Given:
Mass = 31.0 kg
Height = 18.00 m
FInal height = 8.00 m
Speed, v = 7.70 m/s
Let's find the mechanical energy lost due to friction.
Apply the conservation of mass:
[tex]\frac{1}{2}mv^2=mg\Delta h[/tex]Total mechanical energy at the point 1.
E = PE + KE
[tex]\begin{gathered} E=\text{mgh}+\frac{1}{2}mu^2 \\ \\ E=(31\times9.8\times18)+(\frac{1}{2}\times21\times0) \\ \\ E_1=5468.4\text{ J} \end{gathered}[/tex]
Total mechanical energy at point 2:
[tex]\begin{gathered} E=mgh_2+\frac{1}{2}mv^2 \\ \\ E=(31\times9.8\times8)+(\frac{1}{2}\times31\times7.7^2) \\ \\ E=2430.4+918.995 \\ \\ E_2=3349.395\text{ J} \end{gathered}[/tex]To find the energy lost due to friction , apply the formula:
Energy lost = E1 - E2
Energy lost = 5468.4 - 3349.395 = 2119.0 J
Therefore, the mechanical energy lost due to friction is 2119 J
ANSWER:
2119 J
