Problem 23.54 describes an electron revolving around a proton in a circle of rad

Question

Problem 23.54 describes an electron revolving around a proton in a circle of radius r. The question states to derive an expression for the electrons speed by equating the electric force to the electron's mass times its acceleration. The problem becomes much simpler if you instead equate the electric force to the centripital force, and I have no problems answering the question using this procedure. However, when I attempt to start off by equating F(electric) to the electrons mass times its acceleration, I get stuck as I can't figure out what to input for position or time in the kinematic equations.

Explanation / Answer

Ummm... yeah. . When they talk about the electron's acceleration, they arereferring to its circular motion. So acceleration is v2/r   and they want you to write .     F = ma   or     F = mv2 /r          and thenreplace F with the electrical force. . In other words, they are telling you to do exactly what youwant to do... electrical force = centripetal force (becausethe centripetal acceleration is the only acceleration). . The kinematics equations are only for motion in onedimension, i.e. motion in a straight line.

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