A completely submerged chunk of metal sinks in water with an acceleration equal to one-fifth of g (where g = 9.8 m/s\ Find the specific gravity (defined above) of this metal. Note, ignore all drag effects in the fluid.
To find the specific gravity of the metal, we first need to understand the concept of specific gravity.
Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance. The reference substance is usually water. It provides a measure of how dense or heavy a substance is compared to water.
In this case, the metal is completely submerged in water, and we are given that its acceleration is equal to one-fifth of the acceleration due to gravity (g = 9.8 m/s²). We can use this information to determine the specific gravity.
To start, we need to find the density of the metal. The acceleration of the metal is given by:
a = g - ρw * V * g / m
Where:
- a is the acceleration of the metal,
- g is the acceleration due to gravity,
- ρw is the density of water,
- V is the volume of the metal,
- m is the mass of the metal.
Since the metal is completely submerged, the buoyant force acting on it is equal to the weight of the water it displaces. This buoyant force can be calculated using Archimedes' principle:
Fb = ρw * V * g
Where:
- Fb is the buoyant force,
- ρw is the density of water,
- V is the volume of the metal,
- g is the acceleration due to gravity.
By substituting this equation into the equation for acceleration, we get:
a = g - Fb / m
Now, we are given that the acceleration a is equal to one-fifth of g. Substituting these values into the equation, we have:
1/5 * g = g - (ρw * V * g) / m
Simplifying this equation, we can solve for the specific gravity (SG):
SG = (ρw * V) / m
Now that we have the equation for SG, we can evaluate the specific gravity.
Note: To calculate the specific gravity precisely, you will need to know the density of water (ρw), volume of the metal (V), and its mass (m). These values can be obtained by conducting experiments or gathering data from other sources.