A worker drives a 0.562 kg spike into a rail tie with a 2.26 kg sledgehammer. The hammer hits the spike with a speed of 64.4 m/s. If one third of the hammer's kinetic energy is converted to the internal energy of the hammer and spike, how much does the total internal energy increase? Answer in units of J

Given that,

Mass of sledge hammer;

Mh = 2.26 kg

Hammer speed;

Vh = 64.4 m/s

The expression fot the kinetic energy of the hammer is,

K. E (hammer) = ½Mh•Vh²

K. E (hammer) = ½ * 2.26 * 64.4²

K. E (hammer) = 4686.52 J

If one forth of the kinetic energy is converted into internal energy, then

ΔU = ¼ * K. E (hammer)

∆U = ¼ * 4686.52

∆U = 1171.63 J

Thus, the increase in total internal energy will be 1171.63 J.