an aluminum object has a mass of 27 kg & a density of 2700 kg/m^3. it is hung from a rope under the surface of water (density=1000 kg/m^3). what is the volume of the object and the tension in the string, while the object hangs from it & also under the surface of the water?
none of these
To find the volume of the aluminum object, you can use the formula:
Volume = Mass / Density
Given that the mass of the object is 27 kg and the density of aluminum is 2700 kg/m^3, you can substitute these values into the equation:
Volume = 27 kg / 2700 kg/m^3
Simplifying the equation will give you the volume of the object in cubic meters.
Now let's calculate the volume of the object:
Volume = 27 kg / 2700 kg/m^3 = 0.01 m^3
Therefore, the volume of the aluminum object is 0.01 cubic meters.
Now, let's determine the tension in the string while the object hangs under the surface of the water.
When an object is submerged in a fluid, it experiences two main forces:
1. The gravitational force acting downward, given by the formula:
Force_gravity = Mass * gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
Force_gravity = 27 kg * 9.8 m/s^2 = 264.6 N
2. The buoyant force acting upward, given by the formula:
Force_buoyant = Density_fluid * Volume_displaced * gravitational acceleration
The density of water is 1000 kg/m^3.
Volume_displaced = Volume of the object
Force_buoyant = 1000 kg/m^3 * 0.01 m^3 * 9.8 m/s^2
Simplifying the equation will give you the buoyant force on the object.
Force_buoyant = 98 N
Since the object is in equilibrium, the tension in the string must be equal to the combined forces acting on it. Therefore, the tension in the string is given by:
Tension = Force_gravity - Force_buoyant
Tension = 264.6 N - 98 N = 166.6 N
Therefore, the tension in the string while the aluminum object hangs under the surface of the water is 166.6 N.
In conclusion, the volume of the aluminum object is 0.01 cubic meters and the tension in the string while the object hangs under the surface of the water is 166.6 N.