A 500 g mass is weighed in air and then in water. This experiment is repeated with salt water (density of 1.2 g/mL) and methylated spirits (density of 0.8 g/mL). Compare the weight of the body in these liquids to the results for water. Explain the differences.
To analyze the weight of the 500 g mass in different liquids, let's calculate the buoyant force and subtract it from the weight in air.
Weight in air = 500 g
1. In Water:
Density of water = 1 g/mL
Weight in water = Weight in air - Buoyant Force
Density of water = mass of water / volume of water
1 g/mL = mass of water / volume of water
1 g/mL = 500 g / volume of water
volume of water = 500 mL
Weight in water = 500 g - (500 mL * density of water)
Weight in water = 500 g - (500 mL * 1 g/mL)
Weight in water = 500 g - 500 g
Weight in water = 0 g
The weight of the 500 g mass in water is 0 g. This means that the mass experiences an upward buoyant force equal to its weight, leading to a net weight of 0 g.
2. In Saltwater:
Density of saltwater = 1.2 g/mL
Weight in saltwater = Weight in air - Buoyant Force
Density of saltwater = mass of saltwater / volume of saltwater
1.2 g/mL = mass of saltwater / volume of saltwater
1.2 g/mL = 500 g / volume of saltwater
volume of saltwater = 500 g / 1.2 g/mL
volume of saltwater ≈ 416.67 mL
Weight in saltwater = 500 g - (416.67 mL * 1.2 g/mL)
Weight in saltwater = 500 g - 499.99 g
Weight in saltwater ≈ 0.01 g
The weight of the 500 g mass in saltwater is approximately 0.01 g. This implies that the mass experiences a slightly upward buoyant force, but it is very small compared to the buoyant force in regular water.
3. In Methylated Spirits:
Density of methylated spirits = 0.8 g/mL
Weight in methylated spirits = Weight in air - Buoyant Force
Density of methylated spirits = mass of methylated spirits / volume of methylated spirits
0.8 g/mL = mass of methylated spirits / volume of methylated spirits
0.8 g/mL = 500 g / volume of methylated spirits
volume of methylated spirits = 500 g / 0.8 g/mL
volume of methylated spirits ≈ 625 mL
Weight in methylated spirits = 500 g - (625 mL * 0.8 g/mL)
Weight in methylated spirits = 500 g - 500 g
Weight in methylated spirits = 0 g
The weight of the 500 g mass in methylated spirits is 0 g. Similar to water, the mass in methylated spirits also experiences a buoyant force equal to its weight, resulting in a net weight of 0 g.
Differences:
- The weight of the body in water is 0 g, indicating that it experiences an upward buoyant force equal to its weight.
- The weight of the body in saltwater is slightly positive (0.01 g), suggesting that it experiences a smaller upward buoyant force compared to water.
- The weight of the body in methylated spirits is also 0 g, indicating that it experiences an upward buoyant force equal to its weight, similar to water.
These differences occur due to the variation in density of the liquids. The greater the density of the liquid, the more upward buoyant force is exerted on the mass. In saltwater with a density of 1.2 g/mL, the mass experiences a slightly lower buoyant force since the density is higher compared to regular water. On the other hand, in methylated spirits with a density of 0.8 g/mL, the density is lower compared to water, resulting in a similar buoyant force.
To compare the weight of the 500 g mass in different liquids (water, salt water, and methylated spirits), we need to consider the concept of buoyancy and Archimedes' principle.
1. Weight of the mass in air: The mass weighs 500 g in air due to the force of gravity acting on it.
2. Weight of the mass in water: When the mass is submerged in water, it experiences an upward buoyant force due to the displacement of water. This buoyant force reduces the weight of the mass. Archimedes' principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. Therefore, the weight of the mass in water will be less than 500 g.
3. Weight of the mass in salt water: Salt water has a higher density (1.2 g/mL) compared to regular water. As a result, the volume of water displaced by the mass in salt water will be less than in regular water. Since the buoyant force is directly proportional to the volume of fluid displaced, the buoyant force on the mass in salt water will be less. Therefore, the weight of the mass in salt water will be less than in regular water.
4. Weight of the mass in methylated spirits: Methylated spirits have a lower density (0.8 g/mL) compared to regular water. This means that the mass will displace a higher volume of methylated spirits compared to water. As a result, there will be a higher buoyant force acting on the mass in methylated spirits. Therefore, the weight of the mass in methylated spirits will be less than in regular water.
To summarize:
- The weight of the mass in water will be less than 500 g due to the buoyant force.
- The weight of the mass in salt water will be less than in regular water due to the higher density of salt water.
- The weight of the mass in methylated spirits will be less than in regular water due to the lower density of methylated spirits.