To determine which machine has the greatest output force, let's calculate the output force for each machine. The output force (F_out) for a machine can be calculated using the formula:
[tex]\[ \text{Output Force} = \text{Mechanical Advantage} \times \text{Input Force} \][/tex]
Let's proceed with the calculations for each machine step by step:
1. Machine A:
[tex]\[ \text{Mechanical Advantage} = 5.5 \][/tex]
[tex]\[ \text{Input Force} = 300 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 5.5 \times 300 = 1650.0 \, \text{N} \][/tex]
2. Machine B:
[tex]\[ \text{Mechanical Advantage} = 2.8 \][/tex]
[tex]\[ \text{Input Force} = 350 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 2.8 \times 350 = 980.0 \, \text{N} \][/tex]
3. Machine C:
[tex]\[ \text{Mechanical Advantage} = 4.0 \][/tex]
[tex]\[ \text{Input Force} = 400 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 4.0 \times 400 = 1600.0 \, \text{N} \][/tex]
4. Machine D:
[tex]\[ \text{Mechanical Advantage} = 2.0 \][/tex]
[tex]\[ \text{Input Force} = 375 \, \text{N} \][/tex]
[tex]\[ \text{Output Force} = 2.0 \times 375 = 750.0 \, \text{N} \][/tex]
Now, we compare the calculated output forces:
- Machine A: 1650.0 N
- Machine B: 980.0 N
- Machine C: 1600.0 N
- Machine D: 750.0 N
Clearly, the highest output force among these machines is 1650.0 N for Machine A.
So, the answer is:
A
