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Sound and Vibration

Q- A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?

Mechanics: Conservation of momentum

Q- Two railroad cars moving on same track towards each other. One of mass 10000 kg with speed 0.3 m/s and the other of mass 15000 kg with speed of 0.1 m/s.

(a) What is the magnitude of their common velocity after they coule together?

(b) How much kinetic energy is lost during collision?   

Solution:

Thermodynamics: Specific Heat Capacity

Q- A well-sealed room contains 80 kg of air at 200 kPa and 25°C. Now solar energy enters the room from windows at an average rate of 1 kJ/s while a 100-W fan is turned on to circulate the air in the room. If heat transfer through the walls is negligible, what will be the air temperature in the room in 30 min?

Solution:

Rotation: Toppling

Q- I have a 1.5 m tall air compressor that weights 50 kg with a 0.5 m square base. I have a cart that is 1m x 2m. The surface of the cart where the compressor will be mounted is 0.25 m off the ground. The cart wheels are in the corners, it is rated to carry 500 kg and weighs 75 kg. If the compressor is placed centered on the cart, will it have a tip over problem because of a high center of gravity.

Solution:

Electrostatics: Induced Charges

Q- A point charge q is placed between two infinitely large conducting parallel planes with distance d between them, such that it is at a distance x from one plane.  Find the charges induced on each plane.

Solution:

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