Answer:
h = 14.4 m
Explanation:
The height can be calculated by energy conservation:
[tex] K_{r} + K_{t} - W = E_{p} [/tex]
Where:
W: is the work
[tex]E_{p}[/tex]: is the potential energy
[tex]K_{r}[/tex]: is the rotational kinetic energy
[tex]K_{t}[/tex]: is the transitional kinetic energy
Initially, the wheel has rotational kinetic energy and translational kinetic energy, and then when stops it has potential energy.
[tex] K_{r} + K_{t} - W = E_{p} [/tex]
[tex] \frac{1}{2}I\omega_{0}^{2} + \frac{1}{2}mv^{2} - W = mgh [/tex]
Where:
I: is the moment of inertia = 0.800 mr²
ω₀: is the angular speed = 25.0 rad/s
m: is the mass = P/g = 397 N/9.81 m*s⁻² = 40.5 kg
v: is the tangential speed = ω₀r²
Now, by solving the above equation for h we have:
[tex] h = \frac{\frac{1}{2}(I\omega_{0}^{2} + mv^{2}) - W}{mg} [/tex]
[tex] h = \frac{\frac{1}{2}(I\omega_{0}^{2} + m(\omega_{0}*r)^{2}) - W}{mg} [/tex]
[tex] h = \frac{\frac{1}{2}(0.800*40.5 kg*(0.600 m)^{2}*(25.0 rad/s)^{2} + 40.5 kg*(25.0 rad/s*0.600 m)^{2}) - 2500 J}{40.5 kg*9.81 m/s^{2}} = 14.4 m [/tex]
Therefore, the height is 14.4 m.
I hope it helps you!
