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Experiment No. Experiment No. Experiment No. Experiment No. 5555

Objective :Objective :Objective :Objective : To find the mechanical advantage, velocity ratio and efficiency of

a simple screw jack and plot the graph between :

(i) Efficiency v/s Load

(ii) Effort v/s Load.

Apparatus :Apparatus :Apparatus :Apparatus : Screw jack apparatus, slotted weights, string, outside caliper etc.

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Apparatus DescriptionApparatus DescriptionApparatus DescriptionApparatus Description

SCREW JACK

A screw jack is simply a ramp wrapped around an axle, with

the axle rotated by a handle used as a lever.

A screw jack consists of the following parts:

1. Screw threads: It consists of threads that may be square

or V in shape. However square threads are more efficient

than V threads and are used for power transmission.

2. Head: The screw has a head on its upper end on which the

load W rests.

3. Nut: In the case of a screw jack, the threads of the screw

will slide around upon the fixed threads of the nut fixed in

the frame and which generally forms a part of the body of

the screw jack.

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TheoryTheoryTheoryTheory

Screw jack is used to raise heavy loads. The apparatus works on a

simple principle of screw and nut. The axial distance between the

corresponding threads is known as PITCH. Let this pitch be p & d

is the diameter of the flanged table on which the load w is to be

placed and lifted.

Let the table turns through one revolution.

Load rises in one revolution = length of the screw jack = l

l = 2pitch

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Or l = 2p

Effort moved in one revolution = D

VelocityVelocityVelocityVelocity ratioratioratioratio

= distance moved by effort / distance moved by load

= D/l

= D/2*p

Total effort in the two hangers including the weight of the

hangers=P

Mechanical advantage = W/P

% = M.A. /V.R. *100

Mechanical advantage (MA)Mechanical advantage (MA)Mechanical advantage (MA)Mechanical advantage (MA) is the factor by which a mechanism multiplies the force put into it. It is the ratio of the

force exerted by a machine (the output) to the force exerted on

the machine, usually by an operator (the input). The theoretical

mechanical advantage of a system is the ratio of the force that

performs the useful work to the force applied, assuming there is

no friction in the system. In practice, the actual mechanical

advantage will be less than the theoretical value by an amount

determined by the amount of friction.

i.e., M.A. = AppliedEffortLiftedLoad

= PW

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Procedure : Procedure : Procedure : Procedure :

1. Wrap the string round the circumference of the

flanged table and pass it over the pulley.

Similarly, wrap another string over the

circumference of the flanged table and take it

over the second pulley. The free ends of both

the strings be tied to the two hangers where the

weights are to be hanged,

2. Measure the pitch of the thread with the help of

the Vernier Caliper.

3. Place the load W on the screw head and some

weight on hangers so that the load W is just

lifted. The effort P is equal to the sum of the

weights hanged in the two hangers.

4. Increase the loads and find the corresponding

efforts applied for the consecutive readings.

5. Calculate mechanical advantage, velocity ratio

and efficiency in each case.

6. Plot the graph between efficiency v/s load,

effort v/s load.

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Observations : Observations : Observations : Observations : (i) Circumference of table = 39.88 cm.

(ii) Load of screw = 2 x p = 12 mm.

(iii) Velocity ratio = D = 33.23

L

Calculations : Calculations : Calculations : Calculations :

Diameter of load pulley = 127 mm.

Pitch of screw jack = 6 mm.

Weight of screw jack system = 5.875 K.g.

Velocity Ratio (V.R.) = D = 3.14 x 127

2 p 2 x 6

(V.R.) = 398.78 = 33.23

12

S.No. Load

Effort

M.A. =

W/P

% = ( M.A./

V.R.) * 100

kg (W)

P Kg= P1

+ P2

1 5.875+0.969=6.844 0.570 12.00 36.11

2 5.875+1.927=7.802 0.650 12.00 36.11

3 5.875+2.427=8.302 0.680 12.20 36.71

4 5.875+2.929=8.804 0.720 12.22 36.79

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1. Mechanical Advantage (M.A.) = W = 6.844

P 0.570

M.A. = 12.00

% = M.A. x 100 V.R.

% = 12.00 x 100 = 36.11 33.23

2. Mechanical Advantage (M.A.) = W = 7.802

P 0.650

M.A. = 12.00

% = M.A. x 100 V.R.

% = 11.44 x 100 = 36.11 33.23

3. Mechanical Advantage (M.A.) = W = 8.302

P 0.680

M.A. = 12.20

% = M.A. x 100

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V.R.

% = 12.20 x 100 = 36.71 33.23

4. Mechanical Advantage (M.A.) = W = 8.804

P 0.720

M.A. = 12.22

% = M.A. x 100 V.R.

% = 12.22 x 100 = 36.79 33.23

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Graphical analysisGraphical analysisGraphical analysisGraphical analysis Graph Graph Graph Graph 1111

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Graph Graph Graph Graph 2222

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RRRResult:esult:esult:esult: The Mechanical Advantage of the given simple screwjack = 12.10.

Velocity Ratio = 33.23

Efficiency = 36.43%

Conclusion: Conclusion: Conclusion: Conclusion: A. On analysis of Effort v/s Load graph, we observe that that

a minimum initial effort has to be applied even when the load is

zero, and then the effort varies linearly with load with a low

value of slope of the straight line being formed. Hence, we

conclude that a large amount of load can be lifted by applying

comparatively much lesser effort.

B. On analysis of Efficiency v/s Load, we conclude that the

efficiency of an apparatus remains constant even if the load

is varied, and hence the Mechanical Advantage is also constant.

pppprecautions : recautions : recautions : recautions : 1. Use both the pulleys to find the values of effort P to

avoid the side thrust.

2. The load and effort should move slowly. 3. Add weights in hangers gently. 4. Lubricate the screw to decrease friction. 5. The string should not overlap. 6. There should be no knot in the string. 7. See that both the pans should move downwards.

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Sources of ErrorSources of ErrorSources of ErrorSources of Error

1. The friction offered by pulleys is bound to introduce some

error in the readings. No matter what amount of lubrication

is done, pulleys can never be made completely frictionless.

2. Friction due to the screws of the screw jack may also

introduce error.

3. If the string is not inextensible or if it overlaps or if there

is a knot in the string, then it will result in error.

4. Weights in the pan may be added forcefully. This should not

happen, as this will introduce the impulse causing an error.

References: References: References: References:

Write ups provided in the Applied Mechanics Lab.

www.wikipedia.org/wiki/jackscrew

Applied Mechanics-Statics and Strengths of Materials

by U.C.Jindal

Encyclopedia : Encarta