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A flexible inextensible string of length L is threaded into a smooth tube, into which it snugly fits. The tube contains a right-angled bend and is positioned in the vertical plane so that one arm is vertical and the other horizontal. Initially, at t = 0, a length Y o of the string is hanging down in the vertical atm. The string is released and slides through the tube, so that at any subsequent time t later, it is moving with a speed dy/dt , where yet) is the length of the string that is then hanging vertically. (a) Show that in terms of the variable-mass problem v rel = 0, so that the equation of motion has the form mdvldt = F ext . (b) Show that the specific equation of motion is d 2 y/dt 2 = gy/L. (c) Show that is a solution to the equation of motion [by substitution into (b)] and discuss the solution.

A flexible inextensible string of length L is threaded into a smooth tube, into which it snugly fits. The tube contains a right-angled bend and is positioned in the vertical plane so
that one arm is vertical and the other horizontal. Initially, at t = 0, a length Yo of the string is hanging down in the vertical atm. The string is released and slides through the
tube, so that at any subsequent time t later, it is moving with a speed dy/dt, where yet) is the length of the string that is then hanging vertically. (a) Show that in terms of the variable-mass problem vrel = 0, so that the equation of motion has the form mdvldt = Fext. (b) Show that the specific equation of motion is d2y/dt2 = gy/L. (c) Show that
is a solution to the equation of motion [by substitution into
(b)] and discuss the solution.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
8 years ago
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