A typical human head has a mass of 5.0 kg. If the head is moving at some speed and strikes a fixed surface, it will come to rest. A helmet can help protect against injury; the foam in the helmet allows the head to come to rest over a longer distance, reducing the force on the head. The foam in helmets is generally designed to fail at a certain large force below the threshold of damage to the head. If this force is exceeded, the foam begins to compress.
If the foam in a helmet compresses by 1.5 cm under a force of 2500 N (below the threshold for damage to the head), what is the maximum speed the head could have on impact?
Use energy concepts to solve this problem.