Question

The 10-Mg barge B supports a 2-Mg automobile A. If someone drives the automobile to the other side of the barge, determine how far the barge moves. Neglect the resistance of the water.

Solution

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Assuming the barge will move to the left,

Applying the conservation of linear momentum,

(+)      mAvA+mBvB=mAvA+mBvB(\xleftarrow{+})\;\;\;m_Av_A+m_Bv_B=m_A{v_A}'+m_B{v_B}'

2000vA+10000vB=2000(0)+10000(0)2000v_A+10000v_B=2000(0)+10000(0)

2000vA=10000vB2000v_A=-10000v_B

vA=5vBv_A=-5v_B

sA=5sB      (1)s_A=-5s_B\;\;\;(1)

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