It is desired to study the rather rapid vertical motion of the moving contact of

Question

It is desired to study the rather rapid vertical motion of the moving contact of a magnetically operated switch. To do this, the contact is attached to one end (O) of a horizontal fishline of total mass 5 g (5X10^-3 kg) and total length 12.5m. The other end of the mass line passes over a small effectively pulley, and a mass of 10 kg is hung from it, as shown in the sketch. The contact is actuated so that the switch (initially open) goes into the closed position, remains closed for a short time, and opens again. Shortly thereafter the string is photographed, using a high speed flash, and it is found to be deformed between 5 and 6 m, as shown (x=0 is the point O where the string is connected to the contact.)

(a) For how long was the switch completely closed?

(b) Draw a graph of the displacement of the contact as a function of time, taking t=0 to be the instant at wich the contact first began to move.

(c) What was the max speed of the contact? Did it occur during closing or during opening of the switch?

(d) At what value of t was the photograph taken? (Assume g = 10m/s^2)

Explanation / Answer

a) speed of the wave = c = ?(T/(m/L)) = ?(10*10/(5e-3/12.5)) = 500 m/s ?t = ?x/c = (6-5)/500 = 0.002 s c) It occurs during closing: ?t' = ?x'/c = (5.2-5)/500 = 0.0004 s v = ?y/?t' = 5e-3/0.0004 = 12.5 m/s d) t = 5/500 = 0.01 s

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