I am trying to solve number 89 in my physics book. I understand how to solve thi

Question

I am trying to solve number 89 in my physics book. I understand how to solve this problem using force but do not understand how to solve it using the energy work therum.

the question states: three objects with masses m1=5 kg, m2=10 kg and m3= 15kg, respectively, are attached by strings over frictionless pulleys. The horizontal surface exerts a force of friction of 30N on m2. if the system is released from rest, use energy concepts to find the speed of m3 after it moves down 4.0m.

The picture has all three blocks connected with one string. M2 sits on a table while m1 and m3 hang at equal lenghts off the table.

Please help me to understand how to solve this problem using the energy concepts.

Explanation / Answer

conservation of energy
kinetic energy of system + work done against friction=loss of petential energy
since all masses are attached with string all masses have same velocity
0.5*(m1+m2+m3)*v^2 + 30*4 = (m1+m3)*4*g
15*v^2 +120 = 20*4*9.8
solving
v =6.65 m/s^2

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