The calculated speed is 3.8 m/s. The system's gravitational potential energy and kinetic energy combined will always remain constant.
So: E=50.0 kg*2.5 m*9.8 m/s2
= 1225 kg*m2/s2
= 1225 J
Since m1 will be lifted when m2 falls, m1 will experience some gravitational potential energy.
E=27.0 kg*2.5m*9.8 m/s2
= 661.5 kg*m2/s2
= 661.5 J E
= 1225 J - 661.5 J
= 563.5 J
Therefore, the system will have 563.5 Joules of kinetic energy when m2 hits the ground. sqrt(E/39.7 kg)
= v sqrt(563.5 J/39.7 kg)
= v sqrt(14.19395466 m2/s2)
= v 3.767486518 m/s
= v E
= 39.7 kg v2 E/39.7 kg
= v2
Since that is the lowest precision datum available, round to 2 significant figures to arrive at a speed of 3.8 m/s.
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