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Solve the following :

Question:

The two blocks in an Atwood machine have masses $2.0 \mathrm{~kg}$ and $3.0 \mathrm{~kg}$. Find the work done by gravity during the fourth second after the svstem is released from rest.

Solution:

$T-3 g+3 a=01$

$T-2 g-2 a=02$

Solving equation 1 and 2

$\mathrm{a}=\frac{\stackrel{\boldsymbol{E}}{5}}{5 \mathrm{~m} / \mathrm{s}^{2}}$

Now,

$S=\frac{a}{2}(2 m-1)$

$S=\frac{g / 5}{2}[2 \times 4-1]$

$\mathrm{h}=\mathrm{S}=6.86 \mathrm{~m}$

Mass

$\mathrm{m}=\mathrm{m}_{1}-\mathrm{m}_{2}$

$\mathrm{m}=3-2=1 \mathrm{~kg}$

Decrease in P.E. = mgh

P.E. $=1 \times 9.8 \times 6.86$

P.E. $=67 \mathrm{~J}$