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?
11.Through a pipe 15.0cm in diameter, water is pumped from the Gefersa River
up to Burayu town, located on the west side of Addis Ababa. Suppose, the
river is at an elevation of 564m, and the village is at an elevation of 2096m.
(a) What is the minimum pressure at which the water must be pumped if it is
to arrive at the town? (b) If 4500m3 are pumped per day, what is the speed
of the water in the pipe?
12.On an unknown temperature scale, the freezing point of water is -15.0°U and
the boiling point is +60.0°U. Develop a linear conversion equation between this
temperature scale and the Fahrenheit scale.
W9. To calculate the buoyant force, we need to use the formula:
Buoyant Force = Volume submerged x density of fluid x acceleration due to gravity
Given that the body is 95% submerged, the volume submerged can be calculated as follows:
Volume submerged = (95/100) x Total volume
Now, if the total volume is V, then the volume submerged is 0.95V. The buoyant force can then be calculated as:
Buoyant Force = 0.95V x density of water x 9.81 m/s^2
W10. (a) Before the metal is immersed, the tension in the string is equal to the weight of the aluminum block:
Tension = mg = 1.00kg x 9.81 m/s^2 = 9.81 N
(b) After the metal is immersed, the tension in the string will decrease because the buoyant force will partially support the weight of the block. The tension can be calculated as:
Tension = mg - Buoyant Force
W11. To calculate the speed with which the water exits the nozzle, we can use the principle of conservation of mass, which states that the volume flow rate remains constant throughout the hose and nozzle:
Area of hose x speed of water in hose = Area of nozzle x speed of water in nozzle
Using the given diameters, we can calculate the areas:
Area of hose = π(0.0635m/2)^2 = 0.00318m^2
Area of nozzle = π(0.022m/2)^2 = 0.000379m^2
Now, we can substitute these values into the conservation of mass equation to solve for the speed of water in the nozzle.
W12. (a) To calculate the minimum pressure at which the water must be pumped to arrive at the town, we need to consider the change in height the water is pumped:
ΔP = ρgh
Where:
ρ = density of water
g = acceleration due to gravity
h = change in height
Substitute the values and calculate the pressure.
(b) To calculate the speed of the water in the pipe, we can use the principle of conservation of energy, which states that the sum of the pressure energy, kinetic energy, and potential energy remains constant throughout the system. We can calculate the speed using this principle.
W13. To develop a linear conversion equation between the unknown temperature scale (U) and the Fahrenheit scale, we can use the two reference points given:
U1 = -15.0°U corresponds to -10°C on the Celsius scale
U2 = +60.0°U corresponds to 140°C on the Celsius scale
Using these two reference points, we can set up a linear equation and solve for the conversion between the U scale and the Fahrenheit scale.