Classical Mechanics Answers

1. A manometer containing oil (p = 850 kg/m³) is attached to a tank filled with air. If the oil-level difference between the two columns is I50 cm and the atmospheric pressure is 98 kPa, determine the absolute pressure of the air in the tank.

2. Pressure is often given in terms of a liquid column and is expressed as “pressure head." Express the standard atmospheric pressure in terms of (a) mercury (SG = 13.6). (b) water (SG = 1.0). and (c) glycerin (SG = 1.26) columns. Explain why we usually use mercury in manometers.

1. A pressure gauge connected to a tank reads 500 kPa at a location where the atmospheric pressure is 94 kPa. Determine the absolute pressure in the tank.

2. Determine the atmospheric pressure at a location where the barometric reading is 735 mmHg. Take the density of mercury to be 13,600 kg/m³.

1. The 5-m-wide wall is in the form of a parabola. If the depth of the water is h = 4 m, determine the magnitude and direction of the resultant force on the wall.

2. The Tainter gate for a water channel is 1.5 m wide and in the closed position, as shown. Determine the magnitude of the resultant force of the water acting on the gate. Also, what is the smallest torque T that must be applied to open the gate if its weight is 30 kN and its center of gravity is at G.

1. Determine the placement d of the pin on the 0.5-m-wide rectangular gate so that it is on the verge to rotate clockwise (open) when wastewater reaches a height h = 2.5 m. What is the resultant force acting on the gate?

2. The tank is filled to its top with an industrial solvent, ethyl ether. Determine the resultant force acting on the plate ABC, and its location on the plate measured from edge AB of the tank. Use the formula method. Take p_cc = 715 kg/m³.

Part 1. The tide gate opens automatically when the tidewater at B subsides, allowing the marsh at A to drain. For the water level h = 4 m, determine the horizontal reaction at the smooth stop C. The gate has a width of 2 m. At what height h will the gate be on the verge of opening?

Part 2. Determine the critical height h of the water level where the concrete gravity darn starts to tip over. The density of concrete is p_c = 240 Mg/m³. Hint: Work the problem using a 1-m width of the dam.

Part 1. Water in the reservoir is used to control the water pressure in the pipe at A. If h = 200 mm, determine this pressure when the mercury is at the elevation shown. Take p_Hg = 13 550 kg/m³. Neglect the diameter of the pipe.

Part 2. The two tanks A and B are connected using a manometer. If waste oil is poured into tank A to a depth of h = 0.6 m, determine the pressure of the entrapped air in tank B. Air is also trapped in line CD as shown. Take p_o = 900 kg/m³ p_W = 1000 kg/m³.

Part 1. If the absolute pressure in a tank is 140 kPa, determine the pressure head in mm of mercury. the atmospheric pressure is 100 kPa.

Part 2. Oxygen in a tank has an absolute pressure of 130 kPa. Determine the pressure head in mm of mercury. The atmospheric pressure is 102 kPa.

Consider the following:

If two equal mass objects have the same net force acting on them, then they will be experiencing the same change in speed.

(a) Is this statement valid?

(b) If you contend the statement is valid, how do you know?

(c) If you contend the statement is invalid, what is wrong with it?

(d) If the statement is invalid, restate it to give a valid statement.

(e) Is the valid statement (original, or your revision) a conditional or bi-conditional? How do you know?

(f) Would the following investigation test, i.e. provide data to either support or contradict, the valid hypothesis (either the original or your revision), or will it fail to test the hypothesis? Explain.

A person runs a ski mobile on a frozen lake varying how the speed changes during the runs for 24 trials and measures the net force that acts on the ski mobile. Each time she finds if the speed changes there is net force.

What do you mean by eccentricity

Isaac applies a force of 40N at an angle of 60°up from the horizontal to a wooden rod using a spring scale.If he generatesa torque of 73 m.N,how long was the rod?