For which of the following situations would mechanical energy be conserved? The collision of two billiard balls. A skier skiing down a snow-covered hill at constant speed. A bullet colliding and being embedded in a block of wood. A heavy block sliding along a rough surface.

Mechanical energy is conserved in a system when there are no non-conservative forces acting on it, such as friction or air resistance.

1. The collision of two billiard balls: Mechanical energy is conserved in this situation. This is because the collision between the two balls can be considered an elastic collision, where both momentum and kinetic energy are conserved.

2. A skier skiing down a snow-covered hill at constant speed: Mechanical energy is also conserved in this situation. The skier is converting potential energy (due to height on the hill) into kinetic energy (due to speed) and vice versa, assuming no energy is lost to friction or air resistance.

3. A bullet colliding and being embedded in a block of wood: Mechanical energy is not conserved in this situation. This is an inelastic collision, where the bullet loses kinetic energy by deforming and heating up the bullet and the block of wood.

4. A heavy block sliding along a rough surface: Mechanical energy is not conserved in this situation. The friction between the block and the surface converts some of the block's kinetic energy into heat, which is then dissipated into the environment.

So, mechanical energy would be conserved in the situations of the two billiard balls colliding and the skier skiing down a hill at constant speed.