The ideal mechanical advantage (IMA) of a hydraulic lift is given by the ratio of the distance the input piston moves to the distance the output piston moves. Mathematically, this can be expressed as:
\[ \text{IMA} = \frac{d_{\text{input}}}{d_{\text{output}}} \]
Where:
- \( d_{\text{input}} \) is the distance the input platform is depressed,
- \( d_{\text{output}} \) is the distance the output platform is lifted.
Given that the ideal mechanical advantage (IMA) is 25 and the input platform is depressed by 100 cm, we can rearrange the formula to solve for the distance the output platform is lifted:
\[ d_{\text{output}} = \frac{d_{\text{input}}}{\text{IMA}} \]
Substituting the known values:
\[ d_{\text{output}} = \frac{100 , \text{cm}}{25} = 4 , \text{cm} \]
Therefore, the output platform can be lifted 4 cm.
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