A1-d nanomechanical oscillator is fabricated on a silicon microchip to have a mechanical resonance frequency of w 2t x 4.3 ghz (a) what are the energies (in ev) of the oscillator ground and first excited states? (b) compare the ground-to-first-excited-state energy difference with the ground-to-first-excited- state energy difference in the hydrogen atom. by how many times is it bigger or smaller? (c) consider the ground state wavefunction for the harmonic oscillator, derived in class. use this to show that the expectation values of the kinetic energy and potential energy operators are equal for this wavefunction. how do these relate to the ground state energy? (d) the oscillator is cooled to its ground state using the methods of laser cooing. given a mass of 31 fg (femtograms), what are the quantum mechanical uncertainties in its position and speed after the cooling if the oscillator remains in the ground state, how low must the temperature be (to avoid excitations to the first excited state)?

For problems 1-3, consider a simple dc brush motor with a permanent magnet stator. with an an consider a simple dc brush motor with a permanent magnet ae supply voltage of 100 v, the no-load speed of the motor is 1000 rpm. this motor can provide a torque of 1.9 n-m at 800 rpm drawing a current of 2 a current are both zero at no load.) 1. with an armature supply voltage of 100 v, the motor is operated at 900 rpm. what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input? what is the energy efficiency of the motor? with an armature supply voltage of 100 v, the motor is operated at 1100 rpm (where it acts as a generator). what torque input is required? what mechanical power is required what current is generated? what is the electrical power generated? what is the energy efficiency of the motor acting as a generator? 2. with an armature supply voltage raised to 120 v, the motor is operated at 1000 rpm. what is the no-load speed? what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input what is the energy efficiency of the motor? 3.

Most short-period comets do not have randomly oriented orbits because

Researchers conducted an experiment to identify the effects of three different hand sanitizers on the growth of bacteria. the researchers grew one type of bacteria in twenty-four identical covered petri dishes. then, they opened eighteen petri dishes and applied the three hand sanitizers to six petri dishes each. they left the remaining six petri dishes closed as a control group. when the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. the researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. which statement best explains why the researchers’ conclusion was not justified? the experiment tested too many variables. the control group was not treated the same as the experimental group. the sample size of twenty-four petri dishes is not large enough. the single type of bacteria is not adequate to make any conclusions.