A block and tackle system has 5 pulleys. If an effort of 1000 N is needed in downward direction to raise a load of 4500 N, calculate:
(a) the mechanical advantage,
(b) the velocity ratio, and
(c) the efficiency of the system

Answer

To solve the problem step by step, we will calculate the mechanical advantage, velocity ratio, and efficiency of the block and tackle system with 5 pulleys.

### Step 1: Calculate the Mechanical Advantage (MA)
The mechanical advantage (MA) is defined as the ratio of the load (output force) to the effort (input force).

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

**Given:**
- Load = 4500 N
- Effort = 1000 N

**Calculation:**
\[ \text{MA} = \frac{4500 \, \text{N}}{1000 \, \text{N}} = 4.5 \]

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

**Given:**
- Number of pulleys = 5

**Calculation:**
\[ \text{VR} = 5 \]

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

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

**Calculation:**
\[ \eta = \left( \frac{4.5}{5} \right) \times 100 = 90\% \]

### Final Answers:
(a) Mechanical Advantage = 4.5
(b) Velocity Ratio = 5
(c) Efficiency = 90%

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