A lever with a load arm of 0.8 meter has a mechanical advantage of 6. What is the length of the effort arm?

The load arm is 0.8 meters.
The mechanical advantage (MA) is 6.
From the formula $\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$, we can rearrange to find the effort arm:

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

$$\text{Effort arm} = 6 \times 0.8\, \text{m}$$ $$\text{Effort arm} = 4.8\, \text{m}$$

The length of the effort arm is $\boxed{\text{4.8 meters}}$.

2.4.5

The effort arm is 0.4 meters.
The mechanical advantage (MA) is 0.5.
From the formula $\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$, we can rearrange to find the load arm:

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

$$\text{Load arm} = \frac{0.4\, \text{m}}{0.5}$$ $$\text{Load arm} = 0.8\, \text{m}$$

The length of the load arm is $\boxed{\text{0.8 meters}}$.

2.4.7

The load arm is 0.75 meters.
The mechanical advantage (MA) is 0.33.
From the formula $\text{MA} = \frac{\text{Effort arm}}{\text{Load arm}}$, we can rearrange to find the effort arm:

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

$$\text{Effort arm} = 0.33 \times 0.75\, \text{m}$$ $$\text{Effort arm} = 0.2475\, \text{m}$$

The length of the effort arm is $\boxed{\text{0.2475 meters}}$.

2.5.1

The input arm (effort arm) is 3 meters.
The output arm (load arm) is 0.75 meters.
The formula for mechanical advantage (MA) is:

$$\text{MA} = \frac{\text{Input arm}}{\text{Output arm}}$$

$$\text{MA} = \frac{3\, \text{m}}{0.75\, \text{m}}$$ $$\text{MA} = 4$$

The mechanical advantage of the lever is $\boxed{\text{4}}$.