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written 4.8 years ago by |
$m = 4\ kg$
$M = 45 kg$
$sin \ \alpha = \frac{200}{350}$
$\alpha \ = \ 34.85°$
$sin \ \beta = \frac{160}{300}$
$\beta = 32.23°$
$h = \sqrt{ 350^2 – 200^2}$
$h = 287.228\ mm$
$q = \frac{tan \ \beta}{tan \ \alpha} = 0.91$
For $r = 200\ mm, N = ?$
$0.2872 = \frac{895}{N^2} \ ( 1 + \frac{45}{2 \times 4} (1 + 0.91))$
$N = 191.303\ rpm.$
$\rightarrow$ C = 0.01 (Given)
$\rightarrow$ Effort, $P = C[ \frac{2m}{1 + q} + M] g$
$= 0.01 [ \frac{2 \times 4}{1 + 0.91} + 45] \times 9.81$
$P = 4.825\ N$
$\rightarrow$ Power = $\frac{4c^2}{1 + 2c} [ m + \frac{M}{2} (1 +q)] g.h$
$= \frac{4 \times 0.01^2}{1 + 2 \times 0.01} ( 4 + \frac{45}{2} (1 + 0.91)] 9.81 \times 0.2872$
Power $= 0.052\ N.m$