The Energetic Hammerhead: A Stamping Machine Story

What is the change in total energy of the hammerhead?

A piston motion moves a 50 lbm hammerhead vertically down 3 ft from rest to a velocity of 150 ft/s in a stamping machine.

Final answer: The change in total energy of the hammerhead is calculated by subtracting its initial potential energy from its final kinetic energy, which comes out to be 557673.8 ft*lbf.

Answer:

The change in total energy of the 50 lbm hammerhead in the stamping machine can be calculated using the principles of Physics, specifically the principle of conservation of energy.

Imagine a powerful stamping machine where a 50 lbm hammerhead is raised, only to come crashing down with incredible force. The piston motion moves the hammerhead vertically down a distance of 3 ft from rest to a velocity of 150 ft/s. As the hammerhead gains speed and momentum, its energy undergoes a significant transformation.

At the beginning of its descent, the hammerhead possesses gravitational potential energy due to its height above the ground. This potential energy can be calculated using the formula m*g*h, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, the initial potential energy of the hammerhead is 50 lbm * 32.174 ft/s^2 * 3 ft = 4826.2 ft*lbf.

As the hammerhead accelerates downward and reaches a velocity of 150 ft/s, it gains kinetic energy, which is calculated using the formula 1/2*m*v^2, where m is the mass and v is the velocity. The final kinetic energy of the hammerhead is 1/2 * 50 lbm * (150 ft/s)^2 = 562500 ft*lbf.

The change in total energy of the hammerhead is simply the difference between its final energy (kinetic) and its initial energy (potential). By subtracting the initial potential energy from the final kinetic energy, we find that the change in total energy is 562500 ft*lbf - 4826.2 ft*lbf = 557673.8 ft*lbf. This represents the transformation of energy from potential to kinetic as the hammerhead accelerates down in the stamping machine.