Answer: [tex]1302.25\ N[/tex]
Explanation:
Given
Inclination of hill [tex]\theta=8^{\circ}[/tex]
Each revolution moves 6 m along its path
Diameter of the circle [tex]D=30\ cm[/tex]
the total mass of the cyclist and his bike [tex]M=150\ kg[/tex]
Suppose a single pedal cyclist gain a vertical height of [tex]\Delta y[/tex]
[tex]\therefore \sin \theta =\dfrac{\Delta y}{6}\\\\\Delta y=6\sin 8^{\circ}[/tex]
Average force cause to gain in Potential energy
[tex]\therefore\ F_{avg}\cdot 2\pi r=Mg\Delta y\\\Rightarrow F_{avg}=\dfrac{150\times 9.8\times 6\sin 8^{\circ}}{2\pi\cdot 0.15}\\\\\Rightarrow F_{avg}=1302.25\ N[/tex]
Thus, the average force is [tex]1302.25\ N[/tex]
