A large block of mass M slides on a frictionless horiztonal surface and is attac

Question

A large block of mass M slides on a frictionless horiztonal surface and is attached to a wall by a ideal spring of contant k. An ideal string is attached to the block and runs over an ideal pulley to a second block of mass m. In equilibrium, m hangs a distance L below the pulley, as in Fig. 8.48. An external force is applied to pull m down to a distance 1.5L below the pulley.
(a) What work is done by the external force to pull m down?
(b) If m is now released, how far below the pulley is it when it nexts comes to rest?
(c) What is the upward speed of m as a function of its distance s below the pulley?
(d) What is the tension in the string as a function of s?

A large block of mass M slides on a frictionless horizontal surface and is attached to a wall by a ideal spring of constant k. An ideal string is attached to the block and runs over an ideal pulley to a second block of mass m. In equilibrium, m hangs a distance L below the pulley, as in Fig. 8.48. An external force is applied to pull m down to a distance 1.5L below the pulley. What work is done by the external force to pull m down? If m is now released, how far below the pulley is it when it nexts comes to rest? What is the upward speed of m as a function of its distance s below the pulley? What is the tension in the string as a function of s?

Explanation / Answer

a) W = kL^2 /8

b) s_top = L/2

c) v = {2[W-k(s-L)^2 / 2]/(m+M)}^1/2

d) T = mg -mk(s-L)/(m+M)

for all equations above S is measured frm the pully down to the mass, with down defined as the pasitive S direction

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