Question
A pulley system has a mechanical advantage of 3, and an object weighing 9 Newtons must be lifted 15 meters. How much force must be applied to lift the object?
Answers
GPT-4o mini
To find the force that must be applied to lift the object using a pulley system with a mechanical advantage (MA) of 3, we can use the formula for mechanical advantage:
\[
MA = \frac{F_{\text{load}}}{F_{\text{applied}}}
\]
Where:
- \(F_{\text{load}}\) is the weight of the object (9 Newtons),
- \(F_{\text{applied}}\) is the force applied.
We can rearrange the formula to solve for \(F_{\text{applied}}\):
\[
F_{\text{applied}} = \frac{F_{\text{load}}}{MA}
\]
Substituting the given values into the formula:
\[
F_{\text{applied}} = \frac{9 \, \text{N}}{3} = 3 \, \text{N}
\]
So, the force that must be applied to lift the object is:
\[
\boxed{3 \, \text{N}}
\]
\[
MA = \frac{F_{\text{load}}}{F_{\text{applied}}}
\]
Where:
- \(F_{\text{load}}\) is the weight of the object (9 Newtons),
- \(F_{\text{applied}}\) is the force applied.
We can rearrange the formula to solve for \(F_{\text{applied}}\):
\[
F_{\text{applied}} = \frac{F_{\text{load}}}{MA}
\]
Substituting the given values into the formula:
\[
F_{\text{applied}} = \frac{9 \, \text{N}}{3} = 3 \, \text{N}
\]
So, the force that must be applied to lift the object is:
\[
\boxed{3 \, \text{N}}
\]