While fishing, you get bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50s, what is the angle that the fishing line makes with the vertical?

Answer :

Centripetal acceleration (Ac)

= (1/2)v^2/r^2

Gravity = 9.8

Angle with vertical tan = tan ^-1 (Ac/g)

You will get that the answer will be 76.1

Hope this helps

Answer: The correct answer is 75.6 degree.

Explanation:

Calculate the angular velocity.

[tex]\omega =\frac{2\pi }{T}[/tex]

Here, T is the time.

Put T=0.50 s.

[tex]\omega =\frac{2\pi }{0.50}[/tex]

[tex]\omega =12.6\ rad\ per\ second[/tex]

If T is the tension acting on the sinker then tension equals to the centripetal force due to the circular motion as the sinker is moving in the circular motion.

[tex]T=mL\omega ^{2}[/tex]

Here, m is the mass of the sinker and L is the length of the sinker.

By resolving the components of the tension, the vertical component of the tension equals to the weight of the sinker.

[tex]Tcos\theta =mg[/tex]

Calculate the angle  that the fishing line makes with the vertical.

[tex]cos\theta =\frac{mg}{T}[/tex]

[tex]\theta =cos^{-1}(\frac{mg}{T})[/tex]

Put [tex]T=mL\omega ^{2}[/tex].

[tex]\theta =cos^{-1}(\frac{g}{L\omega ^{2}})[/tex]

Put L= 0.25 , g= 9.8 meter per second and [tex]\omega =12.6\ rad\ per\ second[/tex].

[tex]\theta =cos^{-1}(\frac{9.8}{(0.25)\(12.6) ^{2}})[/tex]

[tex]\theta =cos^{-1}(0.25)[/tex]

[tex]\theta =1.32[/tex]

Convert radian into degree by multiplying 57.3 degree.

[tex]\theta =75.6[/tex]

Therefore, the angle that the fishing line makes with the vertical is 75.6 degree.

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