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A block of mass m is being lifted vertically by a uniform
Chapter , Problem 71(choose chapter or problem)
A block of mass m is being lifted vertically by a uniform rope of mass M and length L. The rope is being pulled upward by a force applied to its top end, and the rope and block are accelerating upward with an acceleration of magnitude a. Show that the tension in the rope at a distance x (where x < L) above the block is given by (a + g)[m + (x/L)M].
Questions & Answers
QUESTION:
A block of mass m is being lifted vertically by a uniform rope of mass M and length L. The rope is being pulled upward by a force applied to its top end, and the rope and block are accelerating upward with an acceleration of magnitude a. Show that the tension in the rope at a distance x (where x < L) above the block is given by (a + g)[m + (x/L)M].
ANSWER:Step 1 of 2
Mass of the block: m
Mass of the rope: M
Length of the rope: L
We will calculate mass per unit length:
Mass per unit length of the rope is: \(\frac{M}{L}\)
Mass of the rope at a distance “x” from the block: \(\frac{M}{L} x\)