An object weighing 400.0g in air is immersed in water after being tied to a string connected to a balance. The scale now reads 364.6g.
a.) Find the loss of weight(in gram of weight) when completely submersed in water.
b.) Find the volume of the object in cm^3 and in m^3.
c.) Find the density of the object in g/cm^3 and in kg/m^3.
d.) Find the buoyant force in N on the object when it is completely submerged in water.
a) Subtract 364.6 g from the weight in air. You get 35.4 g (weight)
b) Divide the weight loss (from a) by the weight density of water, 1.0 g/cm^3. Answer: 35.4 cm^3
c) Divide the object mass (which part (a) calls the weight) by the Volume from (b). You get 11.3 g/cm^3
d) The buoyant force in (a) is in grams weight. It equals the mass in grams. Convert to mass in kg and multiply that by g (9.8 m/s^2) for buoyant force in Newtons.
To answer each part of the question, we'll go step by step. Let's start with part a.
a) Loss of weight in grams:
The loss of weight can be calculated by subtracting the weight in water from the weight in air. Given that the weight in air is 400.0g, and the weight in water is 364.6g, we can find the loss of weight by subtracting:
Loss of weight = Weight in air - Weight in water
Loss of weight = 400.0g - 364.6g
Loss of weight = 35.4g
Therefore, the loss of weight when completely submerged in water is 35.4 grams.
Moving on to part b.
b) Volume of the object:
To find the volume of the object, we can utilize Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the liquid displaced by the submerged object. The buoyant force can be calculated by multiplying the loss of weight in water by the density of water.
First, we need to convert the loss of weight from grams to kilograms:
Loss of weight = 35.4g * (1kg / 1000g) = 0.0354kg
The density of water is approximately 1000 kg/m^3.
Next, we can find the volume:
Volume = Loss of weight / Density of water
Volume = 0.0354kg / 1000 kg/m^3
Volume = 0.0000354 m^3
To convert the volume to cm^3, we can multiply by 1,000,000 (since 1m^3 equals 1,000,000 cm^3):
Volume in cm^3 = Volume in m^3 * 1,000,000
Volume in cm^3 = 0.0000354 m^3 * 1,000,000
Volume in cm^3 = 35.4 cm^3
Therefore, the volume of the object is 35.4 cm^3 and 0.0000354 m^3.
Moving on to part c.
c) Density of the object:
The density of an object can be calculated by dividing its mass by its volume. In this case, the mass of the object is given as 400.0g.
Density = Mass / Volume
Density = 400.0g / 35.4 cm^3
Density = 11.3 g/cm^3
To convert the density to kg/m^3, we need to divide by 1000:
Density in kg/m^3 = Density in g/cm^3 / 1000
Density in kg/m^3 = 11.3 g/cm^3 / 1000
Density in kg/m^3 = 0.0113 kg/m^3
Therefore, the density of the object is 11.3 g/cm^3 and 0.0113 kg/m^3.
Moving on to the final part.
d) Buoyant force on the object:
The buoyant force is the force exerted by a fluid on a submerged object. It can be calculated as the weight of the fluid displaced by the object, which is equal to the weight of the water the object displaces. The buoyant force can be found by multiplying the density of water by the volume of the object.
Buoyant force = Density of water * Volume of the object
Buoyant force = 1000 kg/m^3 * 0.0000354 m^3
Buoyant force = 0.0354 N
Therefore, the buoyant force on the object when it is completely submerged in water is 0.0354 Newtons.