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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?
Blocks with masses of 2, 3, and 5 are lined up in a row on a frictionless table. All three are pushed forward by a 59 force applied to the 2 block. How much force does the 3.00 kg black exert on the 5 kg block.
An electromagnetic wave in a vacuum has an instantaneous magnetic field strength of 0.000000735 T at a certain point. What is the instantaneous electric field strength of the wave at this point
A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92e-25 kg and charge 3.20e-19 C from related species. calculate the thermal energy produced in the cup
The position of a particle in cm is given by x = (7) cos 9?t, where t is in seconds, What is the frequency, What is the period, What is the amplitude of the particle's motion
Two water waves meet at the same point, one having a displacement above equilibrium of 17 cm, what is the resulting displacement above equilibrium
Obtain the wavelength in vacuum for blue light, whose frequency is 6.58 1014 Hz
a man with a mass of 80 kg sits on a chair of mass 10 kg.a find the weights of the man and the chair.b the chair exerts
We have to do work to lift something against the force of gravity. How much work is required to lift your textbook (about 2 kg) from your backpack on the floor to the desk (about 1 meter)?
If we drop a small metal sphere into the water and watch its motion, it will quickly reach terminal velocity. what is the Reynold's number of this sphere
For a research project, a student needs a solenoid thatproduces an interior magnetic field of 0.0300 T. Determine the number of layers of wire needed and the total length of the wire
a hospital patient has been given 131i half life 8.04 days which decays at 4.5 times the acceptable level for exposure
A conducting spherical shell with inner radius a and outer radius b has a positive charg Q located at its center. derive expressions for the electric field magnitude in terms of the distance r from the center
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