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patriot [66]
3 years ago
6

A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its ax

le and has the shape of a solid uniform disk. After the bucket has been released, what is the angular acceleration of the pulley
Physics
1 answer:
levacccp [35]3 years ago
7 0

Answer:

\alpha = 6.431\,\frac{rad}{s^{2}}

Explanation:

The pulley is modelled by the Newton's Laws, whose equation of equilibrium is:

\Sigma M = T \cdot R = \frac{1}{2}\cdot M \cdot R^{2}\cdot \alpha

Given that tension is equal to the weight of the bucket, the angular acceleration experimented by the pulley is:

T = \frac{1}{2}\cdot M \cdot R \cdot \alpha

m_{b}\cdot g = \frac{1}{2}\cdot M \cdot R \cdot \alpha

\alpha = \frac{2\cdot m_{b}\cdot g}{M\cdot R}

\alpha = \frac{2\cdot (1.53\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{(7.07\,kg)\cdot (0.66\,m)}

\alpha = 6.431\,\frac{rad}{s^{2}}

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