W9. Calculate the buoyant force, if a floating body is 95% submerged in water.
12. A piece of aluminum with mass 1.00kg and density 2700kg/m3 is suspended
from a string and then completely immersed in a container of water. Calculate
the tension in the string (a) before and (b) after the metal is immersed.
10.Water flows through a fire hose of diameter 6.35cm at a rate of 0.0120m3/s.
The fire hose ends in a nozzle of inner diameter 2.20cm. What is the speed
with which the water exits the nozzle?
9. To calculate the buoyant force when a floating body is 95% submerged in water, we need to first calculate the volume of the body that is submerged. Let's say the total volume of the body is V and it is submerged to a depth of h, then the volume submerged is 0.95V (95% of V).
The buoyant force is equal to the weight of the water displaced by the submerged portion of the body. Since the body is floating, the weight of the body is equal to the buoyant force.
Buoyant force = weight of water displaced
Buoyant force = density of water x volume submerged x gravitational acceleration
Buoyant force = density of water x 0.95V x g
10. To calculate the speed at which the water exits the nozzle of the fire hose, we can use the principle of conservation of mass, which states that the mass flow rate at any point in a system must remain constant.
Let A1 be the cross-sectional area of the fire hose (π*(6.35cm)^2 / 4) and A2 be the cross-sectional area of the nozzle (π*(2.20cm)^2 / 4).
Given that the flow rate Q = 0.0120 m^3/s = v1 * A1 = v2 * A2, where v1 is the speed of the water in the fire hose and v2 is the speed of the water exiting the nozzle.
Therefore, v2 = v1 * (A1 / A2). Calculate v2 using these formulas.