AM225 - Conical Pendulum

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Title: Conical Pendulum

Aim: See your laboratory manual

Apparatus: See your laboratory manual

                     

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**Also See è How To Write Your Mechanical Laboratory Reports For Maximum Performance**

THEORY:

          A conical pendulum is a pendulum that is spun round in a circle instead of swung backwards and forwards. In this experiment a mass is attached to a string and made to spin in a circle of fixed radius, the time period of the motion is related to the length of the string. By varying the length and measuring Time period the acceleration of gravity can be found.

**GENERAL KNOWLEDGE**

          A conical pendulum is a weight (or bob) fixed on the end of a string (or rod) suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of rocking back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string (or rod) tracing out a cone. The conical pendulum was first studied by the English scientist Robert Hooke around 1660 ^[1] as a model for the orbital motion of planets. Later it was used as the timekeeping element in a few mechanical clocks and other clockwork timing devices.

THEORY 1:

Above is a free body diagram for the mass. If the forces are resolved vertically and horizontally:

Vertically the forces are balanced so mg=Fcosθ

Where F is the tension

Horizontally there is centripetal acceleration so mω²r=Fsinθ

Where

m = mass
ω = Angular velocity
r = radius

Dividing gives

mg/mω²r =Fcosθ/Fsinθ =1/ tanθ

But

tanθ = r/h

so,

 ω²r/g= r/h

from the definition

ω = 2π/T so 4π²/gT² = 1/h

Where T = time period

Squaring gives

h² = g²T⁴/16π⁴

From Pythagoras                              L² = h² + r² so h²=L² – r²

Finally

L²=g²T⁴/16π⁴ + r²

By changing L and measuring T keeping r constant use a graphical method to find g.

For Procedures, See your Mechanical Laboratory Manual.

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Observations :-

1.       

Applications:-

1.

PRECAUTIONS:

For Precautions, See General Laboratory Precautions

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**Also See è How To Write Your Mechanical Laboratory Reports For Maximum Performance**

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About Stephen Djes

Stephen Djes is a passionate Graduate of Engineering from the University of Benin, and he is geared towards helping fellow engineering students in the great institution of UNIBEN to do better at academics.