Explain all the mechanisms that cause an increase in muscle force production.

Force production occurs in the myofibrils, which are chains of sarcomeres running from one end of the fiber to the other. Energy for contraction comes from metabolism of fats and sugars.

The force a muscle generates is dependent on the length of the muscle and the shortening velocity of the muscle. These two fundamental properties of muscles affect biomechanical properties including limiting running speed, strength, and jumping distance and height.

Force-Length Relationship

The force-length relationship in muscle indicates that muscles generate the greatest force when at their resting, or ideal length, and the least amount of force when shortened or stretched relative to the resting length. When a skeletal muscle fiber contracts, myosin heads attach to actin to form cross-bridges followed by the thin filaments sliding over the thick filaments as the heads pull the actin, and this results in sarcomere shortening, creating the tension of the muscle contraction. The cross-bridges can only form where thin and thick filaments already overlap, so that the length of the sarcomere has a direct influence on the force generated when the sarcomere shortens. This is also called the length-tension relationship.

There's also the force-velocity relationship in case you want more information. By the way, what textbook are you using?

This should explain it better: http://michaeldmann.net/mann14.html