a density bottle weighs 0.25N when empty,and 0.75N when filled with water and 0.65N when filled with alcohol. Find the volume of the empty bottle and the density of the alchohol.
To find the volume of the empty density bottle, we can use the fact that the weight of an object is equal to its mass multiplied by the acceleration due to gravity (w = m*g).
Given that the weight of the empty density bottle is 0.25N, we have:
0.25N = m*g
To find the mass of the empty bottle, we need to know the acceleration due to gravity. Let's assume it is 9.8 m/s^2, which is the approximate value on Earth. Therefore:
0.25N = m * 9.8m/s^2
Solving for mass (m), we get:
m = 0.25N / 9.8m/s^2
Now, let's move on to finding the volume of the density bottle when filled with water.
We know that the weight of the density bottle filled with water is 0.75N. In this case, the weight includes the weight of the empty bottle and the weight of the water.
0.75N = (m_empty + m_water) * 9.8m/s^2
Since we already know the mass of the empty bottle (m_empty) from the previous calculation, we can rewrite the equation as:
0.75N = (0.25N / 9.8m/s^2 + m_water) * 9.8m/s^2
Simplifying the equation, we get:
0.75N = (0.25N + m_water * 9.8m/s^2)
Now, let's find the mass of the water (m_water):
m_water = (0.75N - 0.25N) / 9.8m/s^2
Finally, to find the volume of the empty density bottle, we need to divide the mass of the empty bottle by the density of water (ρ_water):
Volume_empty = m_empty / ρ_water
Now, moving on to finding the density of alcohol:
We know that the weight of the density bottle filled with alcohol is 0.65N. In this case, the weight includes the weight of the empty bottle and the weight of the alcohol.
0.65N = (m_empty + m_alcohol) * 9.8m/s^2
Again, since we already know the mass of the empty bottle (m_empty), we can rewrite the equation as:
0.65N = (0.25N / 9.8m/s^2 + m_alcohol) * 9.8m/s^2
Simplifying the equation, we get:
0.65N = (0.25N + m_alcohol * 9.8m/s^2)
Now, let's find the mass of the alcohol (m_alcohol):
m_alcohol = (0.65N - 0.25N) / 9.8m/s^2
Finally, to find the density of the alcohol (ρ_alcohol), divide the mass of the alcohol by the volume of the empty density bottle:
ρ_alcohol = m_alcohol / Volume_empty