You are given four pulleys and three strings. Draw a neat and labelled diagram to use them so as to obtain a maximum mechanical advantage equal to 8. In your diagram mark the directions of load L, effort E and tension in each strand.
What assumptions have you made to Obtain the required mechanical advantage ?

Answer

To solve the problem of obtaining a maximum mechanical advantage of 8 using four pulleys and three strings, we will follow these steps:

### Step 1: Understand Mechanical Advantage
Mechanical advantage (MA) is defined as the ratio of the load force (L) to the effort force (E) applied. In this case, we need to achieve an MA of 8, which means:
\[ MA = \frac{L}{E} = 8 \]

### Step 2: Determine the Configuration of Pulleys
To achieve a mechanical advantage of 8 with four pulleys and three strings, we can use a combination of fixed and movable pulleys.

### Step 3: Draw the Diagram
1. **Draw the Support**: Start by drawing a horizontal line at the top to represent the rigid support.
2. **Draw the Pulleys**:
- Draw four pulleys (A, B, C, D) in a vertical arrangement.
- The first pulley (A) is fixed to the support.
- The second pulley (B) is movable and connected to the load (L).
- The third pulley (C) is also movable and connected to the second pulley (B).
- The fourth pulley (D) is fixed and connected to the effort (E).

3. **Label the Load and Effort**:
- Mark the load (L) connected to pulley B.
- Mark the effort (E) applied at the top of pulley D.

4. **Indicate the Strings and Tensions**:
- Draw three strings connecting the pulleys.
- Label the tension in each string (T1, T2, T3).

### Step 4: Label Directions
- Indicate the direction of the load (downward).
- Indicate the direction of the effort (upward).
- Indicate the direction of tension in each string (upward in the case of movable pulleys).

### Step 5: Calculate Mechanical Advantage
The mechanical advantage can be calculated as follows:
- For a system with 3 strings supporting the load, the mechanical advantage is equal to the number of supporting strings.
- Therefore, with 3 strings, the mechanical advantage is 3.
- Since we are using 4 pulleys, we can achieve a mechanical advantage of 8 by doubling the effect of the three strings through the arrangement of the pulleys.

### Final Diagram
- Make sure the diagram is neat and clearly labeled with:
- Load (L)
- Effort (E)
- Tensions (T1, T2, T3)
- Pulleys (A, B, C, D)

### Assumptions Made
1. **No Friction**: It is assumed that there is no friction in the pulley bearings.
2. **Massless Pulleys and Strings**: It is assumed that the pulleys and strings are massless, which simplifies calculations.
3. **Ideal Conditions**: The system is assumed to operate under ideal conditions without any losses.