Solve the following LEVER PROBLEMS. 2.4.1 A lever used to lift a heavy box has an effort arm of 4 meters and a load arm of 0.5 meters. What is the mechanical advantage of the lever?

The effort arm is 4 meters.
The load arm is 0.5 meters.
The formula for mechanical advantage (MA) is:

$$\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$$

$$\text{MA} = \frac{4\, \text{m}}{0.5\, \text{m}}$$ $$\text{MA} = 8$$

The mechanical advantage of the lever is $\boxed{\text{8}}$.

2.4.2

The effort arm is 3 meters.
The load arm is 2 meters.
The formula for mechanical advantage (MA) is:

$$\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$$

$$\text{MA} = \frac{3\, \text{m}}{2\, \text{m}}$$ $$\text{MA} = 1.5$$

The mechanical advantage of the lever is $\boxed{\text{1.5}}$.

2.4.3

The effort arm is 2 meters.
The mechanical advantage (MA) is 4.
From the formula $\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$, we can rearrange to find the load arm:

$$\text{Load arm} = \frac{\text{Effort arm}}{\text{MA}}$$

$$\text{Load arm} = \frac{2\, \text{m}}{4}$$ $$\text{Load arm} = 0.5\, \text{m}$$

The load arm's length is $\boxed{\text{0.5 meters}}$.