Question

How many movable pulleys are there in a system of 4 pulleys? What is the mechanical advantage and velocity ratio of this system? If the efficiency of the system is 80%, what effort is required to lift a load of 40 kgf from this system?

Answer 1

Given:

Total number of pulleys (n) = 4

Efficiency (η) = 80% = `80/100` = 0.8

Load (L) = 40 kgf

1. Number of Movable Pulleys:

In a standard block and tackle system with an even number of total pulleys (4), the pulleys are shared equally between the upper fixed block and the lower movable block.

Fixed (Top) block = 2 pulleys

Movable (Bottom) block = 2 movable pulleys

2. Velocity Ratio (VR) and Mechanical Advantage (MA):

For a block and tackle system, the velocity ratio is always equal to the total number of pulleys in the system.

VR = 4

Use the relation between MA, VR, and Efficiency (η):

MA = Efficiency (η) × Velocity Ratio (VR)

= 0.8 × 4

= 3.2

3. Calculation of Effort (E):

Using the formula for mechanical advantage:

MA = `"Load (L)"/"Effort (E)"`

3.2 = `40/E`

E = `40/3.2`

E = `400/32`

E = 12.5 kgf