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A 500-kg ball at the end of a 30-m cable suspended from a crane is used to demolish an old building.

Part A

If the ball has an initial angular displacement of 30? from the vertical, determine its speed at the bottom of the arc.

Express your answer to two significant figures and include the appropriate units.

Respuesta :

Answer:

Velocity will be equal to 8.88 m/sec  

Explanation:

We have given mass m = 500 kg

Length of cable l = 30 m

Angular displacement of the ball [tex]\Theta =30^{\circ}[/tex]

Gravitational potential energy of the ball at the displaced position is equal to [tex]U=mgl(1-cos\Theta )[/tex]

Maximum kinetic energy of the ball [tex]Ke=\frac{1}{2}mv^2[/tex]

According to energy conservation

[tex]\frac{1}{2}mv^2=mgl(1-cos\Theta )[/tex]

[tex]v=\sqrt{2gl(1-cos\Theta )}=\sqrt{2\times 9.8\times 30\times (1-cos30^{\circ})}=8.875m/sec[/tex]

So velocity will be equal to 8.88 m/sec

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