Question

b) A block and tackle system of velocity ratio 3 is used to raise a load of 120 kgf
through a height of 2 m. If the efficiency of the pulley system is 80% then
calculate
i) Effort needed.
ii)Displacement of the effort required​

Answer 1

Given that,

Velocity ratio = 3

Load = 120 kgf

Height = 2 m

Efficiency = 80%

We need to calculate the mechanical advantage

Using formula of efficiency

$\eta=\dfrac{M.A}{V.R}$

$M.A=\eta\times V.R$

Where, $\eta$ = Efficiency

M.A = mechanical advantage

V.R = velocity ratio

Put the value into the formula

$M.A=80\times3$

$M.A=240$

(I). We need to calculate the effort

Using formula of effort

$M.A=\dfrac{L}{E}$

$E=\dfrac{L}{M.A}$

Put the value into the formula

$E=\dfrac{120}{240}$

$E=0.5\ kgf$

(II). We need to calculate the displacement of the effort

Using formula of displacement of the effort

$d_{e}=h\times V.S$

Put the value into the formula

$d_{e}=2\times3$

$d_{e}=6\ m$

Hence, (I). The effort needed is 0.5 kgf.

(II). The displacement of the effort is 6 m.

Answer 2

Given that,

Velocity ratio = 3

Load = 120 kgf

Height = 2 m

Efficiency = 80%

We need to calculate the mechanical advantage

Using formula of efficiency

$\eta=\dfrac{M.A}{V.R}$

$M.A=\eta\times V.R$

Where, $\eta$ = Efficiency

M.A = mechanical advantage

V.R = velocity ratio

Put the value into the formula

$M.A=80\times3$

$M.A=240$

(I). We need to calculate the effort

Using formula of effort

$M.A=\dfrac{L}{E}$

$E=\dfrac{L}{M.A}$

Put the value into the formula

$E=\dfrac{120}{240}$

$E=0.5\ kgf$

(II). We need to calculate the displacement of the effort

Using formula of displacement of the effort

$d_{e}=h\times V.S$

Put the value into the formula

$d_{e}=2\times3$

$d_{e}=6\ m$

Hence, (I). The effort needed is 0.5 kgf.

(II). The displacement of the effort is 6 m.

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