Question

The diagram shows a pulley used to lift an iron beam of length 3 m and weight 100 kgf, lying on the ground.

1. Calculate the minimum effort needed to just lift the beam off the ground. [Assume no loss of energy]
2. When the beam is being lifted from the ground, with the other end touching the ground, state with a reason whether the effort needed keeps on increasing, decreasing or remains constant.

Answer 1

(a) Let the upward force at the end of the beam be R.

At the instant when the beam is just about to lift from the ground, take moments about the end of the beam still touching the ground.

The weight of the beam acts at its centre, i.e. at a distance of 1.5 m from the pivot.

Therefore,

R × 3 = 100 × 1.5

R \[=\frac{100\times1.5}{3}\]

R = 50 kgf

The block and tackle has 4 supporting strands. Assuming no loss of energy,

Mechanical Advantage = 4

\[ \text{Effort} = \frac{\text{Load}}{\text{Mechanical Advantage}} \]

Here, the load on the pulley is R = 50 kgf.

E = \[\frac{50}{4}\]

E = 12.5 kgf​

Therefore, the minimum effort required to just lift the beam from the ground is 12.5 kgf​.

(b) The effort remains constant. As the beam turns about the end touching the ground, the perpendicular distances of both the upward force R and the weight from the pivot decrease in the same proportion. Therefore, their moment ratio remains unchanged. Hence, the force required at the beam's end and the effort required from the pulley system remain constant.