To determine the students' order based on the mechanical advantages of their machines, we need to first understand what mechanical advantage (MA) is. Mechanical advantage is calculated using the formula:
[tex]\[ \text{Mechanical Advantage} = \frac{\text{Output Force}}{\text{Input Force}} \][/tex]
Given the input and output forces of each student’s machine, we can compute their mechanical advantages as follows:
1. For Brian:
[tex]\[ \text{Input Force} = 150 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 300 \, \text{N} \][/tex]
[tex]\[ \text{Mechanical Advantage} = \frac{300}{150} = 2.0 \][/tex]
2. For Lian:
[tex]\[ \text{Input Force} = 400 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 350 \, \text{N} \][/tex]
[tex]\[ \text{Mechanical Advantage} = \frac{350}{400} = 0.875 \][/tex]
3. For Dipak:
[tex]\[ \text{Input Force} = 250 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 450 \, \text{N} \][/tex]
[tex]\[ \text{Mechanical Advantage} = \frac{450}{250} = 1.8 \][/tex]
4. For Aida:
[tex]\[ \text{Input Force} = 300 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 375 \, \text{N} \][/tex]
[tex]\[ \text{Mechanical Advantage} = \frac{375}{300} = 1.25 \][/tex]
Now, we need to list these mechanical advantages in ascending order (from least to greatest) and match them to the corresponding students:
- Lian: [tex]\(0.875\)[/tex]
- Aida: [tex]\(1.25\)[/tex]
- Dipak: [tex]\(1.8\)[/tex]
- Brian: [tex]\(2.0\)[/tex]
Therefore, the correct order from the student whose machine has the least mechanical advantage to the student whose machine has the greatest mechanical advantage is:
[tex]\[ \text{Lian, Aida, Dipak, Brian} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\text{Lian, Aida, Dipak, Brian}} \][/tex]
