Final answer:
To determine the steel's density, we use the equilibrium condition, where the weight of the wooden block and steel object equals the weight of the water displaced by the block. The volume of water displaced equals the block's volume. The steel's density is the object's mass divided by the wooden block's volume.
Step-by-step explanation:
To find the density of the steel object, we need to first recognize that the equilibrium condition means the combined weight of the wooden block and the steel object equals the weight of the water displaced by the submerged volume of the wooden block. Since the block is completely submerged when the steel object is on top, the volume of water displaced is equal to the volume of the wooden block.
The weight of the water displaced can be calculated using the known density of water (1,000 kg/m3) and the volume of the wooden block (5.23 × 10−4 m3). Therefore, the weight of the water displaced is (1,000 kg/m3)(5.23 × 10−4 m3) × 9.81 m/s2. This weight is equal to the combined weight of the block and the steel object.
The mass of the steel object is 0.370 kg, so its weight is (0.370 kg)(9.81 m/s2). To find the density of steel, divide the mass of steel by the volume of water displaced, which is also the volume of the steel since it is fully submerged. The density of a substance is defined as the mass per unit volume; therefore, the solution will be the quotient of the steel object's mass and the volume of the wooden block which has been displaced.