QuestionJune 22, 2025

Geraint Thomas of Great Britain won the 2018 Tour de France. Suppose he had 140Nm of torque about the crankshaft of his bike after applying a force of 800N vertically.What is the length of Geraint's crankshaft on his racing bike? 2.52mm 112,000mm 175mm 5.71mm

Geraint Thomas of Great Britain won the 2018 Tour de France. Suppose he had 140Nm of torque about the crankshaft of his bike after applying a force of 800N vertically.What is the length of Geraint's crankshaft on his racing bike? 2.52mm 112,000mm 175mm 5.71mm
Geraint Thomas of Great Britain won the 2018 Tour de France. Suppose he had 140Nm of torque about the crankshaft of his bike after applying a force of 800N vertically.What is the length of Geraint's crankshaft on his racing bike? 2.52mm 112,000mm 175mm 5.71mm

Solution
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Answer

175mm Explanation 1. Use the Torque Formula Torque (\tau) is given by \tau = r \cdot F \cdot \sin(\theta), where r is the length of the crankshaft, F is the force applied, and \theta is the angle between the force and the lever arm. Here, \theta = 90^\circ, so \sin(90^\circ) = 1. Thus, \tau = r \cdot F. 2. Solve for the Length of the Crankshaft Given \tau = 140 \, \text{Nm} and F = 800 \, \text{N}, solve for r: \[ r = \frac{\tau}{F} = \frac{140}{800} = 0.175 \, \text{m} = 175 \, \text{mm}. \]

Explanation

1. Use the Torque Formula<br /> Torque ($\tau$) is given by $\tau = r \cdot F \cdot \sin(\theta)$, where $r$ is the length of the crankshaft, $F$ is the force applied, and $\theta$ is the angle between the force and the lever arm. Here, $\theta = 90^\circ$, so $\sin(90^\circ) = 1$. Thus, $\tau = r \cdot F$.<br /><br />2. Solve for the Length of the Crankshaft<br /> Given $\tau = 140 \, \text{Nm}$ and $F = 800 \, \text{N}$, solve for $r$: <br />\[ r = \frac{\tau}{F} = \frac{140}{800} = 0.175 \, \text{m} = 175 \, \text{mm}. \]
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