Question

Problem 5 (Lumberjack Riding a Log) An 75-kg lumberjack stands at one end of a 350-kg floating log, as shown in the figure. Both the log and the lumberjack are at rest initially 27m/ (a) If the lumberjack now trots toward the other end of the log, with a speed of 3.0 m/s relative to the log, what is the lumberjack's speed relative to the shore? Ignore friction between the log and the water. (b) If the mass of the log had been greater, would the lumberjack's speed relative to the shore be greater than, less than, or the same as in part (a)? (c) Check your answer to part (b) by calculating the lumberjack's speed relative to the shore for the case of a 450-kg log.

Answer 1

Given: mass of lumberjack (m) = 75 kg a) mass of log (M_1) = 350 kg Velocity of lumberjack, with respect to log = 3 m/s along x- direction There is no friction force between water and log (05 considered): resulting no force is applied in the horizontal direction. Thus, centre of gravity or centre of mass of lumberjack plus log system remains same. Lastly, velocity of centre of mass remains constants Velocity of lumberjack, with respect to share is man, shore = w x Velocity of lumberjack w.r.t log is log = vx Velocity of log (due to recoiling) w.r.t shore is shore = V x Since Vem lumberjack plus log system is zero Then V man, shore = v_log, shore + V man, log W = -V + V V = W + V since no horizontal force is acting. Thus the linear momentum of the system remains constant. Initially