Potential Energy EX 7

Since the blocks are sliding on an inclined plane, we have to compute the heights that each one of them moves. $m_1$ moves down $h=0.3\sin (37^{\circ })=(0.3)(0.6)=0.18m$ and $m_2$ moves up $h=0.3\sin (20^{\circ })=(0.3)(0.34)=0.10m$. The change in gravitational potential energy is negative for $m_1$ and positive for $m_2$.

$\mathrm{\Delta }U=-m_{1}gh=-(2)(10)(0.18)=-3.6J$

$\mathrm{\Delta }U=m_{2}gh=(3)(10)(0.10)=3.0J$

Therefore, the total change in gravitational potential energy is

$\mathrm{\Delta }U=-3.6+3.0=-0.6J$

Note that in this case the blocks moved spontaneously from rest. As expected, it was found that the total change of the potential energy is negative.