Engineering Mechanics Lab Manual

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M.H.SABOO SIDDIK

COLLEGE OF ENGG.

Prof.Shaikh Ibrahim Ismail

Automobile Engg. Dept.

Engineering Mechanics

Laboratory Manual

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail CONTENTS

NO. EXPERIMENT PAGE

1 Polygon Law of Coplanar Forces

To verify the polygon law of coplanar Forces for a concurrent force system.

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2 Support Reactions of a beam

To find experimentally the reactions at the supports of a simply supported beam and verify the same with analytical values.

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3 Bell crank Lever

To verify the principle of moments using the bell crank lever apparatus.

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4 Friction Plane

To determine the coefficient of static friction between two surfaces.

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5 Moment of Inertia of Flywheel

To find screw jack and determine the coefficient of friction between the threads of the screw.

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6 Compound Pendulum

To estimate the value of acceleration due to gravity using a compound pendulum.

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GENERAL INSTRUCTION FOR PREPARING MECHANICS PRACTICAL FILE

The report of the experiments performed in the Mechanics Laboratory need to be written in a paper standard format. All such reports of various experiments performed would make the Mechanics Practical File. General instructions for writing a report on the experiments performed are listed below.

 Use one side ruled and the other side lank A-4 size Journal sheets.

 On the ruled side of the first sheet write in big font the Title (name) of the experiment.  On the blank side of first sheet draw Apparatus diagram.

On ruled side of second sheet write  Aim

 Apparatus/Materials required  Theory/Principle

 Procedure

 On the blank side of second sheet draw FBD and make observation table.

On the ruled side of third sheet continue to write the procedure, show Calculations and present the results/conclusion.

 If required more sheets may be used.  Use millimeter graph papers wherever Required.

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail

EXPERIMENT NO. 1

POLYGON LAW

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DIAGRAM: OBSERVATION TABLE: SR NO. F1 (N) F2 (N) F3 (N) F4 (N) F5 (N) Θ (deg.) α (deg.) β (deg.) γ (deg.) 1 2 3

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail EXPERIMENT NO.1 DATE: ________

GENERAL CO-PLANAR FORCE SYSTEM

AIM: To verify the conditions of equilibrium for a general coplanar force system.

APPARATUS: wooden board, pulleys with clamps, a sheet of paper, loads with hooks at one

end and weights.

THEORY: The conditions of equilibrium

ΣFx = 0, ΣFy = 0 & ΣM=0.

PROCEDURE: Pin a sheet of drawing paper on the board. Tie four threads/cords on the

corners of a wooden plank and pass the cords over the pulleys, clamped in different positions on the board and suspend weights at the end of the cords. Adjust the weights until equilibrium of the system is established. Mark the lines of action of the forces on the paper and note down their magnitudes. Remove the paper. Draw the lines of actions of all the forces and verify

ΣFx = 0 , ΣFy = 0

Take any point on the paper. Draw perpendiculars from this point to the lines of actions of all forces and enter perpendicular distances in the observation table. Show that anti-clockwise moment is equal to clockwise moments, which satisfy the condition, that ΣM=0.

Repeat the experiment for different weights to get 2 more readings.

RESULT

1. The force polygons for the three sets of observations were drawn and found to be closed polygons. Hence the Polygon Law of Coplanar Force is verified.

2. The unknown weight found experimentally is _____________ N. Within limits of experimental error, these values are found to be same and hence the experiment is verified.

__________________

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EXPERIMENT NO. 2

SUPPORT REACTIONS OF A BEAM

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail OBSERVATION TABLE:- Sr. No. W1 (Kg) W2 (Kg) X1 (Kg) X2 (Kg) Observed Reactions Analytical Reactions R1 (N) R2 (N) R1 (N) R2 (N) 1. 2. 3.

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EXPERIMENT NO.2 DATE: ________ BEAM REACTION

AIM:-To find experimentally the reactions at the supports of a simply supported beam and

compare the results with analytical values.

APPARATUS:-Simply supported beam setup, hangers, and loads.

THEORY:-Beam is a structural member usually horizontal and straight provided to carry

loads that are vertical or inclined to its axis. A simply supported beam is one whose ends are resting freely on the supports that provide only vertical reactions. Simply supported beam becomes unstable if it is subjected to oblique or inclined loads. When simply supported beam is subjected to only vertical loads, its FBD forms a system of parallel forces in equilibrium. Conditions of equilibrium = 0 and ΣM=0 can be applied to determine the support reactions analytically.

PROCEDURE:-

1. Place the beam of length L on simple supports. Not e that below both the simple supports there is a spring arrangement. On loading, 1 he spring compresses due to the reaction force and this compressive force is indicated on the dial.

2. Arrange the load hangers arbitrarily on the beam and set the left and right dial pointers to zero. This will nullify the effect due to self weight of the beam and the hangers.

3. Suspend the loads from the hangers. Note the load values W1 W2, and so on and their distances X1, X2 and so on from the left support.

4. Note the left and right support dial readings.

5. Repeat the above steps 1 to 4 by changing the weights in the hangers and also the hanger position for two more sets of observations.

6. Compare the experimental values with analytical values obtained by applying Conditions of Equilibrium

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail RESULT:-

The support reactions obtained experimentally are nearly equal to the analytical values. The difference is within the limits of experimental error. Hence the experiment is verified.

__________________ Teacher’s Signature

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EXPERIMENT NO.3

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BELL CRANK LEVER

AIM:-To verify the Principle of Moments using the Bell Crank Lever apparatus. APPARATUS:- Bell crank lever apparatus, hangers, weights, scale.

THEORY:-Principle of Moments states, ‘the algebraic sum of the moments of a system of

coplanar forces about any point in the plane is equal to the moment of the resultant force of the system about the same point’.

This principle would be verified for a bell crank lever arrangement.

A lever whose two arms form a right angle, or nearly a right angle and having its fulcrum at the apex of the angle is referred to as a bell crank lever. These levers were originally used to operate the bell from a long distance especially where change in direction of bell wires was involved and hence the name. Now bell crank levers are used in machines to convert the direction of reciprocation movement.

PROCEDURE:-

1. Arrange three hangers at arbitrary locations on the horizontal arm. Note the locations x1 ,

x2, and x3 of these hangers from the hinge. Adjust the tension in the spring connected to the

vertical arm such that the two pointers come in the same vertical line. In this position the horizontal arm is truly horizontal. Note the tensile force in the spring as the initial tension Ti .

Also note the location Y of the spring from the hinge.

2. Hang the weights W1, W2 and W3 from the hangers. This will cause the arms to tilt and the pointers to move away from each other. Now adjust the tension in the spring such that the pointers once again come in the same vertical line. The horizontal arm is once again in its horizontal position. Note the tensile force in the spring as the final tension Tf. The tensile

force T on the vertical arm is the difference Tf — Ti.

3. Since the external forces are being supported by the single hinge at the apex of the arms, implies that the resultant of these external applied forces passes through the supporting hinge. Therefore to verify the principle of moments we need to take moments (ΣM) of all the external forces (which includes the weights of the hangers hanging from the horizontal arm and the tension in the spring connected to the vertical arm) about the hinge and if the total sum is zero, verifies the law of moments since the moment of the resultant is also zero at the hinge.

4. Repeat the above steps by changing the weights and their location on the horizontal arm for two more set of observations.

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail PRECAUTIONS:-

1 . Do not overload the horizontal arm as it may bend or crack at the hinge.

2. Note if any, the zero error of the spring balance and accordingly correct the readings. of the tensile force.

3. Carefully place the loads in the hangers as they may slip and cause accident.

RESULT:-

The sum of moments of all the applied external forces on the bell crank lever, within limits of experimental error being close to zero, is in accordance to the Principle of Moments.

Hence the experiment is verified.

__________________

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EXPERIMENT NO.4

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FRICTION AIM:-To find the Coefficient of Friction between two surfaces.

APPARATUS:- Inclined Plane with pulley, weights,Trolleys,weight pan etc. THEORY

Friction force is developed whenever there is a motion or tendency of motion of one body with respect to the other body involving rubbing of the surfaces of contact. Friction is therefore a resistance force to sliding between two bodies produced at the common surfaces of contact.

Friction occurs because no surface is perfectly smooth, however flat it may appear. On every surface there are ‘microscopic hills and valleys’ and due to this the surfaces get interlocked making it difficult for one surface to slide over the other. During static state the friction force developed at the contact surface depends on the magnitude of the disturbing force. When the body is on the verge of motion the contact surface offers maximum frictional force called as ‘Limiting Frictional Force’.

In 1781 the French Physicist Charles de Coulomb found that the limiting frictional force did not depend on the area of contact but depends on the materials involved and the pressure (normal reaction) between them.

Thus frictional force F α N or F = μsN

Here μs is the coefficient of static friction, a term introduced by Coulomb. The value of

lies between 0 and 1 and it depends on both the surfaces of contact.

Coefficient of static friction ‘μs’ between two surfaces can be found out experimentally by

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OBSERVATION TABLE: Type of Surface Weight in trolley (W) Angle of the Plane (Ѳ) Weight in pan (P) Coefficient of friction (μ) Average (μ) Angle of repose, φ Analytical Experimental Wood Metal

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The minimum angle of an inclined plane at which a body kept on it slides down the plane without the application of any external force is known as Angle of Repose. It is denoted by letter φ .

Angle of repose, φ = tan-1

μs

PROCEDURE

1. Set the inclined plane with glass top at some angle with the horizontal. Note the inclination θ of the plane on the quadrant scale. Take a box of known weight, note its bottom surface (whether surface is soft wood, or sand paper, or card board etc,) and weight W (weight of box + weights in the box)

2. Tie a string to the box and passing the string over a smooth pulley, attach an effort pan to it.

3. Slowly add weights in the effort pan. A stage would come when the effort pan just slides down pulling the box up the plane. Using fractional weights up to a least count of 5 gm, find the least possible weight in the pan that causes the box to just slide up the plane. Note the weight in the effort pan. This is force ‘P’.

4. Repeat the above steps 1 to 3 by changing the weights in the box for two more sets of observations.

RESULT:-

1. The coefficient of friction between mica and wood is --- 2. The coefficient of friction between mica and metal is ---

________________ Teacher’s Signature

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EXPERIMENT NO. 5

MOMENT OF INERTIA

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MOMENT OF INERTIA OF A FLYWHEEL AIM

To find moment of inertia of a flywheel.

APPARATUS

The flywheel mounted on ball bearings, stop watch, set of weights, pan, string, meter scale.

THEORY

A flywheel; is a heavy metal wheel attached to the shaft of the prime mover (motor or engine). Flywheels have most of their mass concentrated on the circumstances, thereby giving high moment of inertia. We know rotating bodies possess kinetic energy given by the relation

K.E = 1/2 Iω2. Hence if moment of inertia I is increased, K.E also increases.

Flywheels thus store the kinetic energy and release it back to the system when required. They are therefore called as ‘reservoir of energy’.

An imported application of a flywheel is in a mechanical press where for a fraction of time high energy is required for actual punching, shearing or forming. This energy is supplied by the flywheel. During the longer non active period, the speed of the flywheel is built up slowly by a low powered motor. Thus the motor is not overloaded and also results in energy saving. In automobiles, the flywheel is provided by the combustion in the cylinders and provides energy for the compression stroke in the pistons.

PROCEDURE

1. Wind a string around the shaft of the flywheel. Attach a pan of known weight from the end of the string. Hold the pan i.e. does not allow the flywheel to rotate.

2. Measure the diameter of the axle with a vernier caliper.

3. Add some weight in the pan and note the total mass ‘m’ of the pan. Also note the height ‘h’ of the base of the pan from the ground.

4. Hold a stop watch and now release the pan. The pan accelerates and gains velocity as it travels down. Note the time and rotations ‘N1’ turned by the flywheel till the pan touches the

ground.

5. When the pan hits the ground it gets detached from the flywheel. The flywheel continues to rotate. Note the rotations ‘N2’ turned by the flywheel from the moment the pan touches the

ground till the flywheel stops.

6. Repeat the above steps by changing the height of the pan from the ground and the moment weight in the pan for one more set of observations.

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OBSERVATION TABLE

SR NO DESCRIPTION 1st set 2nd set

1 Radius of axle ,r = m m

2 Height of fall , h = m m

3 Total mass of pan , m = kg kg

4 No. of rotations made by the flywheel till the pan touches the ground , N1 =

Nos. Nos.

5 No. of rotations made from the moment the pan touches the ground till the flywheel stops , N2=

Nos. Nos.

6 Time taken by the pan to touch the ground , t = sec sec

7 Moment of inertia of flywheel ,I = kgm2 kgm2

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail CALCULATIONS

Rectilinear motion of pan

Taking s = height of fall h, u = 0 and t = time taken by pan to touch the ground. Use s = ut + 1/2 at2 and find acceleration of pan = ____________ m/s2

Use v = u + at and find velocity of the pan as it strikes the ground. V = _______m/s Rotation motion of flywheel.

USE ω = v/r and find angular velocity of the flywheel at the instant the pan to touches the ground. ω = ______________r/s

Use the formula to find moment of inertia

I = 2mgh – mr2ω2(1 + N1/N2)

ω2(1 + N1/N2)

RESULT:

Mean moment of inertia of the flywheel is _____________ kgm2

_________________ Teacher’s Signature

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EXPERIMENT NO.6

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail EXPERIMENT NO. DATE: ________

MOMENT OF INERTIA OF THE COMPOUND PENDULUM. AIM:-To find the moment of inertia of the compound pendulum.

APPARATUS :

A steel rod with holes in it for suspension (bar pendulum), A knife edged fulcrum, stop watch, meter scale.

THEORY

Compound pendulum is defined as a right body suspended in a vertical plane, from a point on the body other than centre of gravity. On giving small angular displacements, it oscillates and perform harmonic motion.

We have

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OBSERVATIONS:-

Mass of uniform bar,m= ---kg No. of oscillations = 20 Length of the bar L = 1m ANALYTICALLY, IG = mL2/12 OBSERVATION TABLE: Sr.No. b (meter) T (sec.) t =T/20 (sec.) Io=(t2mgb/4π) IG=(IO -mb2) IG average 1. 2. 3.

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M.H.Saboo Siddik College Of Engineering, Mumbai-8 By Prof. Shaikh Ibrahim Ismail RESULT:-

Moment of inertia of the compound pendulum (experimental) =……… Moment of inertia of the compound pendulum (analytical) =………

_________________ Teacher’s Signature

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