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Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli
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A cyclist intends to cycle up a 7.8° hill whose vertical height is 150 m. Assuming the

Chapter 6, Problem 46P

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QUESTION:

Problem 46P

A cyclist intends to cycle up a 7.8° hill whose vertical height is 150 m. Assuming the mass of bicycle plus cyclist is 75 kg, (a) calculate how much work must be done against gravity, (b) If each complete revolution of the pedals moves the bike 5.1 m 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 36 cm.

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QUESTION:

Problem 46P

A cyclist intends to cycle up a 7.8° hill whose vertical height is 150 m. Assuming the mass of bicycle plus cyclist is 75 kg, (a) calculate how much work must be done against gravity, (b) If each complete revolution of the pedals moves the bike 5.1 m 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 36 cm.

ANSWER:

Solution

Step 1 of 2

  1. We need to find out how much work must be done against gravity.

        The work done against gravity is nothing but the change in the potential energy.

                        

                        

Given,

        The mass of bicycle plus cyclist is

The vertical height of the hill is

So,

                        

The work done against the gravity is .

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