a 17g object dropped in water makes the volume rise from 6 to 20 ml: what is its volume, what is its density?
To find the volume and density of the object, we can use the information given.
First, let's calculate the change in volume. The volume increased from 6 ml to 20 ml. So, the change in volume is:
Change in Volume = Final Volume - Initial Volume = 20 ml - 6 ml = 14 ml
According to Archimedes' principle, when an object is submerged in a fluid, it displaces an amount of fluid equal to its own volume. This principle helps us find the volume of the object. The change in volume is equal to the volume of the object.
Therefore, the volume of the object is 14 ml.
Next, let's calculate the density of the object. The density of an object is given by the formula:
Density = Mass / Volume
In this case, the mass of the object is not given directly. However, we can use the information about its effect on water volume to indirectly calculate the density.
When the object is dropped into the water, it makes the volume rise from 6 ml to 20 ml. This rise in volume is due to the displacement of water by the object. The weight (mass) of the water displaced is equal to the weight (mass) of the object.
We can use the formula for density to determine the mass:
Density = Mass_water / Volume_water = Mass_object / Volume_object
We can rearrange the formula to solve for the mass of the object:
Mass_object = Density * Volume_object
Substituting the given values into the formula:
Mass_object = Density * 14 ml
Now we need to determine the mass of the water displaced. The density of water is approximately 1 g/ml. So, the mass of the water is:
Mass_water = Density_water * Change in Volume
Substituting the values:
Mass_water = 1 g/ml * 14 ml = 14 g
Since the mass of the water displaced is equal to the mass of the object, we can equate the two equations:
Mass_object = Mass_water
Density * 14 ml = 14 g
Now it becomes a simple equation to solve for the density:
Density = 14 g / 14 ml = 1 g/ml
Therefore, the volume of the object is 14 ml, and the density of the object is 1 g/ml.