Question

A pulley system with VR = 4 is used to lift a load of 175 kgf through a vertical height of 15 m. The effort required is 50 kgf in the downward direction.

(g = 10 N kg^-1)

Calculate

1) Distance moved by the effort

2) Work done by the effort

3) M.A. of the pulley system

4) Efficiency of the pulley system

Answer 1

1) Displacement due to the effort is VR = 4

Load (L)= 175 kgf
Effort (E)= 50 kgf

Load displacement (d_L)=15 m

`VR = d_E/d_L`

Effort displacement (d_E) =  4 x d_L = 4 x 15  = 60 m

Distance moved by the effort is 60 m

2) Work done by the effort is calculated using the following formula.

Work done by effort (W_E)= Force_Effort x d_E

W_E = 50 x 60 = 30000 J

3) Mechanical advantage of the pulley system is calculated as

MA of the pulley system = `"Load (L)"/"Effort (E)"` = `175/50 = 3.5`

4) Efficiency of the pulley is the ratio of work output to the work input required by the system

Efficiency of the pulley system (η) = `"Work output (Work Done by Load)"/"Work input (Work Done by Effort)"`

Work done by load = Force_Load x d_{L = 175 x 15 = 2625 kgf}

_{:. η = `2625/3000` = 0.875 x 100 = 87.5 %}