Answer:
the energy loss due to friction = 0.2344 ft-lb
Explanation:
The principle of conservation of energy is used to calculate the loss of energy due to friction.
The difference between the gain in potential (Mθ) due to the restoring moment M = 62.1 lb-in and loss in potential energy due to weight (mgh) and kinetic energy as a result of restoration [tex](\frac{1}{2}*I_{AC}* \omega ^2)[/tex] of AC adds up to the energy loss ( ΔE).
Expressing the formula; we have:
ΔE = [tex]M \theta - mgh - \frac{1}{2}*I_{AC}* \omega^2[/tex]
ΔE = [tex]M \theta - mgh - \frac{1}{2}*\frac{mb^2}{12}* (\frac{v}{r})^2[/tex]
From the diagram below; the weight of the slender = W
acceleration due to gravity = g
length of the slender bar = r
the couple = M
the vertical guide velocity = v
and the angle = θ
ΔE = [tex]\frac{62.1}{12}*\frac{\pi}{4}-4.3*\frac{8}{12} *(1-\frac{1}{\sqrt{2}})- [\frac{1}{2}*(\frac{1}{12})*\frac{4.3}{32.2}*(\frac{16}{12})^2*(\frac{11.6}{\frac{8}{12}})^2][/tex]
ΔE = 4.064 - 0.8396 - 2.99
ΔE = 0.2344 ft-lb
Thus, the energy loss due to friction = 0.2344 ft-lb
