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A washing machine’s two spin cycles are 328 rev/min and 542 rev/min. The diameter of the drum is 0.43 m.

a. What is the ratio of the centripetal accelerations for the fast and slow spin cycles? Recall that ac=v2r
and v = rω
b. What is the ratio of the linear velocity of an object at the surface of the drum for the fast and slow spin cycles?
c. Find the maximum centripetal acceleration in terms of g for the washing machine.

Respuesta :

  • Diameter=0.43m
  • Radius=0.21m

#1

[tex]\\ \tt\rightarrowtail \dfrac{a_1}{a_2}=\dfrac{(v1)^2r}{(v2)^2r}[/tex]

  • putting v=rw

[tex]\\ \tt\rightarrowtail \dfrac{a_1}{a_2}=\dfrac{r^3\omega_1^2}{r^3\omega_2^2}[/tex]

  • Cancel r^3

[tex]\\ \tt\rightarrowtail \dfrac{a_1}{a_2}=\dfrac{(328)^2}{(542)^2}[/tex]

[tex]\\ \tt\rightarrowtail a_1:a_2=107584:293764[/tex]

#2

[tex]\\ \tt\rightarrowtail v_1:v_2=328:542=164:271[/tex]

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