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20 17 Nanchang one-mode answer mathematics
(1) the induced electromotive force is E 1=BL(v2-v 1),

The induced current is I 1=E 12R,

Let F 1 represent the ampere force of the magnetic field on each rod,

Ampere force: F 1=I 1BL,

Let a 1 and a2 represent the acceleration of ab rod, cd rod and object M respectively, and F2 represents the tension in the rope.

According to Newton's law, F 1=ma 1, Mg-F2=Ma2, F2-F 1=ma2,

From the above solution: a 1=B2L2(v2? v 1)2Rm,a2=2MgR? B2L2(v2? v 1)2R(M+M);

(2) At last, the acceleration of ab rod and cd rod is the same, let it be a and the speed difference be △v,

The induced electromotive force is E2=BL△v, and the induced current is I2=E22R.

Let F3 represent the magnitude of the magnetic field ampere force on each rod, then: F3=I2BL,

F4 represents the tension in the rope, which is known from Newton's law:

F3 = mA, Mg-F4 = mA, F4-F3 = mA,

From the above solution, it can be seen that △ V = 2RMMG (2m+m) B2L2;

Answer: (1) When the speeds of ab and cd reach v 1 and v2 respectively, the acceleration of the two levers is B2L2(v2? v 1)2Rm、2MgR? B2L2(v2? v 1)2R(M+M);

(2) The final speed difference between 2)ab rod and cd rod is 2 rmmg (2m+m) B2l2.