Unformatted text preview: ME 302 Homework 2 Due Friday, Jan. 21 Book Problems: The concept problems can all be done on a single piece of paper. Please start all other problems on a fresh sheet of paper. 1‐5C, 1‐8C, 1‐10C, 2‐64, 2‐82E 1): A 5‐kg piston in a cylinder with a diameter of 100 mm is loaded with a linear spring (F=kx) where k is the spring constant and x is the displacement of the spring) and an outside atmospheric pressure of 100 kPa. The spring exerts no force on the piston when it is at the bottom of the cylinder. The pressure and volume of the cylinder are initially 400 kPa and 0.4 L, respectively. A valve is opened to let some air in, causing the piston to rise by 2 cm. Find: a) the deflection of the spring when the pressure in the cylinder is 400 kPa (Ans: 0.05094m) b) the spring constant, k (Ans: 45.29 kN/m) and c) the final pressure after the piston has risen (Ans: 515.3 kPa) . 2): A liquid with density ρ is filled on the top of a piston with mass mp in a cylinder with cross‐
sectional area A. The distance between the top of the piston and the top of the tank is H when the piston is at the bottom of the cylinder. Air is let in under the piston so it pushes up spilling the liquid over the edge. Deduce the formula for the air pressure as a function of piston displacement, h. h H ...
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 sectional area A.

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