Problem Set 8

These problems on fluids and oscillations are due November 14. The reading is Ch 10 and Ch 11.

(1) Ch 10 P 19 An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is (a) 28.0 cm higher, (b) 4.2 cm lower, than the mercury in the tube connected to the tank?

(2) Ch 10 P 20 In working out his principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long, thin tube of radius r=0.30 cmvertically into a wine barrel of radius R=21 cm. He found that when the barrel was filled with water and the tube filled to a height of 12 m, the barrel burst. Calculate (a) the mass of water in the tube, and (b) the net force exerted by the water in the barrel on the lid just before rupture.

(3) Ch 10 P 25 A spherical balloon has a radius of 7.35 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

(4) Ch 10 P 43 If wind blows at 35 m/s over a house, what is the net force on the roof if its area is 240 m^2 and is flat?

(5) Ch 10 P 68 A hydraulic lift is used to jack a 970-kg car 12 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 250 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 12 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 12 cm? (e) Show that energy is conserved.

(6) Ch 11 P 5 An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it?

(8) Ch 11 P 13 An object with mass 3.0 kg is attached to a spring with spring stiffness constant 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s (a) Calculate the amplitude of the motion. (b) Calculate the maximum velocity attained by the object. [Hint: Use conservation of energy.]

(9) Ch 11 P 19 A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0.65 s. (a) Write down the equation giving the pumpkin’s position y as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. (b) How long will it take to get to the equilibrium position for the first time? (c) What will be the pumpkin’s maximum speed? (d) What will be its maximum acceleration, and where will that first be attained?