Velocity Task Introduction: The pedal of a bicycle is attached to a crank arm that revolves when the pedal is pushed by a person's foot. As the crank arm turns, it pulls a chain that is attached to the rear wheel of the bicycle, causing the bicycle to move forward. G 118 18 cm 16 cm A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank arm is 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedaling the bicycle such that the crank arm rotates once every second. Questions: 1. Write an equation that models the vertical position of the foot with respect to the ground, starting from the lowest point, as the crank arm turns. 2. What is the rate of change of the vertical position of the foot when it is at the midline? Explain your answer 3. How fast, in kilometres per hour, is the bicycle moving? 4. Determine an equation that would model the foot's position when the cyclist is traveling 5 km/h. Compare this equation to your equation from question 1 and explain any differences. 5. Use calculus to explain why the rotation velocity of a point on the perimeter of a wheel is the same as the velocity of the pedal. Use examples to support your answer.

Velocity Task Introduction: The pedal of a bicycle is attached to a crank arm that revolves when the pedal is pushed by a person's foot. As the crank arm turns, it pulls a chain that is attached to the rear wheel of the bicycle, causing the bicycle to move forward. G 118 18 cm 16 cm A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank arm is 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedaling the bicycle such that the crank arm rotates once every second. Questions: 1. Write an equation that models the vertical position of the foot with respect to the ground, starting from the lowest point, as the crank arm turns. 2. What is the rate of change of the vertical position of the foot when it is at the midline? Explain your answer 3. How fast, in kilometres per hour, is the bicycle moving? 4. Determine an equation that would model the foot's position when the cyclist is traveling 5 km/h. Compare this equation to your equation from question 1 and explain any differences. 5. Use calculus to explain why the rotation velocity of a point on the perimeter of a wheel is the same as the velocity of the pedal. Use examples to support your answer.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

Velocity Task
Introduction: The pedal of a bicycle is attached to a crank arm that revolves when the
pedal is pushed by a person's foot. As the crank arm turns, it pulls a chain that is
attached to the rear wheel of the bicycle, causing the bicycle to move forward.
C
1
18 cm
16 cm
A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank arm
is 18 cm. At its lowest point, the pedal is 16 cm'above the ground. A person is pedaling
the bicycle such that the crank arm rotates once every second.
Questions:
1. Write an equation that models the vertical position of the foot with respect to the
ground, starting from the lowest point, as the crank arm turns.
2. What is the rate of change of the vertical position of the foot when it is at the
midline? Explain your answer
3.
How fast, in kilometres per hour, is the bicycle moving?
4. Determine an equation that would model the foot's position when the cyclist is
traveling 5 km/h. Compare this equation to your equation from question 1 and
explain any differences.
5. Use calculus to explain why the rotation velocity of a point on the perimeter of a
wheel is the same as the velocity of the pedal. Use examples to support your
answer.
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