Examkin

Soru

Zorluk: ZorBuoyancy and Archimedes' Principle

A solid machine part is suspended from a spring scale. In the air, the scale reads 60 N60 \text{ N}. When the part is completely submerged in water, the scale reads 40 N40 \text{ N}. The part is then removed, dried, and completely submerged in a vat of unknown oil, where the scale reads 45 N45 \text{ N}. Based on these readings, what is the density of the oil compared to the density of water?

  1. 0.75 times the density of waterCevap
  2. B
    1.33 times the density of water
  3. C
    0.25 times the density of water
  4. D
    1.13 times the density of water

Cevap

The oil is 0.75 times the density of water.
According to Archimedes' principle, buoyant force equals the weight of the displaced fluid (Fb=ρ⋅V⋅gF_b = \rho \cdot V \cdot g). The buoyant force in water is 60 N−40 N=20 N60 \text{ N} - 40 \text{ N} = 20 \text{ N}. The buoyant force in the oil is 60 N−45 N=15 N60 \text{ N} - 45 \text{ N} = 15 \text{ N}. Because the part is fully submerged in both instances, the displaced volume (VV) is identical. Therefore, the buoyant forces are directly proportional to the fluid densities. The ratio of the oil's density to the water's density is the ratio of their buoyant forces: 15 N/20 N=0.7515 \text{ N} / 20 \text{ N} = 0.75.

Adım Adım Çözüm

1
Calculate the buoyant force exerted by the water.
60 N−40 N=20 N60 \text{ N} - 40 \text{ N} = 20 \text{ N}
The buoyant force is equal to the object's true weight in air minus its apparent weight when submerged.
2
Calculate the buoyant force exerted by the oil.
60 N−45 N=15 N60 \text{ N} - 45 \text{ N} = 15 \text{ N}
To compare the lifting effect of the two fluids, we need to know the specific buoyant force each exerts on the identical volume.
3
Calculate the ratio of the oil's density to the water's density.
15 N/20 N=0.7515 \text{ N} / 20 \text{ N} = 0.75
Because the same object is completely submerged in both fluids, the displaced volume is constant. Therefore, the buoyant forces are directly proportional to the densities of the fluids.

Anahtar Kavram

Apparent weight and Archimedes' Principle
Bu soruyu puanla

Konular

Buoyancy and Archimedes' Principle

Bu konudan daha fazla soru