a 1.0kg beaker containgin 2.00kg of oil with a density of 916kg/m3 rests on a scale. a 2.0kg block of iron is suspended from a spring scale and completly submerged in the oil, find the euilibrium readings of both scales.density of iron 7860.
first the bouyancy supplied to the iron block:
bouyancy=volume*densityoil=2/7860 * 916
work that out.
then the scale above is supporting 2kg-bouyancy.
the scale below is supporting the beaker, the oil, and the bouyancy force.
To find the equilibrium readings of both scales, we need to consider the forces acting on each object.
Let's start with the beaker containing the oil. Since it is at rest, the net force acting on it must be zero. The only forces acting on the beaker are the gravitational force (weight) and the buoyant force.
The weight of the beaker can be calculated by multiplying its mass (1.0 kg) by the acceleration due to gravity (9.8 m/s^2) using the equation F = m * g.
Weight of beaker = 1.0 kg * 9.8 m/s^2 = 9.8 N
The buoyant force acting on the beaker can be calculated by multiplying the volume of the oil displaced by the beaker by the density of the oil and the acceleration due to gravity.
Volume of oil displaced = Mass of oil / Density of oil = 2.00 kg / 916 kg/m^3 = 0.00218 m^3
Buoyant force = Volume of oil displaced * Density of oil * g = 0.00218 m^3 * 916 kg/m^3 * 9.8 m/s^2 = 19.9 N
Since the net force on the beaker is zero, the reading on the scale is equal to the weight of the beaker minus the buoyant force.
Reading on beaker scale = Weight of beaker - Buoyant force = 9.8 N - 19.9 N = -10.1 N
The negative sign indicates that the beaker experiences an upward force due to the buoyant force.
Now let's consider the block of iron submerged in the oil. Again, the net force acting on the block must be zero. The forces acting on the block are its weight and the buoyant force.
The weight of the block of iron can be calculated in the same way as before:
Weight of iron = Mass of iron * g = 2.0 kg * 9.8 m/s^2 = 19.6 N
The buoyant force acting on the block can be calculated by multiplying the volume of the block submerged in the oil by the density of the oil and the acceleration due to gravity.
Volume of block submerged = Mass of block of iron / Density of iron = 2.0 kg / 7860 kg/m^3 = 0.000254 m^3
Buoyant force on block = Volume of block submerged * Density of oil * g = 0.000254 m^3 * 916 kg/m^3 * 9.8 m/s^2 = 2.22 N
Since the net force on the block is zero, the reading on the spring scale is equal to the weight of the iron minus the buoyant force.
Reading on spring scale = Weight of iron - Buoyant force = 19.6 N - 2.22 N = 17.4 N
Therefore, the equilibrium readings on the scales are approximately:
Beaker scale: -10.1 N
Spring scale: 17.4 N
To find the equilibrium readings of both scales, we need to consider the forces acting on the beaker and the block of iron in the oil.
1. Forces on the beaker:
The weight of the beaker can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight of beaker = 1.0 kg * 9.8 m/s^2 = 9.8 N
The buoyant force acting on the beaker can be calculated using the formula:
Buoyant force = volume displaced * density of fluid * acceleration due to gravity
The volume displaced by the beaker is its own volume, which we'll assume to be negligible.
2. Forces on the block of iron:
The weight of the block of iron can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight of iron block = 2.0 kg * 9.8 m/s^2 = 19.6 N
The buoyant force acting on the iron block can be calculated using the formula:
Buoyant force = volume displaced * density of fluid * acceleration due to gravity
The volume displaced by the iron block can be calculated using the formula:
Volume displaced = mass / density of iron
Volume displaced by iron block = 2.0 kg / 7860 kg/m^3 = 0.000254 m^3
Buoyant force on iron block = 0.000254 m^3 * 916 kg/m^3 * 9.8 m/s^2 = 2.22 N
Now let's calculate the equilibrium readings of both scales. Since the forces are balanced at equilibrium, the scale readings will equal the respective forces:
Equilibrium reading of the scale supporting the beaker = Weight of beaker + Buoyant force on beaker
Equilibrium reading of the scale supporting the block of iron = Weight of iron block - Buoyant force on iron block
Plugging in the values calculated earlier:
Equilibrium reading of the beaker scale = 9.8 N + 0 N = 9.8 N
Equilibrium reading of the block of iron scale = 19.6 N - 2.22 N = 17.38 N
Therefore, the equilibrium reading of the beaker scale is 9.8 N and the equilibrium reading of the block of iron scale is 17.38 N.