Applied Mechanics By R K Rajput - By www.EasyEngineering.net

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EXPERIMENTS 381

5. Put the weights in the pan till the slider just starts moving. Note down the weights.
6. Measure the angle of inclination from the scale provided and find the value of µ.
7. Calculate M.A., V.R. and % efficiency.

Observations :

S.No. Total Weight of µ= P – W sin α M.A. = W V .R. = %η=
weight of Pan + W cos α P cosec α M. A.
the slider weights V. R.
× 100
W in the pan P

www.EaPrecautions :
s1. The plane should be clean and smooth.
yE2. The guide pulley should move freely. It should be lubricated to make it frictionless.
n3. Weight should be added gently in the pan.
g4. The slider should just begin to move slowly, it should not move abruptly.
in5. The direction of thread should be parallel to the inclined plane.
Eexpeerriimnengt N. o. 6Object. To find the mechanical advantage, velocity ratio and efficiency of a simple

nscrew jack.
etApparatus. Screw jack apparatus (Fig. 6.1), weights, string, vernier calliper, outside calli-

per, metre rod etc.

Theory. Screw jack works on the principle of screw and nut. It is used for raising heavy

loads through small efforts.

Let p = pitch of the screw ; F IPitch is axial distance between
D = diameter of flanged table G Jthe corresponding points on two
W = load to be lifted GH JKconsecutive threads.

P = effort required to lift the load.

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382 APPLIED MECHANICS

Flanged
circular table

String

Pan

w Hook
ww.E Fig. 6.1. Simple screw jack apparatus.
asyNow,
distance moved by the effort in one revolution
distance moved by the load in one revolution
V.R. En==

gineand πD
p

M.A.erin∴= load lifted = W
effort applied P

gProcedure :%η= M. A. × 100
.n1. Measure the circumference of the flanged circular table with the help of an inextensibleV. R.

etthread and metre rod. Or measure the diameter of the table with an outside calliper.
2. Measure the pitch of the screw with help of a vernier calliper.

3. Wrap the string round the circumference of the flanged table and pass it over one pulley.
Similarly wrap another string over the circumference of flanged table and take it over the second
pulley. The free ends of both the strings be tied to two pans in which the weights are to be placed.

4. Hang a known weight (W) on the hook (as shown in Fig. 6.1) and some weights in the
pans so that the load W is just lifted, the effort P is equal to the sum of weights placed in both the
pans.

5. Calculate the M.A., V.R. and % η.

6. Repeat the experiment three or four times.

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EXPERIMENTS 383

Observations :

Circumference V.R. = πD Load Effort M.A. %η = M. A.
of the table p on table P = P1 V .R.
S.No. Pitch p + P2 W × 100
= πD W = P

wwwPrecautions:
.1. To avoid the side thrust use both the pulleys to find the value of effort P.
E2. The screw should be well-lubricated to reduce the friction.
a3. The pulleys should be free from friction.
s4. The load and effort should move slowly.
yE5. The strings should not overlap.

6. The string should be free from any knot.

nginEexpeerriiment No. 7Object. To find the mechanical advantage, velocity ratio and efficiency of a worm
nand worm wheel.

gApparatus. Worm and worm wheel apparatus (Fig. 7.1) weights, string, metre rod, outside
.ncalliper, pan etc.

eTheory. The worm and worm wheel apparatus consists of a toothed wheel (known as worm
twheel) fixed with a drum on it. A string is wound round the drum carrying at its one end load W to

be lifted. The worm wheel meshes with a worm which is fixed on a metallic spindle. The spindle
carries a pulley from which a string hangs for application of effort.

Let d = diameter of drum fixed on the toothed or worm wheel

D = diameter of pulley attached to worm
T = number of teeth on worm wheel.

When one revolution is given to the pulley, only one tooth of worm wheel moves if the worm
threads are of single start.

Distance moved by the effort = πD

Distance moved by the load = πd
T

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384 APPLIED MECHANICS

Drum Worm
wheel

Pulley

www PanWorm

String

.E W
asyFig. 7.1 Worm and worm wheel apparatus.
EngV.R.
distance moved by the effort πD
distance moved by the load πd
inee== =

T

rinM.A. TD (Neglecting thickness of string)
d

g.n∴= load lifted = W
effort applied P

%η =et= M. A. × 100 = W/P × 100
V. R. TD/ d

W ×d × 100
P ×T × D

Procedure :
1. Measure the circumference of drum and the pulley with the help of outside calliper.
2. Wrap the string round the drum and attach a load W.
3. Wrap another string round the pulley and attach a pan as shown in Fig. 7.1
4. Go on adding weights in the pan till the load just starts moving upwards.
5. Note down the weights in the effort pan.
6. Calculate M.A., V.R. and %η.
7. Repeat the experiment with different loads.

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EXPERIMENTS 385

Observations :

Weight of pan =
Diameter of the pulley, D =
Diameter of the load drum, d =
Number of teeth on the worm wheel, T =

S. No. Load suspended Total effort P M.A. = W V.R. = T .D. %η = M. A.
W P d × 10V0. R.
= wt. of pan
+ wts. in pan

wwwPrecautions :
.1. Lubricate well the bearings of worm and teeth of worm wheel to decrease the friction.
E2. Add the weights in the pan gently
as3. The pan carrying the weights should not touch the wall.
y4. The load and effort should move slowly.
E5. The string should not overlap on the drum or the pulley.
nginEexpeerriment No. 8Object. To find mechanical advantage, velocity ratio and efficiency of a single
ipurchase crab winch.

nApparatus. Single purchase crab winch apparatus, weights, pan, string etc.
g.netSpindle
Pinion
T1

Gear
Load drum T2

Pan
W

Fig. 8.1. Single purchase crab winch apparatus.

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386 APPLIED MECHANICS

Theory. The single purchase crab winch apparatus consists of two toothed wheels, one
small and the other large one. Smaller wheel is known as a pinion while the larger one is called
gear. These wheels are mounted on two spindles as shown in Fig. 8.1. The gear is attached to the
load drum. A string/rope is wound round the drum which carries the load W to be lifted. Another
string/rope passes round the pulley to which is attached a scale pan in which weights are added to
find the value of effort ‘P’ required to lift the load ‘W ’.

Let T1 = number of teeth on the pinion ;
T2 = number of teeth on the gear ;
D = diameter of the pulley ;

d = diameter of the load drum.

Let the pulley revolve through one revolution, then

Distance moved by the effort = πD
w Number
wwDistanceof revolutions of gear or the load drum = T1
T2

moved.EV.R.bythe load = πd × T1
T2

asyE= = distance moved by the effort
distance moved by the load

πD = D × T2 [Neglecting thickness of string/rope]
ngiM.A. T1 d T1
πd × T2

nee%η= load lifted = W
effort applied P

rProcedure : = M. A. × 100 .
V. R.
in1. Measure the circumference of the pulley and load drum with a string and metre rod or
gmeasure the diameter with an outside calliper.

.n2. Count the number of teeth on the pinion and the wheel.
e3. Wrap a string/rope round the effort pulley and attach a scale pan at its free end.
t4. Wrap another string/rope round the drum to carry load W in such a manner so that as
the effort is applied, the load is lifted up.

5. Hang a load W on the string/rope of the load drum and put the weights in the effort pan
so that load starts moving up gradually.

6. Note down the values of W and P and calculate the M.A., V.R. and efficiency.

7. Repeat the experiment with different loads.

Observations : = T1
= T2
Number of teeth of pinion =D
Number of teeth of gear =d
Diameter of the pulley
Diameter of the load drum

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EXPERIMENTS 387

S. No. Load W Effort P M.A. = W/P V.R. = D × T2 %η= M. A. × 100
d T1 V. R.

Precautions :

1. All the moving parts should be lubricated to reduce friction.

2. Weights should be put gently in the effort pan.
3. Add weight of the pan in the total effort.
4. The strings on the pulley and drum should not overlap.

w 5. Strings should be knot-free.
ww.Eas Experiment No. 9Object. To determine the mechanical advantage, velocity ratio and efficiency of
ythe first system of pulleys.

EApparatus. Set of pulleys, scale pan, weights, strings, hooks etc.
nTheory. Fig. 9.1 shows the pulleys arranged in the first system of pulleys. The upper pulley
gis fixed to the wooden frame whereas the lower pulleys are movable. The weight to be lifted is
ihanged from the lowest pulley.
neerinP 4
gP Fixed
.net3 pulley

2P 2P
2

1, 2, 3, 4P 4P
Movable 1
pulleys P
Pan

W

Fig. 9.1. First system of pulleys

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388 APPLIED MECHANICS

When the effort P moves downwards by a distance y, then

Pulley 3 moves by a distance = y
2

Pulley 2 moves by a distance = 1 × y = y
2 2 22

Pulley 1 moves by a distance = 1 × y = y
2 22 23

∴ The load ‘W’ attached to the pulley 1 moves by a distance

w If there are ‘n’ number of movable pulleys, then distance moved by the load=y
23
ww∴ Velocity ratio,
.EaV.R. = y
2n

syE== distance moved by the effort
distance moved by the load

n2ny= 2n
ginand y

eeriHence M.A. = W
P

ngProcedure : %η = M. A. × 100 = W × 100
.1. Fix one end of the string passing round each pulley to the hook and the second end to theV. R.P × 2n
nblock of next pulley.
et2. Keep all the pulleys movable except the last pulley which is fixed and from which the
effort is to be applied.

3. Hang a load ‘W ’ from the lowest pulley.

4. Add weights in the pan till the load just starts moving up.

5. Note down the effort applied and calculate M.A.

6. Note down the distance moved by the effort and distance moved by the load and find V.R.

7. Verify the velocity with the formula (V.R. = 2n).

8. Find out the % efficiency.

9. Repeat the experiment with different loads.

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EXPERIMENTS 389

Observations : Effort = Distance Distance
S. No. Load wt of the moved by moved by
W (kgf) pan + wt the effort the load

in the =y =x %η
pan
P (kgf) M.A. = W V.R. = y = M. A. × 100
P x V. R.

Precautions :

w 1. The string should be light in weight and inextensible.
w2. The pulleys should be well lubricated to reduce the friction.
w3. The weights should be added gently in the pan.

4. The pulleys should be parallel to one another.

.E5. The load or effort should not touch any object.
a6. While calculating total effort the weight of the pan should be added to the weights placed
sin the pan.
yEnginExperiment No.10Object. To calculate personal horse power on suitable apparatus in laboratory.
eeApparatus. Personal horse power apparatus (Fig. 10.1) consisting of a pulley fitted on a
rframe and a handle, spring balance, ropes, weights, metre rod, revolution counter, stop watch etc.

ing.netPulley

Handle Frame

Weights
Spring
balance

Fig. 10.1. Personal horse power apparatus.

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390 APPLIED MECHANICS

Theory. Power is defined as the rate of doing work. An agent is said to be possess one H.P.
if it is capable of doing 75 mkgf of work per second or 4500 mkgf of work per minute.

With the help of this apparatus it can be known at which rate an individual can do work.

Procedure :

1. Measure the diameter of the pulley.

2. Pass the rope on the pulley hanging vertically downwards.

3. Attach one end of the rope to a spring balance and hang weight ‘W’ from the other end.

4. Rotate the wheel against the load (i.e., from load side to the spring balance side) at
uniform speed for one minute which can be checked from the spring balance which should show a
constant reading.

5. Note down the number of revolutions from the revolution counter.
wCalculations :
6. Note down the reading of spring balance and dead load W.
7. Calculate the horse power.
wLet W = dead load
wS = spring balance reading
.D = diameter of the pulley
EW = number of revolutions per minute.
asThen, Torque, D
yEand 2
T = (W – S)

nObservations : H.P. = 2πNT
4500
ginS. Dai. of
eNo. pulley
ering.net=D(m) = W (kgf)Dead N(r.p.m.) Initial Final Observed Torque, T =
load reading reading reading
(W – S) D H.P. = 2 πNT
of spring of spring of spring 2 4500
balance balance = (Final-
Initial)
(kgf) (kgf)
(kgf)

Precautions :

1. The wheel should be rotated at uniform speed.
2. The apparatus should be rigidly fixed at the base.
3. r.p.m. should be counted carefully.
4. While rotating the pulley hand should not be changed.

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