Please help 2~~

2011-02-26 8:49 pm
1. A certain periodic driving force is applied to a system which has a natural frequency of oscillation. This results in the oscillation of the system. What would happen if the frequency of the periodic driving force is close to the natural frequency of the system?
(1) The displacement of the system from its equilibrium position would always be in phase with the driving force
(2) The amplitude of oscillation would become infinite if there are no damping forces.
(3) The system would eventually oscillate at the frequency of the driving force if some damping forces are present.

2.Two vessels X and Y of volumes Vx and Vy, connected by a tube of negligible volume and kept at temperatures Tx and Ty respectively, contain the same ideal gas. What is the value of the ratio number of molecules of X/ number of molecules of Y?

3. The charge-to-mass ratio for an electron is 1.76 X 10^-11 C kg^-1. What is the ratio of the electrostastic force on an electron situated in an electric field of intensity 200Vm^-1 to the gravitional force on the Earth surface?

4. A charged particle is acclerated across the gap between two parallel metal plates maintained at a certain potential difference in a vacuum. Assuming there is no gravitional force, the energy acquired by the charged particle in crossing the gap depends on
(1) potential difference between the plates
(2) the charge of the charged particle
(3) the width of the gap

5. An electron moves in a circular path in a uniform magnetic field of flux denbsity 1mT. If an alpha particle of the same speed followa an identical path, what must be the magnetic field? Given the mass of an alpha particle is 7200 times that of an electron.

6. An ammeter is connected in series with an elctric motor which is running freely, and the reading noted. When the motor raised a load at a steady speed, the reading of the ammeter will increase to a maximum value and then decrease. Is this statement correct and explain.
更新1:

For Q.1), is statement 3 correct also?

更新2:

For Q.5, are they in same direction?

回答 (1)

2011-02-26 9:40 pm
✔ 最佳答案
Since you give so many questions in one post, I could only give brief answers, as space here is limited.

1. statement (2) is correct. Because no damping ==> no energy dissipation.

2. The pressure of the 2 gases are equalUse P = nRT/V(nx)RTx/Vx = (ny)RTy/Vyhence, (nx)/(ny) = (Ty/Tx).(Vx/Vy)
3.Electrostatic force = e(200), where e is the electronic chargeGravitational force = mg, where m is the electronic masshence, e(200)/mg = 200 x (1.76 x 10^11)/9.81 = 3.6 x 10^12
g is taken to be 9.81 m/s2
[note that you have given the wrong value for the e/m ration for electrons]

4. Energy gained = charge x p.d. across plateshence, statements (1) and (2) are correct.
5. since mv^2/R = qvB
where m is the mass of particle of charge q, v is speed, R is radius, and B is the magnetic flux density.
For electron: mv^2/R = ev(1)For alpha: (7200m)v^2/R = (2e)vBDividing: 7200 = 2B
i.e. B = 3600 mT

6. When the load is raised at steady speed, the current through the motor is constant. The result is apparent by the Law of conservation of energy.


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