PhysicsLAB AP Free Response Question
2006 B1

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An ideal spring of unstretched length 0.20 m is placed horizontally on a frictionless table as shown above. One end of the spring is fixed and the other end is attached to a block of mass M = 8.0 kg. The 8.0 kg block is also attached to a massless string that passes over a small frictionless pulley. A block of mass m = 4.0 kg hangs from the other end of the string. When this spring-and-blocks system is in equilibrium, the length of the spring is 0.25 m and the 4.0 kg block is 0.70 m above the floor.
(a) On the figures below, draw free-body diagrams showing and labeling the forces on each block when the system is in equilibrium.

 (b) Calculate the tension in the string.

 (c) Calculate the force constant of the spring.

The string is now cut at point P.
 (d) Calculate the time taken by the 4.0 kg block to hit the floor.

 (e) Calculate the frequency of oscillation of the 8.0 kg block.

 (f) Calculate the maximum speed attained by the 8.0 kg block.

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