A machine lifts a load of 12 kN using an effort of 4 kN. If the effort moved 8 m, how far will the load move given the machine's efficiency is 70%?

To determine how far the load moves, we can start by analyzing the situation using the concepts of mechanical advantage and efficiency.

First, we calculate the ideal mechanical advantage (IMA) of the machine, which is defined as the ratio of the load to the effort. The load in this scenario is 12 kN, and the effort is 4 kN. Therefore, the IMA can be calculated as:

[

\text{IMA} = \frac{\text{Load}}{\text{Effort}} = \frac{12 , \text{kN}}{4 , \text{kN}} = 3

]

This means that ideally, the machine allows the load to be lifted three times further than the distance the effort moves.

Next, we incorporate the efficiency of the machine to find the actual mechanical advantage (AMA). The efficiency is given as 70%, or 0.7 in decimal form. The relationship between IMA, AMA, and efficiency can be expressed as:

[

\text{Efficiency} = \frac{\text{AMA}}{\text{IMA}}

]

Solving for AMA gives:

[

\text{AMA} = \text{IMA} \times \text