 1000 kg/m^3.
The weight of your friend is given as 80 kg.
We can use the formula for weight, W = m * g, where m is the mass of an object and g is the acceleration due to gravity.
Given that g is approximately 9.8 m/s^2, the weight of your friend is W = 80 kg * 9.8 m/s^2 = 784 N.
Since the weight of the water displaced by your friend is equal to her weight, we have:
Weight of water displaced = 784 N.
The weight of water displaced can also be calculated as the density of water * volume of water displaced * g.
Using this equation, we have:
Density of water = 1000 kg/m^3 and g = 9.8 m/s^2.
Therefore, 1000 kg/m^3 * volume of water displaced * 9.8 m/s^2 = 784 N.
Solving for the volume of water displaced gives us:
Volume of water displaced = 784 N / (1000 kg/m^3 * 9.8 m/s^2).
Volume of water displaced = 0.0799 m^3, or approximately 79.9 liters.
Since the volume of your friend's body is roughly equal to the volume of water displaced, her approximate volume is 79.9 liters.
To calculate your friend's approximate volume, we can use the principle of buoyancy.
Buoyancy is the upward force exerted by a fluid (in this case, freshwater) on an object submerged or partially submerged in it.
To float, your friend's weight must be balanced by the buoyant force. Since your friend can just barely float, we can assume that the buoyant force is equal to her weight.
The weight of an object is given by the formula: weight = mass * gravitational acceleration
The buoyant force is given by the formula: buoyant force = density of fluid * volume submerged * gravitational acceleration
Since the density of freshwater is approximately 1000 kg/m^3 and the gravitational acceleration is approximately 9.8 m/s^2, we can equate the weight and buoyant force equations:
mass * gravitational acceleration = density of fluid * volume submerged * gravitational acceleration
Simplifying the equation:
mass = density of fluid * volume submerged
Now we can rearrange the equation to solve for the volume submerged:
volume submerged = mass / density of fluid
Using your friend's mass of 80 kg and the density of freshwater of 1000 kg/m^3:
volume submerged = 80 kg / 1000 kg/m^3
Calculating the volume submerged:
volume submerged = 0.08 m^3
Since your friend is floating, only a portion of her body is submerged. We assume that the volume submerged is equal to her approximate volume. Therefore, your friend's approximate volume is 0.08 m^3.