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20 13 Foshan two-mode mathematics
After entering the electric field and magnetic field, P is subjected to three forces: electric field force, gravity and Lorentz force.

Electric field force f = QE = 0.3n

Gravity G=mg=0.3N?

It can be seen that the electric field force and gravity are equal in magnitude and opposite in direction, and the two forces are balanced.

Therefore, it is equivalent to that P only receives Lorentz force in electric and magnetic fields, and makes uniform circular motion.

(2)P is subjected to Lorentz force in magnetic field, which provides centripetal force for P to do circular motion.

So qvB=mv2R?

The radius of circular motion of p R=mvqB? ①

Period t = 2π RV = 2π MQB

T= 12s substitute data.

Judging from the known conditions, there is t =1.0s =112t.

So as shown in the figure below:

P = 30 locus central angle θ?

As can be seen from the figure on the right, the trajectory radius r = dsinθ = 0.2msin30 = 0.4m.

Combined with ① formula, v = 0.2m/s.

(3) When P and Q collide, the momentum of the system is conserved and exists.

mv0=mv+mQvQ

Substituting the data can get VQ = 0.6m/s.

After the collision, the horizontal direction of Q is only affected by friction. Applying Newton's second law, there are

μmg=ma

Get a=0.8m/s2.

Because Q moves in a straight line with uniform speed under the action of friction, the speed is taken as the positive direction and the acceleration a=-0.8m/s2.

So the movement time before q stops t' = 0? vQa=0? 0.6? 0.8s=0.75s?

Because t' < t means t'