Answer:
[tex]P = 133.13 Watt[/tex]
Explanation:
Initial angular speed of the ferris wheel is given as
[tex]\omega_i = 2\pi f[/tex]
[tex]\omega_i = 2\pi(8.5/3600)[/tex]
[tex]\omega_i = 0.015 rad/s[/tex]
final angular speed after friction is given as
[tex]\omega_f = 2\pi f[/tex]
[tex]\omega_f = 2\pi(7.5/3600)[/tex]
[tex]\omega_f = 0.013 rad/s[/tex]
now angular acceleration is given as
[tex]\alpha = \frac{\omega_f - \omega_i}{\Delta t}[/tex]
[tex]\alpha = \frac{0.015 - 0.013}{15}[/tex]
[tex]\alpha = 1.27 \times 10^{-4} rad/s^2[/tex]
now torque due to friction on the wheel is given as
[tex]\tau = I \alpha[/tex]
[tex]\tau = (6.97 \times 10^7)(1.27 \times 10^{-4})[/tex]
[tex]\tau = 8875.3 N m[/tex]
Now the power required to rotate it with initial given speed is
[tex]P = \tau \omega[/tex]
[tex]P = 8875.3 \times 0.015[/tex]
[tex]P = 133.13 Watt[/tex]
