Is Linear Momentum Conserved in This Case?

[Heisenberg7]

Homework Statement

A box with edge 1.5 m is sliding across a floor with speed of 4 m/s. The leading lower edge of the box strikes an upraised floor tile with a completely inelastic impact. What is the angular velocity of the box immediately after the box hits the tile? The mass of the box is 9 kg.

Relevant Equations

$\vec{P} = const$

Hello,

I actually solved this problem using conservation of angular momentum, but I was wondering if linear momentum is conserved. Here's my thought process:
(block + tile system) The block is going to hit the tile with some force $\vec{F}$. Due to the Newton's third law, that force is also going to act on the block itself. These are internal forces, so they play no role in our investigation. Now, here comes the problem. When the block hits the tile, the tile has to move slightly which could possibly cause an external force due to the floor. This implies that linear momentum of our block + tile system is not conserved.

There is another problem though. The tile itself is a part of the floor. So, if we were to consider the block + floor system, the linear momentum would be conserved, wouldn't it?

 

[kuruman]

Yes, the linear momentum of the block and the tile and the house to which the tile is attached and the Earth to which the house is attached is conserved. You have to have an isolated system, i.e. no external forces.