To lift a heavy load of 600 N vertically, load is attached to a block and tackle system of 4 pulleys [2 pulleys each]. The free end of rope is tied to a uniform lever of length 2 m pivoted at one end at a distance of 0.5 m from the fulcrum. A man applies effort E at the other end of lever. Assume the system to be ideal.

Calculate :

(a) The mechanical advantage of the pulley system and tension T to support the load.

(b) The least value of effort E applied to lift the load.

(c) Is there any advantage of attaching a lever to the pulley system?

Given,

• Load = 600 N
• Number of pulleys = 4
• Length of the lever = 2 m
• Distance of pivot point from the fulcrum = 0.5 m

In an ideal block and tackle system, the mechanical advantage (M.A.) is equal to the number of supporting strands of the rope, which is equal to the total number of pulleys.

So,

$\text {M.A.} = \text {Number of pulleys} = 4$

Now, M.A. of the pulley system is also given by,

$\text {M.A.} = \dfrac{\text {Load}}{\text {Effort}} \\[1em]$

Here the effort applied on the pulley is the tension T in the rope.

Therefore,

$\text {M.A.} = \dfrac{\text {Load}}{\text {Tension (T)}} \\[1em] \Rightarrow \text {T} = \dfrac{\text {Load}}{\text {M.A.}} \\[1em] = \dfrac{600}{4} \\[1em] = 150\ \text N$

Hence, the mechanical advantage of the pulley system is 4 and 150 N is the tension to support the load.

(b) For equilibrium of the lever :

$\text {Moment of force due to tension = Moment of force due to applied effort} \\[1em] \Rightarrow \text {Tension} \times \text {Load arm} = \text {Effort} \times \text {Effort arm} \\[1em] \Rightarrow \text {Effort} = \dfrac {\text {Tension} \times \text {Load arm}}{\text {Effort arm}}$

For minimum effort,

Load arm = Distance of pivot point from the fulcrum = 0.5 m

and

Effort arm = Length of the lever = 2 m

So,

$\text {Effort} = \dfrac {150 \times 0.5}{2} \\[1em] = 75 \times 0.5 \\[1em] = 37.5\ \text N$

Hence, the least effort applied to lift the load is 37.5 N.

(c) Yes, attaching a lever provides additional mechanical advantage because the pulley system already reduces the effort needed to lift the load and the lever further multiplies the applied effort due to its longer effort arm. As a result, the man needs to apply much smaller effort to lift the heavy load.