Question

A 2.5 kg block is placed upon a flat piece of wood with 6.0 kg mass. A 80 N force is applied to the wood. This system is upon the floor the floor with no friction. The static friction between the block and the wood is 0.7 and the kinetic one is 0.3. What is the acceleration for both objects. What would the acceleration be if the wood and floor experience a friction with 0.3 coeficient.

The force is only applied to the wood, so
F - Fk(from block) = ma
80 - 0.3(2.5)(9.8) = 6 a
a = 12.1

And for the block, since it's initial state of movement is to stay where it was, the kinetic

Answer 1

friction force causes it to move. So
Fk = ma
0.3(2.5)(9.8) = 2.5 a
a = 2.94.
Now, when there is friction between the wood and the floor,
F - Fk(from block) - Fk( floor-system) = m(system)a
80 - 0.3(2.5)(9.8) - 0.3(2.5+6)(9.8) = (2.5 + 6) a
a = 5.6
They say the answer is 6.47 though