Q. 4 An 18-cm-long bicycle crank arm,... [FREE SOLUTION]

91影视

Chapter 12: Q. 4 (page 330)

An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60rpm to 90 rpm in 10s .
a. What is the tangential acceleration of the pedal?
b. What length of chain passes over the top of the sprocket during this interval?

Short Answer

Expert verified

a. the tangential acceleration of the pedal is $5.652 脳 10^{鈭� 2} m / {sec}^{2}$

b. the length of chain passes over the top of the sprocket during this interval is $7.85 m$

Step by step solution

Part (a)

The initial and final angular velocity, 60 and 90 rpm respectively, the time period for this change of velocity, 10 seconds, and a

The radius of the crank arm, $r = 18 cm$

$\begin{array}{l} 伪 = \frac{d 蝇}{d t} = \frac{(90 鈭� 60) rpm}{10 sec} = \frac{30 rpm}{10 sec} = \frac{(\frac{30}{60 sec} 脳 \frac{rotation}{min} 脳 \frac{2 蟺 rad}{rotation})}{10 sec} \\ 伪 = 0.314 rad / s^{2} \end{array}$

Tangential acceleration

$\begin{array}{l} a_{t} = r 伪 \\ a_{t} = (18 脳 10^{鈭� 2} m) 脳 (0.314 \frac{rad}{s^{2}}) \\ a_{t} = 5.652 脳 10^{鈭� 2} m / {sec}^{2} \end{array}$

Part (b)

The initial and final angular velocity

$\begin{array}{l} 60 鈥塺辫尘 = 60 鈥塺辫尘鈰� \frac{\frac{2 蟺鈥夆赌塺补诲}{60 鈥塻}}{1 鈥夆€塺辫尘} = 6.28 \frac{rad}{s} \\ 补苍诲鈥� \\ 90 鈥塺辫尘鈥�=鈥� 90 鈥塺辫尘鈰� \frac{\frac{2 蟺鈥塺补诲}{60 鈥塻}}{1 鈥夆€塺辫尘} = 9.42 \frac{rad}{s} \end{array}$

Angle turned by the bicycle crank in

$\begin{array}{l} 胃 = 蝇_{i} t + \frac{1}{2} 伪 t^{2} \\ 胃 = (2 蟺) (10 sec) + \frac{1}{2} (0.314 rad / {sec}^{2}) {(10 sec)}^{2} \\ 胃 = 78.5 \end{array}$

If the length of chain passes over the top of sprocket

$\begin{array}{l} S = 胃 r \\ S = 78.5 脳 (0.10 m) \\ S = 7.85 m \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Part (a)

Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Mechanics and Materials

Physics of Motion

Classical Mechanics

Circular Motion and Gravitation

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.