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A cyclist intends to cycle up a 7.70o hill whose vertical height is 126m. Assuming the mass of bicycle plus person is 75.0kg, calculate how much work must be done against gravity. If each complete revolution of the pedals moves the bike 5.12m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 38.8cm.

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Answer:

92704.5 J

596.44737 N

Explanation:

m = Mass of person + bicycle = 75 kg

g = Acceleration due to gravity = 9.81 m/s²

h = Vertical height = 126 m

[tex]\theta[/tex] = Angle = 7.7°

d = Diameter = 0.388 m

Work done against gravity is given by

[tex]P=mgh\\\Rightarrow P=75\times 9.81\times 126\\\Rightarrow P=92704.5\ J[/tex]

Work done is 92704.5 J

Force required is given by

[tex]F=\dfrac{mgrsin\theta}{\pi d}\\\Rightarrow F=\dfrac{75\times 9.81\times sin7.7\times 5.12}{\pi\times 0.388}\\\Rightarrow F=596.44737\ N[/tex]

The force is 596.44737 N

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