# Finding the masses of two blocks in a pulley system using work-energy theorem

• ph123
In summary, the conversation discusses a scenario where two blocks with different masses are attached to a rope over a pulley. The more massive block starts to descend and after reaching a height of 1m, it has a speed of 1.50m/s. The total mass of the blocks is 13kg, and the conversation then tries to determine the individual masses of the blocks using the conservation of energy principle. However, there is some confusion about the formula used and it is suggested to start from the initial potential and kinetic energy of the system.

#### ph123

Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.00m , its speed is 1.50m/s . If the total mass of the two blocks is 13kg, then what is:
1)the mass of the more massive block
2)the mass of the less massive block

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Since the more massive block descended 1m, then the less massive block must have ascended 1.0m. Also, since the more massive block travels at 1.50m/s, then the less massive block must trave -1.50m/s. Setting the height of the less massive block, m1, as 2.0m, and the height of the more massive block, m2, as 0, then

m1gh + (1/2)m1v1^2 = (1/2)m2v2^2
m1(gh + (1/2)v1^2) = m2(1/2 *v2^2)
m1/m2 = v2^2/(gh + v1^2)
m1/m2 = (1.125 m^2/s^2) / (20.725 m^2/s^2)
m1/m2 = 0.0543

I figured, since given only the combined mass, I had to find the ratio of the masses. I multiplied the ratio (0.0543) times 13kg, and found that m1 = 0.706kg, and 13kg - 0.706kg = 12.294kg. Not right, though. Anyone know where I went wrong?

Yeah. Your equation for conservation of energy isn't right. You didnt factor in the loss of gravitational potential energy of the heavier mass. It should be:

$$m_1gh+0.5m_1v_1^2=m_2gh+0.5m_2v_2^2$$