To determine which wedge requires the least amount of force to do a job, we need to compare the force for each wedge. The force for each wedge can be represented by the ratio of the thickness at the widest part to the slope. A smaller ratio indicates less force required.
Let's analyze each wedge one by one:
1. Wedge [tex]\( W \)[/tex]:
- Thickness: 2 inches
- Slope: 5 inches
Force [tex]\( = \frac{\text{Thickness}_W}{\text{Slope}_W} = \frac{2}{5} = 0.4 \)[/tex]
2. Wedge [tex]\( X \)[/tex]:
- Thickness: 4 inches
- Slope: 8 inches
Force [tex]\( = \frac{\text{Thickness}_X}{\text{Slope}_X} = \frac{4}{8} = 0.5 \)[/tex]
3. Wedge [tex]\( Y \)[/tex]:
- Thickness: 3 inches
- Slope: 9 inches
Force [tex]\( = \frac{\text{Thickness}_Y}{\text{Slope}_Y} = \frac{3}{9} = 0.33 \)[/tex]
4. Wedge [tex]\( Z \)[/tex]:
- Thickness: 5 inches
- Slope: 10 inches
Force [tex]\( = \frac{\text{Thickness}_Z}{\text{Slope}_Z} = \frac{5}{10} = 0.5 \)[/tex]
Now, let's compare the calculated forces:
- Force for [tex]\( W \)[/tex]: 0.4
- Force for [tex]\( X \)[/tex]: 0.5
- Force for [tex]\( Y \)[/tex]: 0.33
- Force for [tex]\( Z \)[/tex]: 0.5
The wedge that requires the least amount of force is the one with the smallest ratio. Comparing the values, [tex]\( W = 0.4 \)[/tex], [tex]\( X = 0.5 \)[/tex], [tex]\( Y = 0.33 \)[/tex], and [tex]\( Z = 0.5 \)[/tex]:
The smallest ratio is 0.33.
Therefore, Wedge [tex]\( Y \)[/tex] requires the least amount of force to do the job.
