To find the maximum output force of the bike wheel given the force applied to the axle, we can use the principle of mechanical advantage in a wheel and axle system.
The mechanical advantage (MA) can be calculated using the ratio of the radii of the wheel and the axle:
\[ MA = \frac{R_{wheel}}{R_{axle}} \]
Where:
- \(R_{wheel} = 0.5 , \text{m}\) (radius of the wheel)
- \(R_{axle} = 0.125 , \text{m}\) (radius of the axle)
Now, substituting the values:
\[ MA = \frac{0.5}{0.125} = 4 \]
Now, the output force can be calculated by multiplying the applied force by the mechanical advantage:
\[ F_{output} = MA \times F_{input} \]
Where:
- \(F_{input} = 800 , \text{N}\)
Thus,
\[ F_{output} = 4 \times 800 , \text{N} = 3200 , \text{N} \]
Therefore, the maximum output force of the bike wheel is 3,200 N.
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