A submerged submarine alters its buoyancy so that it initially accelerates upward at 0.325 m/s^2. What is the submarine's average density at this time? (Hint: the density of sea water is 1.025*10^3 kg/m^3).
The difference of densities will give you the net bouyant force on the sub per m^3. Assume a volume V for the sub.
Mass sub= V*density sub
Bouyant force= bouyantforce/m^3 * V
acceleration=bouyantforce/masssub
This ignores the friction of the water, which is considerable in real life.
A submerged submarine alerts its boyounacy that initially accelerates 0.325m/s squared what is the submarine avareage
To determine the submarine's average density, we can use the relationship between buoyant force, mass, and acceleration. Let's assume the volume of the submarine is V.
1. Mass of the submarine (m_sub) is equal to the product of the volume and the density of the submarine (ρ_sub):
m_sub = V * ρ_sub
2. The buoyant force acting on the submarine is given by the difference in densities between the submarine and the surrounding water, multiplied by the volume:
Buoyant force = (ρ_water - ρ_sub) * V * g,
where ρ_water is the density of sea water (1.025 * 10^3 kg/m^3) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
3. The acceleration of the submarine (a) is equal to the buoyant force divided by the mass of the submarine:
a = Buoyant force / m_sub
Therefore, we can rearrange the equation in step 3 to solve for the submarine's average density (ρ_sub):
ρ_sub = (ρ_water - (a * m_sub) / V) / V
Substituting the given values:
ρ_sub = (1.025 * 10^3 kg/m^3 - (0.325 m/s^2 * V * ρ_sub)) / V
Note that this equation is nonlinear, and we need to know the value of V to solve for ρ_sub.
To find the average density of the submarine, you can use the concept of buoyancy. Buoyancy is the force experienced by an object immersed in a fluid, such as water, and is equal to the weight of the fluid displaced by the object.
In this case, the submarine is accelerating upward, indicating that the buoyant force is greater than the weight of the submarine. By using Newton's second law of motion (F=ma), we can find the buoyant force acting on the submarine.
Let's assume the volume of the submarine is V and the density of sea water is given as 1.025*10^3 kg/m^3. The mass of the submarine, msub, can be calculated by multiplying its volume by its average density: msub = V * densitysub.
The buoyant force per unit volume, also known as the buoyant force density, can be found by multiplying the density of water by the acceleration due to gravity: buoyantforcedensity = densitywater * g.
Since the submarine is accelerating upward at 0.325 m/s^2, the net buoyant force acting on it per unit volume is given by: buoyantforce = buoyantforcedensity * V.
Finally, we can equate this buoyant force to the mass of the submarine multiplied by its acceleration to find the average density: buoyantforce = msub * acceleration.
By substituting the expressions for msub and buoyantforce, we get: buoyantforcedensity * V = (V * densitysub) * acceleration.
Now we can solve for the average density, densitysub: densitysub = buoyantforcedensity * acceleration.
Substituting the known values, buoyantforcedensity = 1.025*10^3 kg/m^3 and acceleration = 0.325 m/s^2, we can calculate the average density of the submarine.