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 :

Explanation:

It is given that,

Radius of the front sprockets, [tex]r_f=8.4\ cm=0.084\ m[/tex]

Radius of the rear sprockets, [tex]r_r=4.91\ cm=0.0491\ m[/tex]

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

(a) Linear speed of the front sprockets, [tex]v_f=r_f\times \omega[/tex]

[tex]v_f=0.084\times 12.3[/tex]    

[tex]v_f=1.0332\ m/s[/tex]

[tex]v_f=103.32\ cm/s[/tex]

Linear speed of the rear sprockets, [tex]v_r=r_r\times \omega[/tex]

[tex]v_r=0.0491\times 12.3[/tex]    

[tex]v_r=0.60393\ m/s[/tex]

[tex]v_r=60.393\ cm/s[/tex]

(b) Let [tex]a_r[/tex] is the centripetal acceleration of the chain as it passes around the rear sprocket.

[tex]a_r=\dfrac{v_r^2}{r_r}[/tex]

[tex]a_r=\dfrac{(60.393)^2}{0.0491}[/tex]

[tex]a_r=74283.39\ m/s^2[/tex]

[tex]a_r=7428339\ cm/s^2[/tex]

`Hence, this is the required solution.

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

${teks-lihat-gambar} lcoley8

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