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
need density of iron
top scale has
2.33 - Viron*916
but Viron = 2.33/density of iron
To find the equilibrium readings of both scales, let's analyze the forces acting on the system.
1. The beaker containing the oil is resting on a scale. The weight of the beaker and the oil will be acting downwards. The equation to calculate the weight is:
Weight = mass * gravitational acceleration
Given that the mass of the beaker and oil is 1.00 kg + 2.29 kg = 3.29 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight:
Weight of beaker and oil = 3.29 kg * 9.8 m/s^2 = 32.142 N
So, the top scale reading will be 32.142 N.
2. The iron block is completely submerged in the oil. It will experience a buoyant force upwards and its weight downwards. The net force on the iron block will be zero for it to be in equilibrium.
The buoyant force is given by:
Buoyant force = Volume of the submerged block * Density of the fluid * Gravitational acceleration
The volume of the submerged block can be calculated using its density and mass:
Volume of block = Mass of block / Density of iron
Given that the mass of the block is 2.33 kg and the density of iron is approximately 7,860 kg/m^3, we can calculate the volume:
Volume of block = 2.33 kg / 7,860 kg/m^3 ≈ 0.000296 m^3
Now we can calculate the buoyant force:
Buoyant force = 0.000296 m^3 * 916 kg/m^3 * 9.8 m/s^2 ≈ 2.7 N
So, the net force acting on the iron block will be its weight minus the buoyant force:
Net force on the block = Weight of block - Buoyant force
Weight of block = mass * gravitational acceleration
Weight of block = 2.33 kg * 9.8 m/s^2 ≈ 22.834 N
Net force on the block = 22.834 N - 2.7 N ≈ 20.134 N
Hence, the bottom scale reading will be approximately 20.134 N.
Therefore, the equilibrium readings of the scales are:
Top scale: 32.142 N
Bottom scale: 20.134 N