In a block and tackle system consisting of 3 pulleys, a load of 75 kgf is raised with an effort of 25 kgf. Find : (i) the mechanical advantage, (ii) the velocity ratio, and (iii) the efficiency.

Answer

To solve the problem step by step, we will find the mechanical advantage, velocity ratio, and efficiency of the block and tackle system.

### Step 1: Calculate the Mechanical Advantage (MA)
Mechanical Advantage (MA) is defined as the ratio of the load (weight being lifted) to the effort (force applied).

**Formula:**
\[ MA = \frac{\text{Load}}{\text{Effort}} \]

**Given:**
- Load = 75 kgf
- Effort = 25 kgf

**Calculation:**
\[ MA = \frac{75 \text{ kgf}}{25 \text{ kgf}} = 3 \]

### Step 2: Calculate the Velocity Ratio (VR)
Velocity Ratio (VR) is defined as the ratio of the distance moved by the effort to the distance moved by the load. In a block and tackle system, the velocity ratio is also equal to the number of pulleys.

**Given:**
- Number of pulleys = 3

**Calculation:**
\[ VR = 3 \]

### Step 3: Calculate the Efficiency (η)
Efficiency is defined as the ratio of mechanical advantage to velocity ratio, multiplied by 100 to express it as a percentage.

**Formula:**
\[ \eta = \left( \frac{MA}{VR} \right) \times 100 \]

**Calculation:**
\[ \eta = \left( \frac{3}{3} \right) \times 100 = 100\% \]

### Final Results:
(i) Mechanical Advantage (MA) = 3
(ii) Velocity Ratio (VR) = 3
(iii) Efficiency (η) = 100%

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