Answer :
Answer:
a) [tex]T=0.40 N[/tex]
b) [tex]T=1.9 s[/tex]
Explanation:
Let's find the radius of the circumference first. We know that bob follows a circular path of circumference 0.94 m, it means that the perimeter is 0.94 m.
The perimeter of a circunference is:
[tex]P=2\pi r=0.94[/tex]
[tex]r=\frac{0.94}{2\pi}=0.15 m[/tex]
Now, we need to find the angle of the pendulum from vertical.
[tex]tan(\alpha)=\frac{r}{L}=\frac{0.15}{0.90}=0.17[/tex]
[tex]\alpha=9.44 ^{\circ}[/tex]
Let's apply Newton's second law to find the tension.
[tex]\sum F=ma_{c}=m\omega^{2}r[/tex]
We use centripetal acceleration here, because we have a circular motion.
The vertical equation of motion will be:
[tex]Tcos(\alpha)=mg[/tex] (1)
The horizontal equation of motion will be:
[tex]Tsin(\alpha)=m\omega^{2}r[/tex] (2)
a) We can find T usinf the equation (1):
[tex]T=\frac {mg}{cos(\alpha)}=\frac{0.04*9.81}{cos(9.44)}=0.40 N[/tex]
We can find the angular velocity (ω) from the equation (2):
[tex]\omega=\sqrt{\frac{Tsin(\alpha)}{mr}}=3.31 rad/s[/tex]
b) We know that the period is T=2π/ω, therefore:
[tex]T=\frac{2\pi}{\omega}=\frac{2\pi}{3.31}=1.9 s[/tex]
I hope it helps you!