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1. The fundamental frequency of a vibrating guitar string is modeled by the following equation:
f=12LTgμ
Where:
f = vibration frequency in HertzL = length of string in meters T = string tension in Newtons μ = string density
Determine the appropriate unit for μ if the preceding equation is to be homogeneous in units?
2. The strength of a tree branch is approximately proportional to its cross-sectional area while its weight is proportional to its volume. If you scale up a branch by a factor two (i.e., double all of its linear dimensions), determine (a) by what factor its strength increased and (b) by what factor its weight increased.
3. The speed of sound in air is approximately 340 m/s. The speed of sound in steel is approximately 5900 m/s. If your friend strikes one end of a steel pipe with a hammer while you listen at the other end, you will hear two distinct sounds: one traveling through the air and the other traveling through the steel pipe. If the pipe is 1.94 seconds elapses between the two distinct sound, how long is the steel pipe.
4. A "teeter-totter" (or "see-saw" if you prefer) has a 50lb child sitting at one end, 10ft from the center pivot point (fulcrum). How far from the center point should a 125lb adult sit in order to balance the teeter-totter?
A wire of radius r and length L and resistivity ρ has a resistance R. Estimate what is the new resistance if the wire is stretched to 4 times its original length
A 4 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell). If the mass accelerates downward at 4.90 m/s2, what is the mass of pulley.
A glass plate having parallel faces and a refractive index of 1.55 lies at the bottom of a liquid of refractive index 1.62. Compute the angle of refraction of this light in the glass
An object is thrown vertically upward with a speed of 19.83mph. How much time from launch will it take to reach the bottom
calculate the electric potential due to a dipole whose dipole moment is 4.5times10-30 cm at a point 1.4times10-9 m
An important news announcement is trans- mitted by radio waves to people who are 122 km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 1.2 m from the newscaster. Take the speed of sound in air to be 345 ..
A concave mirror and a plane mirror (f = 8.30 cm) are facing each other and are separated by a distance of 23.0 cm. An object is placed among the mirrors and is 11.5 cm from each mirror.
A microscope with a tube length of 200 mm achieves a total magnification of 800x with a 40x objective and a 20x eyepiece. How far is the sample from the objective lens
each of the plates of a parallel plate capacitor has an area of 10.6cm2 and a plate separaton difference of 2mm.
question all our household circuits are wired in parallel. below is an example of a simple household circuit with 3
Several children are on a sled pulled by a four-wheeler across a level snow-covered field. determine the work done on the sled by the tension in the rope in 10.0 s
Two carts with masses of 4.80 kg and 2.78 kg move toward each other on a frictionless track with speeds of 4.94m/s and 3.17m/s respectively. The carts stick together after colliding head-on. Find out the final speed.
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