Centrifugal Force Apparatus PDF

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HITEC University Taxila, Department of Mechanical Engineering Lab Manual

Demonstration of Centrifugal Force Apparatus Objectives i.

ii.

Determination of centrifugal force for three different masses attached to a rod at different radii experimentally and theoretically(relationship between force, mass , radius & velocity) Comparison of experimental and theoretical results.

Apparatus:  Centrifugal force apparatus Theoretical Background: The modern interpretation is that centrifugal force in a rotating reference frame is a pseudo-force that appears in equations of motion in rotating frames of reference, to explain effects of inertia as seen in such frames. Leibniz's centrifugal force may be understood as an application of this conception, as a result of his viewing the motion of a planet along the radius vector, that is, from the standpoint of a special reference frame rotating with the planet. Leibniz introduced the notions of Vis viva (kinetic energy) and action, which eventually found full expression in the Lagrangian formulation of mechanics. In deriving Leibniz's radial equation from the Lagrangian standpoint, a rotating reference frame is not used explicitly, but the result is equivalent to that found using Newtonian vector mechanics in a corotating reference frame.

Procedure:  Setup the apparatus with the desired weight at desired length form the center of rotation in the prefixed places with holes in the rotating rod.  Pre-determine the speed of the device in rotations per minute. Engineering Mechanics Lab ManualPrepared By: Miss Atiya Sadiq

    

Start the apparatus and begin the operation. Note the aforementioned values from before. Note the value of force form the machine. Calculate the actual values for the formulas of rotation. Compare these values and then find the percentage error in the readings we took. Derivation: 2

f=

mv r

As f g= f g=−mr w 2

v = rw −m v r

2

2π

As w=2πN => w= 60 ∗N

f g=−mr

Engineering Mechanics Lab ManualPrepared By: Miss Atiya Sadiq

2π2 ∗N 2 2 60

Calculations and Results: At mass = m = 50g and Radius = r = 0.1m

At fixed R.P.M 200

At Fixed R.P.M 200 and Mass 100g

Conclusion and Comments: We have observed that the device used for this experiment has not been recalibrated in a while. Hence there is an evident error in the reading we took for the value of centrifugal force and those which we calculated by the derived formula. The error on average exceeds 10% hence the device is considered to be unable to give satisfactory readings. We recommend that the device is recalibrated. So that the error can be minimized and acceptable values can be concluded.

Engineering Mechanics Lab ManualPrepared By: Miss Atiya Sadiq

Sample Solution process for Theoretical f g :

2

f g=−mr

2π ∗N 2 2 60

M=0.05kg N=200 RPM R = 0.1m

Substituting values: f g=−0.05∗0.1

2π2 ∗2002 602

f g=−2.20 N

Applications:

 The rotation of the space center is so adjusted that the centrifugal can perfectly mimic the value of g so that the astronauts can feel the same sensation as if they are on earth.  To separate a fluid from a mixture of fluids based on its density.  To calculate the hardness of a tire so that it is not deformed beyond safety limits on sudden acceleration.

Engineering Mechanics Lab ManualPrepared By: Miss Atiya Sadiq...