In an experiment to determine the relative density of a plastic cork stopper, the mass of a glass cork stopper in water is 6g, while that of the glass cork stopper in water and plastic cork stopper in air is 12g. What is the mass of both cork stoppers in water if the relative density of the plastic cork stopper is 0.75?
Really is the same as your other problem.
To determine the mass of both cork stoppers in water, we can use the concept of relative density. The relative density is the ratio of the density of a substance to the density of another substance taken as standard. In this case, the standard substance is water.
We are given that the mass of the glass cork stopper in water is 6g. Let's denote the density of water as ρw.
We are also given that the mass of the glass cork stopper in water and the mass of the plastic cork stopper in air is 12g. Let's denote the density of the plastic cork stopper as ρp.
We can set up the following equation:
Mass of glass cork stopper in water / Mass of glass cork stopper in water and plastic cork stopper in air = Density of glass cork stopper / Density of water = ρg / ρw
From this equation, we can rearrange it to find the density of glass cork stopper:
Density of glass cork stopper = (Mass of glass cork stopper in water / Mass of glass cork stopper in water and plastic cork stopper in air) * Density of water
Now, we can substitute the given values:
Density of glass cork stopper = (6g / 12g) * ρw
We are also given that the relative density of the plastic cork stopper is 0.75. The relative density is defined as the density of the substance divided by the density of water:
Relative density of plastic cork stopper = Density of plastic cork stopper / Density of water = ρp / ρw
Substituting the given value:
0.75 = ρp / ρw
Rearranging this equation, we can solve for ρp:
ρp = 0.75 * ρw
Now, let's find the mass of both cork stoppers in water. We know that the relative density is given by:
Mass of glass cork stopper in water / Mass of plastic cork stopper in water = Relative density of plastic cork stopper = 0.75
We can rearrange this equation to find the mass of the plastic cork stopper in water:
Mass of plastic cork stopper in water = Mass of glass cork stopper in water / 0.75
Substituting the given value:
Mass of plastic cork stopper in water = 6g / 0.75 = 8g
Therefore, the mass of the glass cork stopper in water is 6g and the mass of the plastic cork stopper in water is 8g.
To solve this problem, we need to understand the concept of relative density and how to calculate it. The relative density of an object is the ratio of its density to the density of a reference substance. In this case, the reference substance is water.
The formula to calculate the relative density is:
Relative Density = Density of object / Density of water
To find the mass of both cork stoppers in water, we can use the concept of buoyancy. When an object is submerged in a fluid (such as water), it experiences an upward force called buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object.
We can use the following equation to calculate the buoyant force:
Buoyant Force = Weight of water displaced
Since the buoyant force equals the weight of the object in water, we can set up the following equation:
Weight of water displaced = Weight of object in water
Let's denote the mass of the glass cork stopper as M1 and the mass of the plastic cork stopper as M2. We are given the following information:
M1 (glass cork stopper in water) = 6g
M2 (glass cork stopper in water and plastic cork stopper in air) = 12g
Relative density of plastic cork stopper (ρ2/ρwater) = 0.75
We need to find M2 (mass of both cork stoppers in water).
First, we calculate the density of the plastic cork stopper:
Density of plastic cork stopper (ρ2) = Relative density of plastic cork stopper * Density of water
Given that the density of water is 1 g/cm^3, we have:
ρ2 = 0.75 * 1 g/cm^3 = 0.75 g/cm^3
Now, let's set up the equation for the buoyant force:
Buoyant Force = Weight of water displaced
Weight of water displaced = Weight of object in water
For the glass cork stopper (M1) in water:
Buoyant Force1 = Weight of water displaced1
M1 = Weight of object in water1
For the glass cork stopper (M1) and plastic cork stopper (M2) in water:
Buoyant Force2 = Weight of water displaced2
(M1 + M2) = Weight of object in water2
Since the density of water is 1 g/cm^3, the weight of water displaced is equal to the volume of water displaced (in cm^3). Therefore:
Buoyant Force1 = M1
Buoyant Force2 = (M1 + M2)
Now, we can equate the two buoyant forces:
Buoyant Force1 = Buoyant Force2
M1 = (M1 + M2)
Substituting the values we know:
6g = (6g + M2)
Simplifying the equation, we can solve for M2:
M2 = 6g - 6g
M2 = 0g
Therefore, the mass of both cork stoppers in water is zero.