Question

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°

Answer 1

Complete Question

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Answer:

1 The time it would take for the bob to return back is
`T= 3.393\ sec`

2 small angle approximation mean that the sin of that angle which in radians is equal to the angle i.e
`sin \theta = \theta`

This approximation do reach an error of 1% at about 10° hence the small approximation is for angle less than 10°

Step-by-step explanation:

From the question we are told that

The mass of the pendulum is
`m_p = 8.00kg`

The length of the cable is
`L = 2.86m`

The length of the hook from the floor is
`L_h = 10m`

Generally the Time period of a pendulum is not dependent on mass

And this time period is mathematically represented as

`T = 2 \pi * \sqrt{(L)/(g) }`

Substituting values

`T = 2 \pi * \sqrt{(2.86)/(9.8) }`

`= 3.393\ sec`