Two blocks with different masses are attached to either end of a light rope that

Question

Two blocks with different masses are attached to either end of a light rope that passes over a light, frictionless pulley suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended 1.20 m, its speed is 3.00 m/s. If the total mass of the two blocks is 41.0 kg, what is the mass of the heavier block? Express your answer with the appropriate units. If the total mass of the two blocks is 41.0 kg, what is the mass of the lighter block? Express your answer with the appropriate units.

Explanation / Answer

Assume (arbitrarily) that m1 is the heavier block. For this kind of setup, it can be shown that (each) block's acceleration is:

a = g(m1m2)/(m1+m2)

(You can derive this by writing separate "Fnet=ma" equations for each block, then solving the equations simultaneously. I omit the details.)

Now, you can relate the acceleration "a" to distance fallen (d) and final speed (v) using the standard kinematics equation:

v² = 2ad (when starting from rest)

That is: a=v²/(2d). Substitute in to the previous equation:

v²/(2d) = g(m1m2)/(m1+m2)

From which:

m1m2 = v²(m1+m2)/(2gd)
= (3 m/s)²(41.0 kg)/(2*9.8 m/s²*1.20 meters)
= 15.7 kg


So now you have:

m1+m2 = 41.0 kg
m1m2 = 15.7 kg

adding the equations

2m1=56.7 kg

m1=28.35 kg

m2=12.65 kg

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