Centrifugal

Applied Mechanics

U n i v e r s i t y o f M a u r i t i u s

Course:B.Eng Chemical and Environmental Engineering

Module:Applied Mechanics (MECH1213)

Report submitted by

Tirukumaren Periacarpen 0612824,

To

Dr.K.Elahee

Centrifugal Force Experiment

Applied Mechanics

We are all familiar with the effects of centrifugal force, we experience it for example every time we are in a car and take a bend - we feel a force pushing us to the outside of the curve. If, for example, you have placed your sunglasses on the seat next to you it would come as no surprise if, when taking a sharp bend at speed, they slide across the seat.

Centrifugal force is sometimes referred to as a 'fictitious' force, because it is present only for an accelerated object and does not exist in an inertial frame. An inertial frame is where an object moves in a straight line at a constant speed. But Einstein's general theory of relativity allows observers even in a non-inertial frame to regard themselves at rest, and the forces they feel to be real. Centrifugal force is not fictitious, it is a real force.

Centrifugal force arises due to the property of mass known as inertia - the reluctance of a body to change either its speed or direction. A body that is at rest will stay at rest until some force makes it move, and then will continue to move at the same speed and in the same direction unless and until some force changes the way it is moving. This is all neatly summed up by Isaac Newton's three laws of motion.

I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (This is sometimes referred to as The Law of Inertia)

II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.

III. For every action there is an equal and opposite reaction.

An object moving in a circle at a constant speed changes direction and therefore velocity, and so is subject to acceleration towards the centre.The resultant force is called the centrifugal or centripetal force. For and object of mass m moving with speed v in a circle of radius r the magnitude of this force is (mv2/r)

The apparatus allows both v and r to be varied independently with the resultant force being balanced against the tension in a spiral spring.


Applied Mechanics

The TQ TM105 Centrifugal Force Apparatus is designed to demonstrate the relationship between centrifugal force, mass of a rotating body, its distance from the axis, and its angular velocity. It consists of 2 pivoted counter balanced bell-cranked (A) housed in the slideable blocks (B) as shown in fig 1. Various combinations of accurately machined masses (C) can be fitted to the end of the bell of the bell-crank arms. The slideable blocks are held in position by locating pins (D). each block can be fitted in five different radial positions corresponding to five equally spaced holes in each end of the horizontal member (E).

The rotating member is belt driven from a variable speed 12 V d.c electric motor contained in the base unit (F). The motor is controlled by the E67 speed controller. An optical tachometer sensor is also incorporated, and an output socket for connecting the E64 Tachometer Unit is provided on the front of the module unit.

A transparent safety dome covers the rotating assembly. Removal of the dome disconnects the motor from the power supply.

With the upper masses (Ma) at radius r and rotating at ω rad/s, the force on each mass is given by: F = Maω2r.The centrifugal force at the condition of the balance is equal to the weight of the lower mass Mb.

F = Maω2r =Mb g …………………………………………………………………(1)

The angular velocity ω can be determined by measuring the speed of the rotation when the upper masses move outwards.


Applied Mechanics

Introduction:-

When a body moves in a circle, it is accelerated even if its speed is constant. Its velocity is changing and the acceleration acts towards the center of rotation- the centripetal acceleration. It may also have a linear acceleration in the case of motion in the case of motion at non-uniform speed.

Calculation of Centripetal Force.

dv = (rω)dθ

=> dv = rω dθ dt dt

a = ω2r.

Where a : linear acceleration.

Centripetal Force:

From Newton’s Law F = ma = mω2r.

The Centrifugal Force.

This is reaction due to the centrifugal force acting on the centre 0. It is brought by the tension in the string in the case of a body attached to a string undergoing circular motion.


Applied Mechanics

Each factor that affects the centrifugal force can be investigated separately. In the first series of tests, the effects of varying the angular velocity and the mass of the rotating body are determined for a constant radius. The procedure is as follows:

1. Raise the locating pins on the sliding blocks and the position the blocks so that they are both the same distance from the center. Then push down the pins to locate the blocks firmly on the horizontal member. Note the distance from the axis to the pivots of the bell-cranks.

2. Screw a body of mass 25g on each vertical arm of the two bell cranks. Screw a combination of the bodies’ equivalent to; say 125g, on each horizontal arm of the two bell-cranks. The magnitude of the masses on the respective arms of the bell-crank must be the same.

3. Replace the dome and start the motor using the E90 speed control unit. Slowly increase the speed until the bell-cranks are flung outwards with an audible “click”. Note the approximated speed at which this happens. The movement of the bell-crank can also be seen by carefully observing them from a position level with the plane of rotation.

4. Decrease the speed until the bell-cranks return to their original positions, then increase the speed very slowly and repeat the reading. Record the speed indicated on the E64 Tachometer at the instant when the upper arm of the bell-cranks moves outwards. The effect of stiction in the pivots may mean that the two bell-cranks do not move simultaneously. If that is the case, always record the speed when the first one moves. Note that when the bell-cranks move outwards, their configuration is altered so that a substantial reduction in the speed is required to return them to their original positions.

5. By reducing the masses of the lower bodies B by 25g at a time, obtain further results foe each value of Mb (mass of the lower body) down to 25g.

6. Repeat this series of tests for two more values of Ma ( mass of the upper body ), the mass of each of the two upper bodies A (see Table 1).


Applied Mechanics

7. To determine the effect of radius, for the two values of the upper masses Ma,

(Ma = 25, and 50g) conduct series of tests with the slider brackets set at different radial positions. For each different position, take readings of the speed for a range of lower masses Mb, as in the first series of tests (see Table 2). Note: you should have two (2) different Table 2, i.e, one When Ma = 25g, and another one when Ma= 50g.

Mb/g

R= 125 mm

Ma = 40 gN(rpm)

Ma = 65 gN(rpm)

Ma = 90 gN(rpm)

215 200 151 130190 187 142 125165 172 130 117140 156 120 105115 145 108 9290 125 90 8565 105 79 7040 82 65 50Signature

Table 1.0


Applied Mechanics

Mb/g

Ma = 40 g

r = 125 mmN(rpm)

r = 95 mmN(rpm)

r = 65 mmN(rpm)

40 82 92 11065 105 125 14790 125 138 170115 145 162 190140 156 180 218165 172 198 235190 187 212 250215 200 228 270Signature

Table 2.0

Mb/g

Ma = 65 g

r = 125 mmN(rpm)

r = 95 mmN(rpm)

r = 65 mmN(rpm)

40 62 72 8765 81 92 11290 94 109 132115 111 122 150140 122 134 164Signature

Table 3.0


Applied Mechanics

Mb/g

R= 125 mm

Ma = 40 gω2/rad s-2



215 439 250 185190 384 221 171165 324 185 150140 267 158 121115 231 128 92.890 171 88.8 79.265 121 68.4 53.740 73.7 46.3 27.4

Table 1.1

Mb/g

Ma = 40 g

r = 125 mmω2/rad s-2



40 73.7 92.8 13365 121 171 23790 171 209 317115 231 288 396140 267 355 521165 324 430 606190 384 493 685215 439 570 799

Table 2.1

Mb/g

Ma = 65 g





Applied Mechanics

40 42.2 56.8 83.065 72.0 92.8 13890 96.9 130 191115 135 163 247140 163 197 295

Table 3.1


Applied Mechanics

1.3. When r = 125 mm.


Applied Mechanics

When r = 125 mm.

Table 1.2


When Ma = 40 g When Ma = 65 g When Ma = 90 g

Mb/g F = Mb.g /N F = Maω2r/N F = Maω2r/N F = Maω2r/N

215 2.11 2.20 2.03 2.08

190 1.86 1.92 1.80 1.92

165 1.62 1.62 1.50 1.69

140 1.37 1.34 1.28 1.36

115 1.13 1.16 1.04 1.04

90 0.883 0.855 0.722 0.891

65 0.638 0.605 0.556 0.604

40 0.392 0.369 0.376 0.308

Applied Mechanics

When Ma = 40 g.

Table 2.2


When r = 125 mm When r = 95 mm When r = 65 mm


40 0.392 0.369 0.353 0.346

65 0.638 0.605 0.650 0.616

90 0.883 0.855 0.794 0.824

115 1.13 1.16 1.09 1.03

140 1.37 1.34 1.35 1.35

165 1.62 1.62 1.63 1.58

190 1.86 1.92 1.87 1.78

215 2.11 2.20 2.17 2.08

Applied Mechanics

When Ma = 65 g.

Table 3.2


When r = 125 mm When r = 95 mm When r = 65 mm


40 0.392 0.343 0.351 0.351

65 0.638 0.585 0.573 0.583

90 0.883 0.785 0.803 0.807

115 1.13 1.10 1.01 1.04

140 1.37 1.32 1.22 1.25

Applied Mechanics

2.3. When Ma = 40 g.


Applied Mechanics

3.3 When Ma = 65 g.


Applied Mechanics


Applied Mechanics

Compare the measured value of centrifugal force and the theoretical centrifugal force.

Its clearly seen that the value obtained for the centrifugal force is closer to the theoretical one. But when Ma(the upper mass) and the Radius, r increases so do the speed of rotation and in this case the two values are more precise.

The effect of the centrifugal force on the upper mass,Ma and the effect of the lower mass,Mb on the movement of he bell-cranked.

It is observed that, when Mb decreases the centrifugal also decreases, so a lower speed is required to rotate the bell-cranked and to lift the mass Mb.

Internet –

www.DAnote:centrifugal.int.com www.en.wikipedia.org/wiki/centrifugalforce

www.centrifugal/apparatus.edu

www.centrifugalapparatus.com


http://www.centrifugalapparatus.com/

http://www.centrifugal/apparatus.edu

http://www.en.wikipedia.org/wiki/centrifugalforce

Centrifugal

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