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Nat2105 [25]
3 years ago
8

Assume that a 4.00 kg pendulum bob is hanging from a 7.90 m long cable. The cable is attached to a hook in the ceiling 10 m up f

rom the floor. (a) If a person releases the bob, from the small angle approximation, how long will it take the bob to swing back to him? s (b) What is meant by the small angle approximation? any angle less than 3° any angle less than 5° any angle less than 10° any angle less than 15°

Physics
1 answer:
leonid [27]3 years ago
3 0

Answer:

Explanation:

Given

mass of Pendulum m=4 kg

Length of cable= 7.90 m

Distance between roof and Floor=10 m

mg\sin\thetawill Provide Torque

thus mg\sin \theta \times L=I\cdot \alpha

where I=moment of inertia

\alpha=angular acceleration

here \thetais small therefore \sin \theta \approx \theta

\frac{g}{L}\theta =\alpha

thus \omega ^2=\frac{g}{L}

\omega =\sqrt{\frac{g}{L}}

And T\cdot \omega =2\pi

T=2\pi \sqrt{\frac{L}{g}}

T=2\pi \sqrt{\frac{7.90}{9.8}}=5.64 s

Small angle refers to any angle where

\sin \theta \approx \thetai.e. any angle less than 15^{\circ}

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