Two wheel gears are connected by a chain. The larger gear has a radius of 5 centimeters and the

smaller gear has a radius of 3 centimeters. The smaller gear completes 36 revolutions in 20

seconds.

What is the linear velocity of each of the gears in centimeters per minute

Question

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Respuesta :

preety89 preety89 · Answer 1 · 2020-04-12T12:57:57+02:00

Answer:

The center velocity of both gears is same & equal to 2034.72 [tex]\frac{cm}{min}[/tex]

Step-by-step explanation:

Given data

[tex]R_1[/tex] = 5 cm

[tex]R_2[/tex] = 3 cm

[tex]N_2 =[/tex] 36 rev in 20 sec

[tex]\omega_2 = 2 \pi N_2[/tex]

[tex]\omega_2[/tex] = 2 × 3.14 × 1.8

[tex]\omega_2[/tex] = 11.304 [tex]\frac{rad}{s}[/tex]

We know that for the set of gears

[tex]R_1\omega_1 = R_2\omega_2[/tex]

[tex]5 \omega_1 =[/tex] 3 × 11.304

[tex]\omega_1[/tex] = 6.7824 [tex]\frac{rad}{s}[/tex]

liner velocity of the first gear

[tex]V_1 = R_1 \omega_1[/tex]

[tex]V_1 =[/tex] 5 × 6.7824

[tex]V_1 =[/tex] 33.912 [tex]\frac{cm}{s}[/tex]

[tex]V_1 =[/tex] 20.34.72 [tex]\frac{cm}{min}[/tex]

liner velocity of the second gear

[tex]V_{2} = R_2 \omega_2[/tex]

[tex]V_2 =[/tex] 3 × 11.304

[tex]V_2 =[/tex] 2034.72 [tex]\frac{cm}{min}[/tex]

Therefore the center velocity of both gears is same & equal to 2034.72 [tex]\frac{cm}{min}[/tex]