a) what is the density of a log floating in salt water if 42% of its volume is exposed? The density of salt water is 1025 kg/m^3
(b) What is the density of a sample of metal that sinks in water at 7.2 m/s^2
To find the density of the log floating in salt water and the density of the metal sample, we need to use the formula for density: density = mass/volume.
Let's start with part (a) to find the density of the log floating in salt water.
a) To find the density of the log, we need to know the mass and volume of the log.
Since the log is floating in salt water, we know that the density of the log must be lower than the density of salt water (1025 kg/m^3) for it to float.
Let's assume that the volume of the log is V. Since 42% of the volume is exposed, the submerged volume would be 58% of V.
To calculate the density, we need to calculate the mass of the log. We can do this by multiplying the volume of the submerged part (0.58V) by the density of the salt water (1025 kg/m^3).
Therefore, the mass (m) of the log would be: m = density of salt water * submerged volume = 1025 kg/m^3 * 0.58V.
Now we can calculate the density of the log using the formula: density = mass/volume.
density = (1025 kg/m^3 * 0.58V) / V
Simplifying the equation, we get:
density = 0.58 * 1025 kg/m^3
density ≈ 594.5 kg/m^3
Therefore, the density of the log floating in salt water is approximately 594.5 kg/m^3.
b) To find the density of the metal sample, we need to know the mass and volume as well.
We know that the metal sample sinks in water, which means its density is higher than the density of water (1000 kg/m^3) for it to sink.
Using the formula density = mass/volume, we can calculate the density of the metal by dividing its mass by its volume.
Since we are not provided with the mass or volume of the metal sample in this question, we cannot calculate the density of the metal. You would need to know the mass and volume of the metal sample to find its density.