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Allushta [10]
3 years ago
10

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.
Physics
2 answers:
Rudik [331]3 years ago
8 0

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.

steposvetlana [31]3 years ago
3 0

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
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A glider moves along an air track with constant acceleration a. It is projected from the start of the track (x = 0 m) with an in
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vo = 0.175m/s

a = -0.040625 m/s^2

Explanation:

To solve this problem, you will need to use the equations for constant acceleration motion:

x = \frac{1}{2}at^2 +v_ot+x_o \\v_f^2 - v_o^2 = 2(x-x_o)a

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1. x = \frac{1}{2}at^2 +v_ot+x_o\\0.1m = \frac{1}{2}a(8s)^2 +v_o(8s)+0m \\0.1 = 32a + 8v_o

2. v_f^2 - v_o^2 = 2(x-x_o)a\\(-0.15m/s)^2 - v_o^2 = 2(0.1m-0m)a\\0.0225 - v_o^2 = 0.2a\\a = \frac{0.0225 - v_o^2}{0.2} = 0.1125 - 5v_o^2

Replacing in the first equation:

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a = 0.1125 - 5v_o^2\\a = -0.040625  m/s^2

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