A charged particle is connected to a string that is is tied to the pivot point P

Question

A charged particle is connected to a string
that is is tied to the pivot point P. The
particle, string, and pivot point all lie on
a horizontal table (consequently the figure
below is viewed from above the table). The
particle is initially released from rest when
the string makes an angle 71 with a uniform
electric field in the horizontal plane (shown in
the figure).
71 degrees
2.4 m
387 V/m
P
0.012 kg
3 µC
initial
release
!
P parallel
Determine the speed of the particle when
the string is parallel to the electric field.
Answer in units of m/s

Explanation / Answer

Unfortunately, when I prepared this solution, I forgot that the insignificance of gravity in this problem suggests that the particle is massless, making it impossible to define an acceleration given by Newton's Second Law. The reasoning I came up with may still help you get started if you're completely lost. My apologies. The electric force acting on the object essentially exerts a torque on the particle-string system and causes it to undergo an angular acceleration. The dynamics of the problem suggest that the tangential acceleration a is (qEsin?)/m, where ? is the 62 degree angle given in the problem. The particles angular acceleration is related to the tangential by: a/r = a where r is the length of the string (which is the radius of rotation in this case), and a is the angular acceleration. The rest is kinematics (though we must employ rotational kinematics to arrive at the solution)! It seems the logical equation to use is: where ? is the angular speed, a is the angular acceleration, and ? is the angular position of the particle as it rotates in the electric field.

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