Respuesta :
Answer:
a) T = 2.26 N, b) v = 1.68 m / s
Explanation:
We use Newton's second law
Let's set a reference system where the x-axis is radial and the y-axis is vertical, let's decompose the tension of the string
sin 30 = [tex]\frac{T_x}{T}[/tex]
cos 30 = [tex]\frac{T_y}{T}[/tex]
Tₓ = T sin 30
T_y = T cos 30
Y axis
T_y -W = 0
T cos 30 = mg (1)
X axis
Tₓ = m a
they relate it is centripetal
a = v² / r
we substitute
T sin 30 = m[tex]\frac{v^2}{r}[/tex] (2)
a) we substitute in 1
T = [tex]\frac{mg }{cos 30}[/tex]
T = [tex]\frac{ 0.2 \ 9.8}{cos \ 30}[/tex]
T = 2.26 N
b) from equation 2
v² = [tex]\frac{T \ sin 30 \ r}{m}[/tex]
If we know the length of the string
sin 30 = r / L
r = L sin 30
we substitute
v² = [tex]\frac{ T \ sin 30 \ L \ sin 30}{m}[/tex]
v² = [tex]\frac{TL \ sin^2 30}{m}[/tex]
For the problem let us take L = 1 m
let's calculate
v = [tex]\sqrt{ \frac{2.26 \ 1 \ sin^230}{0.2} }[/tex]
v = 1.68 m / s
