Respuesta :
Answer:No
Explanation:
Given
mass [tex]m=40 kg [/tex]
[tex]N=0.4 rev/s[/tex]
[tex]\omega =0.8\pi rad/s[/tex]
time [tex]t=10 s[/tex]
using
[tex]\omega =\omega _0+\alpha \cdot t[/tex]
[tex]0.8\pi =\alpha 10[/tex]
[tex]\alpha =0.08\pi rad/s^2[/tex]
at t=5 s
[tex]\omega _2=0+\alpha 5[/tex]
[tex]\omega _2=0.4\pi rad/s[/tex]
tangential acceleration [tex]a_t=\alpha r[/tex]
[tex]a_t=0.08\pi \times 3=0.08\pi=0.754 m/s^2 [/tex]
centripetal acceleration [tex]a_c=(\omega _2)^2r[/tex]
[tex]a_c=(0.4\pi )^{2}\times 3=4.73 m/s^2[/tex]
[tex]a_{net}=\sqrt{(a_c)^2+(a_t)^2}[/tex]
[tex]a_{net}=\sqrt{(4.73)^2+(0.754)^2}[/tex]
[tex]a_{net}=\sqrt{22.941}[/tex]
[tex]a_{net}=4.789 m/s^2[/tex]
maximum frictional force[tex]=\mu mg[/tex]
[tex]F_r=0.6\times 40\times 10=235.2 N[/tex]
maximum Force due [tex]a_{net}=m\times a_{net}[/tex]
[tex]=40\times 4.789=191.58 N[/tex]
[tex]F_s> ma[/tex]
Therefore child does not fall
