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**Eujacwta** · 05-06-2010, 05:46 AM

A long uniform slab of with mass M is sliding on a "frictionless" horizontal surface with (constant) speed S before a small, dense block with mass 2M is placed on top of the front of it by a person nearby. The small block has an initial velocity of ZERO with respect to the fixed horizontal surface so it immediately starts skidding along the surface of the moving slab. The coefficient of kinetic friction between the block and slab is Mu . As the block skids the slab slows down until the velocities of both objects with respect to the fixed surface are identical; after which they move together. ( The block does NOT reach the back of the slab and fall off!)

a) Develop an expression for the time it takes the block and slab to reach the same velocity. Express your answer in terms of g, Mu, and S.
b) Find an expression for the final speed of both objects with respect to the fixed surface.
c) Find the magnitude of the frictional force between the objects once the slab and block are both gliding with the same speed.

05-06-2010, 05:46 AM	#18
Eujacwta Join Date Nov 2005 Posts 439 Senior Member	A long uniform slab of with mass M is sliding on a "frictionless" horizontal surface with (constant) speed S before a small, dense block with mass 2M is placed on top of the front of it by a person nearby. The small block has an initial velocity of ZERO with respect to the fixed horizontal surface so it immediately starts skidding along the surface of the moving slab. The coefficient of kinetic friction between the block and slab is Mu . As the block skids the slab slows down until the velocities of both objects with respect to the fixed surface are identical; after which they move together. ( The block does NOT reach the back of the slab and fall off!) a) Develop an expression for the time it takes the block and slab to reach the same velocity. Express your answer in terms of g, Mu, and S. b) Find an expression for the final speed of both objects with respect to the fixed surface. c) Find the magnitude of the frictional force between the objects once the slab and block are both gliding with the same speed.
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