Two metal blocks are attached by a cable as shown in the figure below and are submerged at rest near the surface of a lake. If the volumes are V1 = 2.1 m3 and V2 = 1.1 m3, what is the total buoyant force on the two blocks?
Vt = V1 + V2 = 2.1 + 1.1 = 3.2 m^3.
Buoyant force = Wt. of the water displaced:
Fb=3.2m^3*1000kg/m^3*9.8N/kg=31,360 N. =
Buoyant force.
To find the total buoyant force on the two blocks, we need to use the formula for buoyant force, which is given by:
Buoyant force (F) = density (ρ) * volume (V) * gravitational acceleration (g)
The density of water is typically around 1000 kg/m^3. The gravitational acceleration is approximately 9.8 m/s^2.
1. The buoyant force on the first block (F1) can be calculated as:
F1 = ρ * V1 * g
2. Similarly, the buoyant force on the second block (F2) can be calculated as:
F2 = ρ * V2 * g
3. Finally, to find the total buoyant force (F_total), we can add the individual buoyant forces together:
F_total = F1 + F2
Let's substitute the given values and calculate the total buoyant force.
To find the total buoyant force on the two blocks, we need to consider the buoyant force acting on each block separately and then add them together.
The buoyant force is given by the equation F_b = ρ * V * g, where F_b is the buoyant force, ρ is the density of the fluid, V is the volume of the object submerged in the fluid, and g is the acceleration due to gravity.
The first block has a volume of V1 = 2.1 m^3. Let's assume that the density of water is ρ_w = 1000 kg/m^3, which is the typical value for freshwater.
Calculating the buoyant force on the first block:
F_b1 = ρ_w * V1 * g
F_b1 = 1000 kg/m^3 * 2.1 m^3 * 9.8 m/s^2
F_b1 = 20580 N
Similarly, for the second block with a volume of V2 = 1.1 m^3:
F_b2 = ρ_w * V2 * g
F_b2 = 1000 kg/m^3 * 1.1 m^3 * 9.8 m/s^2
F_b2 = 10780 N
Now, to find the total buoyant force, we add these two forces:
Total buoyant force = F_b1 + F_b2
Total buoyant force = 20580 N + 10780 N
Total buoyant force = 31360 N
Therefore, the total buoyant force on the two blocks is 31360 N.