Find velocity of hanging block in a pulley system

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To find the velocity of the hanging block in the pulley system, apply the law of conservation of energy, considering both kinetic energy (KE) and gravitational potential energy (Ug). The work done by friction must also be accounted for, which is determined by the coefficient of kinetic friction and the normal force on the block on the desk. The equation Wother = ΔKE + ΔUg + ΔUel indicates that the total work done by the system equals the change in kinetic energy plus the change in gravitational potential energy. It is not necessary to solve for each mass separately; instead, focus on the overall energy changes in the system. The final velocity can be calculated after accounting for the energy lost to friction.
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A pulley is set up on the edge of a desk. A light string connects a 10 kg block laying on the desk to a 4 kg block hanging off the pulley. The only significant friction is with the desk, and the coefficient of kinetic friction is 0.20. Use the law of conservation of energy to find the speed of the system after the hanging block has dropped 1.5 m.



Wother = ΔKE + ΔUg + ΔUel
KE = 0.5 * m * v2
Ug = m*g*y



in both KE and Ug equations I need to use mass. Do I solve these equations for each of the masses and then add them all together to equal Wother?
 
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You only need to solve the first equation, W is the work done by friction, and the system would gain kinetic energy but lose gravitational potential energy.
 

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