Respuesta :
Answer:
D = 72.68 m
Explanation:
given,
R = 100 m
angular speed = 0.1 rad/s
distance she can be pulled before the centripetal acceleration reaches 5g = 49 m/s².
using conservation of Angular momentum
[tex]I_i\omega_i= I_f\omega_f[/tex]
[tex]mr_i^2\omega_i=m r_f^2\omega_f[/tex]
[tex]\omega_f = \dfrac{r_i^2}{r_f^2}\times \omega_i[/tex]
[tex]\omega_f = \dfrac{r_i^2}{r_f^2}\times \omega_i[/tex]
we know,
centripetal acceleration
[tex]a = \dfrac{v^2}{r}[/tex]
v = r ω
[tex]a =\omega_f^2 r_f [/tex]
[tex]a =(\dfrac{r_i^2}{r_f^2}\times \omega_i)^2 r_f [/tex]
[tex]a =\dfrac{r_i^4\times \omega_i^2}{r_f^3}[/tex]
[tex]r_f^3=\dfrac{100^4\times 0.1^2}{5\times 9.8}[/tex]
[tex]r_f^3=20408.1632[/tex]
[tex]r_f = 27.32\ m[/tex]
distance she has reached inward is equal to
D = 100 - 27.23
D = 72.68 m
