Question

1. A block of mass m slides down a frictionless ramp of unknown length l that makes an angle ? to the horizontal as shown in figure below. The block reaches the bottom of the ramp with speed v. The horizontal surface is frictionless except for a rough patch from distance d to 2d. The coefficient of kinetic friction between the block and the rough patch is 0.25. After the block passes over the rough patch it has a perfectly inelastic collision with another block of mass 2m located at distance 3d from the bottom of the ramp. After the collision the blocks travel to the right and compress the spring of unknown spring constant by an amount ?x = d/8. The answer to each of the questions below must be in terms of m, ?, v, and fundamental constants. (a) Calculate the length of the ramp.

          1. A block of mass m slides down a frictionless ramp of unknown length l that makes an angle ? to the horizontal as shown in figure below. The block reaches the bottom of the ramp with speed v. The horizontal surface is frictionless except for a rough patch from distance d to 2d. The coefficient of kinetic friction between the block and the rough patch is 0.25. After the block passes over the rough patch it has a perfectly inelastic collision with another block of mass 2m located at distance 3d from the bottom of the ramp. After the collision the blocks travel to the right and compress the spring of unknown spring constant by an amount ?x = d/8. The answer to each of the questions below must be in terms of m, ?, v, and fundamental constants.
(a) Calculate the length of the ramp.

1. A block of mass m slides down a frictionless ramp of unknown length l that makes an angle ? to the horizontal as shown in figure below. The block reaches the bottom of the ramp with speed v. The horizontal surface is frictionless except for a rough patch from distance d to 2d. The coefficient of kinetic friction between the block and the rough patch is 0.25. After the block passes over the rough patch it has a perfectly inelastic collision with another block of mass 2m located at distance 3d from the bottom of the ramp. After the collision the blocks travel to the right and compress the spring of unknown spring constant by an amount ?x = d/8. The answer to each of the questions below must be in terms of m, ?, v, and fundamental constants.
(a) Calculate the length of the ramp.

Added by John T.

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