To find the maximum output force at the bike wheel when a force is applied to the axle, we can use the principles of torque.
The torque (τ) produced by the force (F) applied to the axle can be calculated with the formula:
\[ \tau = F \times r \]
where \( r \) is the radius of the axle. Given:
- \( F = 800 \) N
- \( r_{axle} = 0.125 \) m
Calculating the torque for the axle:
\[ \tau_{axle} = 800 , \text{N} \times 0.125 , \text{m} = 100 , \text{N m} \]
Now, the same torque is applied at the wheel, but since the wheel has a larger radius, we can find the output force at the wheel using the same torque formula rearranged for force:
\[ F_{wheel} = \frac{\tau}{r_{wheel}} \]
where \( r_{wheel} = 0.5 \) m. Substituting the values:
\[ F_{wheel} = \frac{100 , \text{N m}}{0.5 , \text{m}} = 200 , \text{N} \]
Thus, the maximum output force of the bike wheel is 200 N.