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Step-by-Step Solution
Step 1: Identify the load (W)
The mass to be lifted is given as 75 kg. To find the load (the weight), use the formula:
$ W = mg $
where $m$ is the mass and $g$ is the acceleration due to gravity (approximately $10 \, \text{m/s}^2$). Hence,
$ W = 75 \times 10 = 750 \, \text{N}.
$
Step 2: Note the effort (P)
The force required to raise the load is given as 250 N. Therefore,
$ P = 250 \, \text{N}.
$
Step 3: Calculate the Mechanical Advantage (MA)
The mechanical advantage is defined as the ratio of the load to the effort. Hence,
$ \text{MA} = \frac{W}{P} = \frac{750}{250} = 3.
$
Step 4: Determine the Velocity Ratio (VR)
The rope is pulled through a distance of 12 m, while the load is lifted through 3 m. The velocity ratio is given by:
$ \text{VR} = \frac{\text{distance traveled by effort}}{\text{distance traveled by load}} = \frac{12}{3} = 4.
$
Step 5: Find the Efficiency of the Pulley System
The efficiency $(\eta)$ of a simple machine is the ratio of its mechanical advantage to its velocity ratio, expressed as a percentage:
$ \eta = \left(\frac{\text{MA}}{\text{VR}}\right) \times 100\% = \left(\frac{3}{4}\right) \times 100\% = 75\%.
$
Answer
The efficiency of the pulley system is 75%.
