The steel ball A of diameter D slides freely on the horizontal rod which leads t

Question

The steel ball A of diameter D slides freely on the horizontal rod which leads to the pole face of the electromagnet. The force of attraction obeys an inverse square law, and the resulting acceleration of the ball is a= K/(L-x)^2, where K is a measure of the strength of the magnetic field. If the ball is released from rest at x = 0, show that the velocity v with which it strikes the pole face is v= 2 sqrt((K(L-(D/2)))/(L*D)). Plot the velocity as a function of x for 0< x < (L-D/2) for the following data: K = 2 and L = 6.

Explanation / Answer

a = dV/dt : where a is accleration, v is velocity and t is time and x is displacement V=dx/dt => dt = dx/V ? a = dV / dx/V => VdV = adx integrate both side while v goes from 0 to v final and x goes from 0 to L where a =K/(L-x)^2 (Vf^2)/2 = K/L ? Vf= v(2K/L)

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