A 4.8 kg container of water sits on a scale A. A cube of aluminum with sides of length 11.0 cm is suspended from a spring scale B so that half of the block is submerged in the water.
What is the reading (in N) on spring scale B The continual question is What is the reading (in N) on scale A?
To find the reading on spring scale B, we need to consider the buoyant force acting on the aluminum cube submerged in water. The buoyant force is equal to the weight of the water displaced by the submerged part of the cube.
The weight of the water displaced can be calculated using the formula:
Weight = Volume x Density x gravitational acceleration
First, we need to determine the volume of the water displaced by the aluminum cube. Since half of the cube is submerged, the volume of water displaced is equal to half the volume of the cube.
Volume of the cube = (side length)^3 = (0.11 m)^3 = 0.001331 m³
Volume of water displaced = (1/2) x 0.001331 m³ = 0.0006655 m³
The density of water is approximately 1000 kg/m³, and gravitational acceleration is approximately 9.8 m/s².
Weight of water displaced = Volume x Density x gravitational acceleration
= 0.0006655 m³ x 1000 kg/m³ x 9.8 m/s²
≈ 6.5043 N
Therefore, the reading on spring scale B is approximately 6.5043 N.
To find the reading on scale A, we need to consider the weight of the container of water. The weight is calculated using the formula:
Weight = mass x gravitational acceleration
Given that the mass of the container of water is 4.8 kg and gravitational acceleration is approximately 9.8 m/s²:
Weight of container = mass x gravitational acceleration
= 4.8 kg x 9.8 m/s²
= 47.04 N
Therefore, the reading on scale A is approximately 47.04 N.
To find the reading on spring scale B, we need to consider the buoyant force on the aluminum cube.
Step 1: Calculate the volume of the aluminum cube.
The volume of a cube is given by V = s^3, where s is the length of the side.
V = (11.0 cm)^3 = 1331.0 cm^3 = 1.331 L = 0.001331 m^3
Step 2: Convert the volume of the aluminum cube to mass.
The density of aluminum is 2,700 kg/m^3.
The mass of the aluminum cube is given by m = ρV, where ρ is the density.
m = (2,700 kg/m^3)(0.001331 m^3) = 3.5947 kg
Step 3: Calculate the weight of the aluminum cube.
The weight of an object is given by W = mg, where m is the mass and g is the acceleration due to gravity.
W = (3.5947 kg)(9.8 m/s^2) = 35.25686 N
Therefore, the reading on spring scale B is 35.25686 N.
To find the reading on scale A, we need to consider the weight of the container of water.
Step 4: Calculate the weight of the water.
The weight of an object is given by W = mg, where m is the mass and g is the acceleration due to gravity.
W = (4.8 kg)(9.8 m/s^2) = 47.04 N
Therefore, the reading on scale A is 47.04 N.