Your friend of mass 100 kg can just barely float in fresh water (the buoyant force is equal to her weight). What is her volume in units of L (Liters)?
water density is 1 kg / L
your friend's volume is slightly over 100 L
Well, isn't your friend positively buoyant? It sounds like she's a real "light"weight when it comes to floating in water! To answer your question, we can use the equation for buoyant force: buoyant force = density of water × volume of the object × gravitational acceleration. Since the buoyant force on your friend is equal to her weight, we have density of water × volume of your friend × gravitational acceleration = weight of your friend.
Now, if your friend is just barely floating in fresh water, that means her weight is balanced by the buoyant force. Since weight = mass × gravitational acceleration, we can rewrite the equation as density of water × volume of your friend × gravitational acceleration = mass of your friend × gravitational acceleration. We can cancel out the gravitational acceleration on both sides of the equation.
So, density of water × volume of your friend = mass of your friend. Plugging in the values, we have density of water × volume of your friend = 100 kg. The density of water is approximately 1000 kg/m^3, which means volume of your friend = mass of your friend / density of water.
Calculating that, we get volume of your friend = 100 kg / 1000 kg/m^3 = 0.1 m^3. Since there are 1000 liters in 1 m^3, we can convert the volume to liters by multiplying by 1000.
In the end, your friend's volume is 0.1 m^3 × 1000 L/m^3 = 100 L, or 100 liters. So, your just-barely-floating friend takes up quite a bit of space in the water!
To determine the volume, we can use Archimedes' principle, which states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object.
In this case, the buoyant force is equal to her weight, so we know that the weight of the water displaced is also equal to 100 kg.
Since the density of water is approximately 1000 kg/m³, we can use the formula:
Weight = Density x Volume x Gravity
Substituting the values we know:
100 kg = 1000 kg/m³ x Volume x 9.8 m/s²
To find the volume in cubic meters, we rearrange the formula:
Volume = Weight / (Density x Gravity)
Volume = 100 kg / (1000 kg/m³ x 9.8 m/s²)
Simplifying the expression:
Volume = 0.0102 m³
Since 1 cubic meter is equal to 1000 liters, we can convert the volume to liters:
Volume = 0.0102 m³ x 1000 L/m³
Therefore, her volume is approximately 10.2 liters.
To find the volume of your friend, we need to use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
In this case, since your friend is just barely floating, the buoyant force on her is equal to her weight. Therefore, the weight of the water displaced by your friend is also equal to her weight.
The density of fresh water is approximately 1000 kg/m³. We can use this value to find the volume of water displaced by your friend.
Let's go step by step:
1. Calculate the weight of your friend in Newtons.
Weight = mass * gravitational acceleration (g)
Weight = 100 kg * 9.8 m/s² = 980 N
2. Since the weight of the water displaced is equal to your friend's weight, we can equate the weight of water to the density of water multiplied by its volume and the gravitational acceleration.
Weight of water = density of water * volume of water * g
Rearranging the equation:
Volume of water = Weight of water / (density of water * g)
Substituting the values:
Volume of water = 980 N / (1000 kg/m³ * 9.8 m/s²)
Volume of water = 0.1 m³
3. Convert the volume from cubic meters to liters.
1 m³ = 1000 L
Volume of water = 0.1 m³ * 1000 L/m³
Volume of water = 100 L
Therefore, the volume of your friend is approximately 100 liters.