Answer to Question #118396 in Mechanics | Relativity for bonidefaye judah

Question

A solid shaft of 10cm diameter transmits 74 kW at 150 rev/min. Calculate (a) the
torque on the shaft, (b) the maximum shear stress developed, (c) the angle of twist in a
length of 1.50m, and (d) the shear stress at a radius of 3cm. Take G = 8 MN/cm2

Answer 1

a)

$$P=\frac{2\pi NT}{60}\to 74000=\frac{2\pi (150)T}{60}$$

$$T=4711\ Nm$$

b)

$$T=\frac{\pi}{16}\tau d^3\to 4711=\frac{\pi}{16}\tau (0.1)^3$$

$$\tau=24\cdot10^6\frac{N}{m^2}$$

c)

$$\frac{T}{J}=\frac{G\theta }{l}\to \frac{T}{ \frac{\pi}{32} d^4}=\frac{G\theta }{l}$$

$$\frac{4711}{ \frac{\pi}{32} (0.1)^4}=\frac{8\cdot 10^{10}\theta }{1.5}$$

$$\theta=0.00899735\ rad=0.5155\degree$$

d)

$$T=\frac{\pi}{16}\tau' \frac{d^4-(2r)^4}{d}\to 4711=\frac{\pi}{16}\tau' \frac{0.1^4-(0.06)^4}{0.1}$$

$$\tau'=2.76\cdot10^7\frac{N}{m^2}$$