Question
In a hydraulic lift whose ideal mechanical advantage is 5, how far can the output platform be lifted when the input platform is depressed 43.0 cm?
Answers
GPT-4o mini
To determine how far the output platform can be lifted in a hydraulic lift with an ideal mechanical advantage (IMA) of 5, we can use the relationship between the input distance and the output distance in a hydraulic system.
The ideal mechanical advantage is defined as:
\[
\text{IMA} = \frac{d_{\text{input}}}{d_{\text{output}}}
\]
Where:
- \( d_{\text{input}} \) is the distance the input platform is moved (43.0 cm).
- \( d_{\text{output}} \) is the distance the output platform is lifted.
From the formula, we can express the output distance as:
\[
d_{\text{output}} = \frac{d_{\text{input}}}{\text{IMA}}
\]
Substituting the given values:
\[
d_{\text{output}} = \frac{43.0 \, \text{cm}}{5}
\]
Calculating this gives:
\[
d_{\text{output}} = 8.6 \, \text{cm}
\]
Therefore, the output platform can be lifted **8.6 cm** when the input platform is depressed by 43.0 cm.
The ideal mechanical advantage is defined as:
\[
\text{IMA} = \frac{d_{\text{input}}}{d_{\text{output}}}
\]
Where:
- \( d_{\text{input}} \) is the distance the input platform is moved (43.0 cm).
- \( d_{\text{output}} \) is the distance the output platform is lifted.
From the formula, we can express the output distance as:
\[
d_{\text{output}} = \frac{d_{\text{input}}}{\text{IMA}}
\]
Substituting the given values:
\[
d_{\text{output}} = \frac{43.0 \, \text{cm}}{5}
\]
Calculating this gives:
\[
d_{\text{output}} = 8.6 \, \text{cm}
\]
Therefore, the output platform can be lifted **8.6 cm** when the input platform is depressed by 43.0 cm.