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lapo4ka [179]
3 years ago
8

A 13.0 kg wheel, essentially a thin hoop with radius 1.80 m, is rotating at 469 rev/min. It must be brought to a stop in 16.0 s.

(a) How much work must be done to stop it? (b) What is the required average power? Give absolute values for both parts.
Physics
1 answer:
Stella [2.4K]3 years ago
7 0

Answer:

Explanation:

Given

mass of wheel m=13 kg

radius of wheel=1.8 m

N=469 rev/min

\omega =\frac{2\pi \times 469}{60}=49.11 rad/s

t=16 s

Angular deceleration in 16 s

\omega =\omega _0+\alpha \cdot t

\alpha =\frac{\omega }{t}=\frac{49.11}{16}=3.069 rad/s^2

Moment of Inertia I=mr^2=13\times 1.8^2=42.12 kg-m^2

Change in kinetic energy =Work done

Change in kinetic Energy=\frac{I\omega ^2}{2}-\frac{I\omega _0^2}{2}

\Delta KE=\frac{42.12\times 49.11^2}{2}=50,792.34 J

(a)Work done =50.79 kJ

(b)Average Power

P_{avg}=\frac{E}{t}=\frac{50.792}{16}=3.174 kW

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