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.
To find the equilibrium readings of both scales, we need to consider the forces acting on the objects.
1. Beaker with oil:
The weight of the beaker with oil can be calculated by multiplying the mass by the acceleration due to gravity (g ≈ 9.8 m/s^2):
Weight of beaker with oil = 1.0 kg * 9.8 m/s^2 = 9.8 N (Newtons)
Since the beaker is at rest on the scale, the scale reading will be equal to the weight of the beaker with the oil.
Scale reading for beaker with oil: 9.8 N
2. Submerged iron block:
To find the buoyant force acting on the iron block submerged in the oil, we need to consider the weight of the displaced oil. The volume of displaced oil is equal to the volume of the submerged iron block.
Mass of iron block = 2.0 kg
Density of iron = 7860 kg/m^3
Volume of iron block = (Mass of iron block) / (Density of iron)
Volume of iron block = 2.0 kg / 7860 kg/m^3 ≈ 0.000254 m^3
The buoyant force can be calculated by multiplying the volume of displaced oil by the density of the oil and acceleration due to gravity:
Buoyant force on iron block = (Volume of displaced oil) * (Density of oil) * (acceleration due to gravity)
Buoyant force on iron block = 0.000254 m^3 * 916 kg/m^3 * 9.8 m/s^2
The weight of the iron block can be calculated as:
Weight of iron block = (Mass of iron block) * (acceleration due to gravity)
Weight of iron block = 2.0 kg * 9.8 m/s^2 = 19.6 N
For equilibrium, the buoyant force on the iron block should equal its weight. Therefore, the spring scale reading will be the weight of the iron block.
Scale reading for iron block: 19.6 N
So, the equilibrium readings for both scales are:
- The beaker scale reads 9.8 N.
- The spring scale reads 19.6 N.