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1. What water pressure must a pump located on the first floor supply to have water on the 11th floor of a building with a gauge pressure of [tex]25 \, \text{lb/in}^2[/tex]? Assume that the distance between each floor is 11 ft.

2. Water flows through a hose with a diameter of 0.24 inches at a velocity of 14.5 m/s. Find the flow rate of the hose in L/min.

3. A high-speed industrial drill with a diameter of 9.8 cm develops 1.85 hp at 750 RPM. What torque and force is applied to the drill bit?

4. The area of the large piston in a hydraulic jack is [tex]0.025 \, \text{m}^2[/tex]. The area of the small piston is [tex]12 \, \text{cm}^2[/tex]. (a) What force must be applied to the small piston if a weight of 800 N is to be lifted?

5. A cylindrical rod of steel (E = 107 GPa, having a yield strength of 90 MPa) is to be subjected to a load of 8500 N (1900 lb). If the length of the rod is 80 cm (31.5 in.), what must be the diameter to allow an elongation of 0.38 cm?

6. Seattle Main Street has an angle of 22 degrees. If a ball initially has a velocity of 18 km/hr and travels 150 yards, what would be its final velocity?

Answer :

To determine the water pressure required for the pump to supply water on the 11th floor of a building, we need to consider the gauge pressure and the height of the building.

The gauge pressure given is 25 lb/in². To convert this to units that match the height measurement (feet), we need to convert pounds per square inch to pounds per square foot. Since there are 12 inches in a foot, we can multiply the gauge pressure by 12² (144) to get the pressure in pounds per square foot. To determine the force that must be applied to the small piston in a hydraulic jack, we can use the principle of Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions.

To calculate the diameter of a steel rod that can withstand a load of 8500 N and allow for an elongation of 0.38 cm, we need to use the formula for stress: Stress = Force / Area and the formula for strain: Strain = Change in length / Original length. First, let's calculate the stress: Stress = 8500 N / Area. Next, let's calculate the strain. Therefore, the diameter of the steel rod should be approximately 1505.46 mm to allow for an elongation of 0.38 cm. To determine the final velocity of a ball on Seattle Main Street with an initial velocity of 18 km/hr and a travel distance of 150 yards, we need to consider the angle of the street and the acceleration due to gravity. Let's assume that the angle of the street refers to the incline or slope of the road. In this case, we need to consider the horizontal and vertical components of the ball's velocity separately.

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