A piece of stone has volume 400cm³ and density 7800kg/m³. It is immersed totally in water of density 1000kg/m³. Calculate the weight of the stone in air and the uptrust of weight.
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Wait weight in air would be 31.2N
7800
You are correct, I made a typo. The weight in air would be 31.2 N.
To calculate the weight of the stone in air, we need to use the formula:
Weight = Volume × Density × g
where:
- Weight is the force exerted by an object due to gravity.
- Volume is the volume of the object.
- Density is the density of the object.
- g is the acceleration due to gravity, which is approximately 9.8 m/s².
First, let's convert the volume from cm³ to m³:
Volume = 400 cm³ = 400 × (1/100) m³ = 4 m³
Now, we can calculate the weight of the stone in air:
Weight = 4 m³ × 7800 kg/m³ × 9.8 m/s²
Weight = 152,880 N
So, the weight of the stone in air is 152,880 Newtons.
Next, let's calculate the upthrust or buoyant force acting on the object. According to Archimedes' principle, the upthrust is equal to the weight of the displaced fluid. In this case, the fluid is water, and its density is 1000 kg/m³.
Since the stone is being immersed totally in water, the volume of water displaced will be equal to the volume of the stone, which is 4 m³.
Now, let's calculate the upthrust:
Upthrust = Volume × Density of water × g
Upthrust = 4 m³ × 1000 kg/m³ × 9.8 m/s²
Upthrust = 39,200 N
So, the upthrust acting on the stone is 39,200 Newtons.
Therefore, the weight of the stone in air is 152,880 N (downward force), and the upthrust is 39,200 N (upward force).
7800 kg/m^3 = 7.8 g/cm^3
so the mass is 7.8 * 400 = 3120 g
weight in air = mg = 30.6 N
in water, subtract the weight of the 400cm^3 of water