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Sound: Resonance

Q- A 1.2 m long tube is closed at one end. A stretched wire is placed near the open end. The wire is 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance it sets the air column in the tube into oscillation at the column’s fundamental frequency. Find

(a) The frequency of air column. And

(b) The tension in the wire.

Thermodynamics

Q- Air enters the compressor of a gas turbine plant (operating at steady state) at ambient conditions of 1 bar, 250C with low velocity and exits at 10 bar, 3500C with a velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min and the power input to the device is 250 kW. Determine the mass flow rate of air through the compressor. Also determine the area A of the exit duct.

Solution:

Electrostatics: Coulomb's Law

Q- Two positive, 1 nC charges are located on the x-axis. Charge Q1 is located at the origin and charge Q2 is located at (4,0) which is 4 cm from the origin.

(a) Calculate the magnitude and direction of the force experienced by Q2 due to Q1

(b) A third charge Q3 of 2 nC is positioned on the y-axis at (0,4) which is 4 cm from the origin. Calculate the magnitude and direction of the total force on Q2 due to both Q1 and Q3.

Solution:

Rotational Motion: Angular Momentum

Q- A horizontal disk of mass 150g and radius 20 cm rotates at 10 rev/min about its axis, without any external torque. A flying bug of mass 15g lands vertically on the disk at a point half way to the center and stick to it. Find the angular speed of the disk just after the collision.

Solution:

Alternating Current Circuits

Q- A source of alternating voltage e = 10√2 sin ωt is connected to a resistor R = 100 Ω and a capacitor C = 0.5 μF in series.

(a) Plot impedance Z and phase difference θ between current and voltage versus frequency for a frequency range of zero to 10 kHz.

(b) Plot voltage across capacitor VC versus frequency for the frequency range of part (a)

(c) Plot voltage across resistor VR versus frequency for the frequency range of part (a).

Solution: