An 77-kg lumberjack stands at one end of a 340-kgfloating log, as shown in the f

Question

An 77-kg lumberjack stands at one end of a 340-kgfloating log, as shown in the following figure (Figure 1) . Both the log and the lumberjack are at rest initially.

Part A. The lumberjack then trots toward the shore with a speed of 2.7 m/s relative to the shore. What is the speed of the log relative to the shore? Ignore friction between the log and the water.

part b. If the mass of the log were greater, would its speed relative to the shore be greater than, less than, or the same as the speed found in part A?

Part c. Check your answer to part B by calculating the speed relative to the shore for a 410-kg log.

Explanation / Answer

a)

Vli = initial velocity of lumberjack = 0 m/s

VLi = initial velocity of log = 0 m/s

Vlf =final velocity of lumberjack = 2.7 m/s

VLf = final velocity of log = ?

m = mass of lumberjack = 77 kg

M = mass of Log = 340 kg

using conservation of momentum

MVLi + m Vli = MVLf + m Vlf

340 (0) + 77 (0) = 340 VLf + 77 (2.7)

VLf = - 0.61 m/s

the negative sign indicates the opposite direction

speed of the log relative to the shore = 0.61 m/s

b)

as the mass of log becomes greater , its speed will decreases since momentum remains constant hence mass and speed depends on each other inversly. if one increase the other decrease.

c)

using conservation of momentum

MVLi + m Vli = MVLf + m Vlf

410 (0) + 77 (0) = 410 VLf + 77 (2.7)

VLf = - 0.51 m/s

the negative sign indicates the opposite direction

speed of the log relative to the shore = 0.51 m/s

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