the set up is: A small object of mass m hangs at rest at the end of a massless e
ID: 1964627 • Letter: T
Question
the set up is:
A small object of mass m hangs at rest at the end of a massless elastic string of relaxed length L whose other end attached to the ceiling of a room. An upward-pointing y-axis has its origin (y = 0) at the position of the stationary mass. In this equilibrium situation, the string is stretched from its relaxed length by a distance mg/k, where mg is the weight of the object and k is the Hooke’s Law force constant of the stretched string. The ceiling is therefore located at y = L + mg/k in the given coordinate system.
the question is:
The object is now pulled downward, further stretching the string, and is released at rest at y =2mg/k at t = 0. The object then moves upward with simple harmonic motion about its equilibrium position at y = 0 of the form y(t) = A cos(t + ), with = (k/m), until it reaches y = mg/k, at which point the string becomes slack. Above y = mg/k the object is still attached to the slack string, but is in free fall with constant acceleration ay = g. What is the maximum value of y reached by the object, expressed in terms of the given symbols k, m, and g? Assume L is long enough so that the object does not hit the ceiling. [Hint: find the upward velocity of the object at y = mg/k.]
Explanation / Answer
energy stored in spring+gravitational energy=mgx 0.5k(2mg/k)^2+mg(2mg/k)=mgx 0.5kmg(2/k)^2+mg(2/k)=x x=mg[4/k] it will go upto y=-2mg/k+4mg/k=2mg/k
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