Question

The front and rear sprockets on a bicycle have radii of 8.40 and 4.91 cm, respectively. The angular speed of the front sprocket is 12.3 rad/s. Determine (a) the linear speed (in cm/s) of the chain as it moves between the sprockets and (b) the centripetal acceleration (in cm/s2) of the chain as it passes around the rear sprocket.

Answer 1

Explanation:

It is given that,

Radius of the front sprockets, $r_f=8.4\ cm=0.084\ m$

Radius of the rear sprockets, $r_r=4.91\ cm=0.0491\ m$

The angular speed of the front sprocket is 12.3 rad/s, $\omega_f=12.3\ rad/s$

(a) Linear speed of the front sprockets, $v_f=r_f\times \omega$

$v_f=0.084\times 12.3$    

$v_f=1.0332\ m/s$

$v_f=103.32\ cm/s$

Linear speed of the rear sprockets, $v_r=r_r\times \omega$

$v_r=0.0491\times 12.3$    

$v_r=0.60393\ m/s$

$v_r=60.393\ cm/s$

(b) Let $a_r$ is the centripetal acceleration of the chain as it passes around the rear sprocket.

$a_r=\dfrac{v_r^2}{r_r}$

$a_r=\dfrac{(60.393)^2}{0.0491}$

$a_r=74283.39\ m/s^2$

$a_r=7428339\ cm/s^2$

`Hence, this is the required solution.

Answer 2

Answer:

a) the linear speed is 103.32 cm/s

b) the centripetal acceleration is 2174.139 cm/s²

Explanation:

the solution is in the attached Word file

Download docx