A beaker of mass 1.2 kg containing 2.1 kg
of water rests on a scale. A 2.2 kg block of aluminum (of density 2700 kg/m3) suspended from a spring scale is submerged in the water.
Find the reading of the upper scale (the spring scale). The acceleration of gravity is 9.81 m/s2 . Answer in units of N.
Find the reading of the bottom scale(scale placed under the beaker).
Answer in units of N.
The lower scale supports the beaker, water, and the buoyant force of water on the aluminum
buoyantforce= densitywater*g*volumeAl
volumeAl= massAl/denstityAl
and what about the spring scale?
is it apparent weight = actual weight - densitywater*g*V ?
yes.
To find the reading of the upper scale (the spring scale), we need to determine the buoyant force acting on the aluminum block submerged in water. The buoyant force is the force exerted by a fluid on an object submerged in it and can be calculated using the formula:
Buoyant force = weight of the fluid displaced by the object
1. Calculate the volume of the aluminum block:
Density = Mass / Volume
Volume = Mass / Density
Volume = 2.2 kg / 2700 kg/m^3
2. Calculate the weight of the water displaced by the aluminum block:
Weight = Volume * Density * g (acceleration due to gravity)
Weight = Volume * 1000 kg/m^3 * 9.81 m/s^2
3. Calculate the reading of the upper scale (spring scale):
Reading = Weight of the water displaced by the aluminum block + Weight of the aluminum block
Reading = Weight + Weight of the aluminum block
Now, let's calculate the individual values.
1. Volume of the aluminum block:
Volume = 2.2 kg / 2700 kg/m^3
Volume ≈ 0.0008148 m^3
2. Weight of the water displaced by the aluminum block:
Weight = Volume * 1000 kg/m^3 * 9.81 m/s^2
Weight ≈ 0.0008148 m^3 * 1000 kg/m^3 * 9.81 m/s^2
3. Reading of the upper scale (spring scale):
Reading = Weight + Weight of the aluminum block
Reading ≈ Weight + (2.2 kg * 9.81 m/s^2)
Now, to find the reading of the bottom scale (scale placed under the beaker), we need to calculate the weight of the beaker and water.
4. Calculate the weight of the beaker and water:
Weight = mass * g
Weight = (1.2 kg + 2.1 kg) * 9.81 m/s^2
So, the final answers are:
Reading of the upper scale (spring scale): Calculated value in Newtons.
Reading of the bottom scale (scale placed under the beaker): Calculated value in Newtons.