whaat happens to the potential energy lost by hammer of pile driver when it falls through a distance and drives a piling into the ground?

PE=mgh

h↓ => PE↓
at the ground PE=0

The potential energy changes to heat and sound energy.

When a hammer of a pile driver falls through a distance and drives a piling into the ground, the potential energy of the hammer is converted into several forms:

1. Kinetic Energy: As the hammer falls, its potential energy is gradually converted into kinetic energy. Kinetic energy is the energy associated with motion. The falling hammer gains speed, and this increase in speed represents the conversion of potential energy to kinetic energy.

2. Sound Energy: When the hammer strikes the piling or the ground, it generates sound energy. This is because the collision between the hammer and the piling causes vibrations in the surrounding air particles, which we perceive as sound.

3. Heat Energy: A portion of the potential energy of the hammer is also converted into heat energy. This occurs due to the friction between the hammer and the air molecules, as well as any friction between the hammer and the piling or ground.

4. Mechanical Work: The majority of the potential energy is transferred into doing mechanical work to drive the piling into the ground. The impact of the hammer exerts a force on the piling, causing it to penetrate the soil or any other material it is being driven into. This force does the work of displacing the particles of the ground and overcoming the resistance of the soil, thereby transferring the potential energy of the hammer into the potential energy stored within the piling-ground system.

To calculate the exact amount of potential energy lost by the hammer, you would need the mass of the hammer, the height it falls from, and any energy losses due to factors like air resistance or friction. With this information, you can use the formula for potential energy (PE = mgh, where m is mass, g is acceleration due to gravity, and h is height) to determine the potential energy loss.