A 1.00-kg beaker containing 2.29 kg of oil (density = 916 kg/m3) rests on a scale. A 2.33-kg block of iron is suspended from a spring scale and is completely submerged in the oil (see figure below). Find the equilibrium readings of both scales.
top scale
N
bottom scale
N
To find the equilibrium readings of both scales, we need to consider the forces acting on the system.
Let's start with the top scale, which measures the normal force exerted by the beaker on the oil. The beaker has a mass of 1.00 kg, so its weight is given by:
Weight of the beaker = mass of the beaker * acceleration due to gravity
= 1.00 kg * 9.8 m/s^2
= 9.8 N
The normal force exerted by the beaker on the oil is equal in magnitude but opposite in direction to the weight of the beaker. Therefore, the equilibrium reading on the top scale is 9.8 N.
Now let's move on to the bottom scale, which measures the net force exerted on the block of iron.
First, we need to calculate the buoyant force acting on the block of iron. The buoyant force is given by:
Buoyant force = weight of the fluid displaced by the submerged object
The block of iron has a mass of 2.33 kg. To calculate the weight of the fluid displaced, we need to find the volume of the block submerged in the oil.
Density of oil = mass of oil / volume of oil
Rearranging the equation, we can find the volume of oil displaced by the block:
Volume of oil displaced = mass of block / density of oil
= 2.33 kg / 916 kg/m^3
= 0.00254 m^3
Now we can calculate the buoyant force:
Buoyant force = density of oil * volume of oil displaced * acceleration due to gravity
= 916 kg/m^3 * 0.00254 m^3 * 9.8 m/s^2
= 22.57 N
Since the block of iron is completely submerged in the oil, the buoyant force is equal in magnitude but opposite in direction to the weight of the block of iron. Therefore, the equilibrium reading on the bottom scale is 22.57 N.
To summarize:
- The equilibrium reading on the top scale is 9.8 N.
- The equilibrium reading on the bottom scale is 22.57 N.