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Hartnell Governor :
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Effort = $p = \frac{S_2 – S_1}{2}$

Power $= p \times h$

Numerical:

$h = \frac{y}{x} (r_2 – r_1)$

$60 = \frac{100}{150} (r_2 – 80)$

$r_2 = 170 \ mm$

$N_1 = 300\ rpm$ $\rightarrow$ $r_1 = 80\ mm$

$N_2 = ?$ $\rightarrow$ $r_2 = 170\ mm$

$\rightarrow$ $S = \frac{S_2 – S_1}{h}$

$S = 25\ N/mm, h = 60\ mm$

# Diagram

$w_1 = \frac{2 \pi \times 300}{60} = 31.41$ rad/sec

$Fc_1 = mr_1 \ w_1^2$

$= 4 \times 0.08 \times 31.41^2$

$= 315.708\ N$

$\sum M_o = 0 \curvearrowright$ +

$[ \frac{mg + S_1}{2} ] (Y_1) – FC_1 (X_1) = 0$

$\frac{S_1}{2} \times 0.1\ – \ 315.708 \times 0.15 = 0$

$S_1 = 947.134 \ N$

[2] $\sum M_o = 0 \curvearrowright$ +

$[ \frac{mg +S_2}{2}] (Y) – Fc_2 (X) = 0$

$\frac{2447.124}{2} \times 0.1\ – \ Fc_2 (0.15) = 0$

$Fc_2 = 815.708 N$

$s = \frac{S_2 – S_1}{h}$

$25 = \frac{S_2 – 947.124}{60}$

$S_2 = 2447.124 \ N$

$\rightarrow$ $Fc_2 = mr_2 w_2^2$

$815.708 = 4 \times 0.17 \times w_2^2$

$w_2 = 34.63 \ rad/sec$

$w_2 = \frac{2 \pi N_2}{60}$

$N_2 = 330.69\ r.p.m$

$\rightarrow$ Effort, $p = \frac{S_2 – S_1}{2}$

$P = 750\ N$

$\rightarrow Power = p \times h = 750 \times 0.06 = 45\ N.m$