307 Power Transmitted by Solid Steel Shaft of Unknown Diameter

$\theta = \dfrac{TL}{JG}$

$4^\circ \left( \dfrac{\pi}{180^\circ} \right) = \dfrac{T(5)(1000)}{\frac{1}{32}\pi d^4 (83\,000)}$

$T = 0.1138d^4$
 

$\tau_{max} = \dfrac{16T}{\pi d^3}$

$80 = \dfrac{16(0.1138d^4)}{\pi d^3}$

$d = 138 \, \text{ mm}$           answer
 

$T = \dfrac{P}{2\pi f}$

$0.1138d^4 = \dfrac{P}{2\pi (20)}$

$P = 14.3d^4 = 14.3(1384)$

$P = 5\,186\,237\,285 \, \text{N} \cdot \text{mm/sec}$

$P = 5\,186\,237.28 \, \text{W}$

$P = 5.19 \, \text{ MW}$           answer