what must be the density of an object with a mass of 5000 grams if the object is to float in water?
See this discussion.
http://science.howstuffworks.com/question254.htm
I think it is 34,500kg/5,000g=6.9kg/g i think
To determine the required density for an object to float in water, you need to understand the concept of buoyancy. Buoyancy is the upward force exerted by a fluid (in this case, water) on an object immersed in it. For an object to float, the buoyant force must equal or exceed the object's weight.
Here's how you can calculate the required density:
1. Determine the weight of the object: Weight = mass × acceleration due to gravity.
In this case, the mass of the object is given as 5000 grams (or 5 kilograms). The acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, Weight = 5 kg × 9.8 m/s^2 = 49 N.
2. Find the buoyant force: Buoyant force = density of fluid × volume of object × acceleration due to gravity.
Since the object is floating in water, the density of the fluid is the density of water, which is approximately 1000 kg/m^3. The acceleration due to gravity remains the same at 9.8 m/s^2.
3. Rearrange the equation to solve for the volume of the object:
Volume of object = buoyant force / (density of fluid × acceleration due to gravity).
Substituting the known values, we have:
Volume of object = 49 N / (1000 kg/m^3 × 9.8 m/s^2) ≈ 0.005 m^3.
4. Finally, calculate the required density using the formula:
Density = mass / volume.
Density = 5 kg / 0.005 m^3 = 1000 kg/m^3.
Therefore, for an object with a mass of 5000 grams (or 5 kilograms) to float in water, it needs to have a density equal to the density of water, which is approximately 1000 kg/m^3.