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1、Exercise:1. A particle moving along x axis starts from x0 with initial velocity v0. Its acceleration can be expressed in a=-kv2 where k is a known constant. Find its velocity function v =v(x) with the coordinate x as variable. 2. A particle moves in xy plane with the motion function as (all in SI).
2、Find (a) its velocity and (b) accelerationin the unit-vector notation. (c) Show that.3. A bullet of mass m is shot into a sand hill along a horizontal path, assume that the drag of the sand is , find the velocity function v(t) if and the gravitation of the bullet can be ignored. 4. what work is done
3、 by a conservative force that moves a particle in xy plane from the initial position to the final position . All quantities are in SI. 5. The angular position of a point on the rim of a rotating wheel is given by , where is in radians and t is in seconds. Find (a) its angular velocities at t=0s and
4、t=4.0s? (b) Calculate its angular acceleration at t=2.0s. (c) Is its angular acceleration constant? 6. A uniform thin rod of mass M and length L can rotate freely about a horizontal axis passing through its top end o (). A bullet of mass m penetrates the rod passing its center of mass when the rod i
5、s in vertical stationary. If the path of the bullet is horizontal with an initial speed vo before penetration and after penetration . Show that (a) the angular velocity of the rod just after the penetration is . (b) Find the maximum angular the rod will swing upward after penetration.AM7. A 1.0g bul
6、let is fired into a block (M=0.50kg) that is mounted on the end of a rod (L=0.60m). The rotational inertia of the rod alone about A is. The block-rod-bullet system then rotates about a fixed axis at point A. Assume the block is small enough to treat as a particle on the end of the rod. Question: (a)
7、 What is the rotational inertia of the block-rod-bullet system about A? (b) If the angular speed of the system about A just after the bullets impact is 4.5rad/s , What is the speed of the bullet just before the impact? 8. A clock moves along the x axis at a speed of 0.800c and reads zero as it passe
8、s the origin. (a) Calculate the Lorentz factor between the rest frame S and the frame S* in which the clock is rest. (b) what time does the clock read as it passes x=180m? 9. What must be the momentum of a particle with mass m so that its total energy is 3 times rest energy? 10. Ideal gas within a c
9、losed chamber undergoes the cycle shown in 4.0P(N/m2)40101.0V(m3)20302.03.0the Fig. Calculate Qnet the net energy added to the gas as heat during one complete cycle.11. One mole of a monatomic ideal gas undergoes the cycle shown in the Fig. temperature at state A is 300K. (a). calculate the temperat
10、ure of state B and C. (b). what is the change in internal energy of the gas between state A and state B? ()(c). the work done by the gas of the whole cycle .(d). the net heat added to the gas during one complete cycle. V(m3)P(Pa)C13100300AB 12. The motion of the electrons in metals is similar to the
11、 motion of molecules in the ideal gases. Its distribution function of speed is not Maxwells curve but given by. (0vvF)(vF v ) the possible maximum speed vF is called Fermi speed. (a) plot the distribution curve qualitatively. (b) Express the coefficient A in terms of vF. (c) Find its average speed v
12、avg. 13. Two containers are at the same temperature. The first contains gas with pressure, molecular mass , and rms speed. The second contains gas with pressure, molecular mass , and average speed . Find the mass ratio . 14. In a quasi-static process of the ideal gas, dW=PdV and dEint=nCvdT. From th
13、e 1st law of thermodynamics show that the change of entropy .Where n is the number of moles, Cv is the molar specific heat of the gas at constant volume, R is the ideal gas constant, (Vi, Ti) and (Vf, Tf) . are the initial and final volumes and temperatures respectively. 15. It is found experimental
14、ly that the electric field in a certain region of Earths atmosphere is directed vertically down. At an altitude of 300m the field is 60.0 N/C; at an altitude of 200m, the field is 100N/C. Find the net charge contained in a cube 100m on edge, with horizontal faces at altitudes of 200m and 300m. Negle
15、ct the curvature of Earth. 16. An isolated sphere conductor of radius R with charge Q. (a) Find the energy U stored in the electric field in the vacuum outside the conductor. (b) If the space is filled with a uniform dielectrics of known what is U* stored in the field outside the conductor then?17.
16、Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R. (a) show that, at a distance r from the cylinder axis (rR .18. A non-uniform but spherically symmetric distribution of charge has a volume density given as follow: (0 r R)(R r ) where is a positive cons
17、tant, r is the distance to the symmetric center O and R is the radius of the charge distribution. Within the charge distribution (r R), show that (a) the charge contained in the co-center sphere of radius r is , (b) Find the magnitude of electric field E(r) within the charge (r R). (c) Find the maxi
18、mum field Emax=E(r*) and the value of r*. 19. In some region of space, the electric potential is the following function of x,y and z: , where the potential is measured in volts and the distance in meter . Find the electric field at the point x=2m, y=2m . (express your answer in vector form) OqR1R2 2
19、0. The Fig. shows a cross section of an isolated spherical metal shell of inner radius R1 and outer radius R2. A point charge q is located at a distance from the center of the shell. If the shell is electrically neutral, (a) what are the induced charges (Qin, Qout) on both surfaces of the shell? (b)
20、 Find the electric potential V(0) at the center O assume V()=0.dAB21. Two large metal plates of equal area S are parallel and closed to each other with charges QA , QB respectively. Ignore the fringing effects, find (a) the surface charge density on each side of both plates, (b) the electric field a
21、t p1, p2 . (c) the electric potential difference between the two plates(d is the distance between palte A and B) 22In a certain region of space, the electric potential is where A,B,C are positive constant. The electric field is ; at which point is the electric field equal to zero .23. A 9.60-C point charge is at the center of a cube with sides of length 0.500m. The electric flux through one of the six faces of the cube is ; the answer would be if the sides were of length 0.250m.7