Answer to Question #199759 in Mechanics | Relativity for Master j

Question

A differential wheel and axle has axles 25 cm and 10 cm in diameter. The load is 750 N and the effort required at an efficiency of 42 percent is 70 N. Calculate the wheel and diameter.

Answer 1

d₁=25 cm

d₂ = 10 cm

Load W = 750 N

Efficiency η = 42 % = 0.42

Effort P=70 N

Velocity ratio VR $= \frac{Distance \;moved \;by \;effort}{Distance \;moved\; by \;load}$

$VR = \frac{2D}{d_1-d_2} \\ = \frac{2D}{25-10} \\ = \frac{2D}{15}=0.1333D$

Mechanical advantage $MA= \frac{Load}{Effort}$

$MA = \frac{W}{P} \\ = \frac{750}{70} = 10.714$

Efficiency $η = \frac{MA}{VR}$

$0.42 = \frac{10.714}{0.1333D} \\ 0.42 \times 0.1333D = 10.714 \\ D = \frac{10.714}{0.055986}=191.37 \;cm$

Answer: 191.37 cm