A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 13.9 kg and, when "full," contains 3.20 kg of air. The density of seawater is 1025 kg/m3. Assume that only its weight and the buoyant force act on the tank.
Determine the magnitude of the net force on the fully submerged tank at the end of a dive (when it no longer contains any air).
so I tried doing 13.9+3.2 * 9.8 and then subtracting it from a previous answer where I had to find the magnitude when it was full of air. i got 157N but its not right
To determine the magnitude of the net force on the fully submerged tank at the end of a dive, we need to consider the weight of the tank, the buoyant force on the tank, and the change in buoyant force as the air is used up.
First, let's find the weight of the tank. We know that the mass of the tank is 13.9 kg, so the weight of the tank is $13.9\text{ kg} \times 9.8 \text{ m/s}^2 = 136.1 \text{ N}$.
Next, let's find the buoyant force on the tank. We know that the tank displaces 15.7 L of seawater, and the density of seawater is 1025 kg/m3. So the buoyant force on the tank is equal to the volume of the displaced seawater times the density of the seawater: $15.7\text{ L} \times 1\text{ m}^3/1000\text{ L} \times 1025 \text{ kg/m}^3 = 16.2 \text{ N}$.
Now, let's find the change in buoyant force as the air is used up. When the tank is full, it contains 3.20 kg of air, which displaces a volume of $\frac{3.20\text{ kg}}{1.2\text{ kg/m}^3} = 2.67\text{ m}^3$ of seawater. So the change in buoyant force is equal to the volume of displaced seawater times the density of seawater: $2.67\text{ m}^3 \times 1025 \text{ kg/m}^3 = 27.4 \text{ N}$.
Finally, we can use these values to find the magnitude of the net force on the fully submerged tank at the end of a dive: $136.1 \text{ N} - 16.2 \text{ N} + 27.4 \text{ N} = 147.3 \text{ N}$. So the magnitude of the net force on the fully submerged tank at the end of a dive is 147.3 N.
The net force on the fully submerged tank at the end of a dive is equal to the buoyant force, which is equal to the weight of the displaced seawater. The weight of the displaced seawater can be calculated using the density of seawater and the volume of the tank.
The volume of the tank is 15.7 L, and the density of seawater is 1025 kg/m3. Therefore, the weight of the displaced seawater is 15.7 L x 1025 kg/m3 = 16,087.5 kg.
The buoyant force is equal to the weight of the displaced seawater, so the net force on the fully submerged tank at the end of a dive is 16,087.5 kg x 9.8 m/s2 = 157,717 N.
Well, it seems like you're getting a little tangled up in those calculations. Let's try to straighten things out.
To determine the net force on the fully submerged tank, we need to consider the weight of the tank and the buoyant force.
First, let's find the weight of the tank. The weight can be calculated by multiplying the mass of the tank by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight of the tank is:
Weight of tank = mass of tank * g
Weight of tank = 13.9 kg * 9.8 m/s^2
Now, let's calculate the buoyant force acting on the tank. The buoyant force can be calculated by multiplying the volume of the displaced seawater by the density of the seawater and the acceleration due to gravity (Archimedes' principle). Therefore, the buoyant force is:
Buoyant force = volume of seawater * density of seawater * g
Buoyant force = 15.7 L * 1025 kg/m^3 * 9.8 m/s^2
Finally, to determine the net force on the fully submerged tank, we need to subtract the weight of the tank from the buoyant force:
Net force = Buoyant force - Weight of tank
Now, try plugging in the values and calculating the net force. And remember, if you get stuck, I'm here to put a little humor into your calculations!
To determine the magnitude of the net force on the fully submerged tank, we need to consider the buoyant force and the weight of the tank.
1. Buoyant Force:
The buoyant force is equal to the weight of the fluid displaced by the submerged object. In this case, the fluid is seawater with a density of 1025 kg/m^3.
The volume of the scuba tank submerged in water is given as 15.7 L, which can be converted to cubic meters by dividing by 1000:
Volume = 15.7 L / 1000 = 0.0157 m^3
The buoyant force is given by:
Buoyant Force = Density of Fluid * Volume Displaced * Gravity
Buoyant Force = 1025 kg/m^3 * 0.0157 m^3 * 9.8 m/s^2
2. Weight of the Tank:
The weight of the tank is the force due to gravity acting on it. The mass of the tank is given as 13.9 kg.
Weight = Mass * Gravity
Weight = 13.9 kg * 9.8 m/s^2
3. Net Force:
The net force on the fully submerged tank is the difference between the buoyant force and the weight of the tank.
Net Force = Buoyant Force - Weight
Substituting the values calculated above, we have:
Net Force = (1025 kg/m^3 * 0.0157 m^3 * 9.8 m/s^2) - (13.9 kg * 9.8 m/s^2)
Simplifying the equation will give you the magnitude of the net force on the fully submerged tank at the end of the dive.
To determine the magnitude of the net force on the fully submerged tank at the end of a dive, we need to consider the buoyant force acting on the tank.
The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is seawater, and the tank displaces 15.7 L of seawater when fully submerged.
First, let's convert the given masses to kilograms, since the density of seawater is given in kg/m3:
Mass of the tank, m_tank = 13.9 kg
Mass of air in the tank (initially), m_air = 3.20 kg
Next, let's find the mass of the seawater displaced by the tank. We can calculate this by converting the volume of seawater displaced to cubic meters and multiplying it by the density of seawater:
Volume of seawater displaced by the tank, V_displaced = 15.7 L = 0.0157 m3
Mass of seawater displaced by the tank, m_displaced = V_displaced * density of seawater = 0.0157 m3 * 1025 kg/m3 = 16.0925 kg
Now we can calculate the buoyant force on the tank when it is fully submerged and contains no air:
Buoyant force, F_buoyant = weight of fluid displaced = m_displaced * g
where g is the acceleration due to gravity (approximately 9.8 m/s2).
F_buoyant = 16.0925 kg * 9.8 m/s^2 = 157.839 N
Since there are no other forces acting on the tank, the magnitude of the net force on the fully submerged tank at the end of a dive is equal to the buoyant force:
Magnitude of the net force = F_buoyant = 157.839 N
So, the correct answer for the magnitude of the net force on the fully submerged tank is approximately 157.839 N.