A tractor moves with a constant velocity $v$ on a horizontal surface. What is the kinetic energy of

Question

A tractor moves with a constant velocity $v$ on a horizontal surface. What is the kinetic energy of its crawler belt if the mass of the belt is $m$?

Professor PC Thomas Classes · Answer

Total KE = KE of CM + KE relative to CM. The CM of the belt translates with the tractor at velocity $v$, so $	ext{KE}_{	ext{CM}} = 0.5 m v^2$. In the tractor's frame (CM frame), every element of the belt moves along the track with speed $v$. Thus, $	ext{KE}_{	ext{rel}} = \int 0.5 (	ext{d}m) v^2 = 0.5 m v^2$. Total KE = $0.5 m v^2 + 0.5 m v^2 = m v^2$.