To determine the force exerted on the resistance by the machine, we need to use the concept of Ideal Mechanical Advantage (IMA). The IMA of a machine is defined by the ratio of the resistance force to the effort force. Mathematically, it can be expressed as:
[tex]\[ \text{IMA} = \frac{\text{resistance force}}{\text{effort force}} \][/tex]
Given the following values:
- IMA = 4
- Effort force = 6.0 newtons
We need to find the resistance force. We can rearrange the formula to solve for the resistance force as:
[tex]\[ \text{resistance force} = \text{IMA} \times \text{effort force} \][/tex]
Substituting the given values into the formula:
[tex]\[ \text{resistance force} = 4 \times 6.0 \][/tex]
[tex]\[ \text{resistance force} = 24.0 \, \text{newtons} \][/tex]
Therefore, the force exerted on the resistance by the machine is [tex]\(24 \, \text{newtons}\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{24 \, \text{N}} \][/tex]
