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To study the effect of load on the depression of a suitably clamped metre scale loaded i at its end; and ii in the middle. Bending of a metre scale loaded at its end. Use of screw gauge to a measure the diameter of a given wire, b measure the thickness of a given sheet; and c determine the volume of an irregular lamina.
Measurement of the weight of a given body a wooden block using the parallelogram law of vector addition. To study the relationship between the force of limiting friction and normal reaction and to find the coefficient of friction between the surface of a moving block and that of a horizontal surface. To find the force constant and effective mass of a helical spring by plotting T 2 — m graph using the method of oscillation.
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Diagrams are well-labelled and neatly drawn. Stay Connected. Which one should be preferred? What additional steps do you need to take to use a physical balance with unequal arms. The minimum mass that can be used from the weight box is 10 g.
Find the possible instrumental error. Instead of placing the mass say a steel block on the pan, suppose it is hanged from the same hook S1 on which the pan P1 is hanging. Will the value of measured mass be same or different?
Determination of density of material of a non-porous block and verification of Archimedes principle: Hint: First hang the small block say steel block from hook S1 and determine its mass in air.
Now put the hanging block in a half water filled measuring cylinder. Measure the mass of block in water. Will it be same, more or less? Also detemine the volume of steel block. Find the density of the material of the block. From the measured masses of the steel block in air and water, verify Archimedes principle. Two pulleys P1 and P2 are provided on its two sides near the upper edge of the board.
A thread carrying hangers for addition of slotted weights is made to pass over the pulleys so that two forces P and Q can be applied by adding weights in the hangers. By suspending the given object, whose weight is to be determined, in the middle of the thread, a third force X is applied. The law states that "when two forces act simultaneously at a point and are represented in magnitude and direction by the two adjacent sides of a parallelogram, then the resultant of forces can be represented both in magnitude and direction by the diagonal of the parallelogram passing through the point of application of the two forces.
Let P and Q be the magnitudes of the two forces and the angle between them. If two known forces P and Q and a third unknown force due to the weight of the given body are made to act at a point O [Fig. Thus, the weight of a given body can be found.
Set the board of Gravesand's apparatus in vertical position by using a plumb-line. Ensure that the pulleys are moving smoothly. Fix a sheet of white paper on the wooden board with drawing pins. Take a sufficiently long piece of string and tie the two hangers at its ends.
Tie another shorter string in the middle of the first string to make a knot at 'O'. Tie the body of unknown weight at the other end of the string. Arrange them on the pulley as shown in Fig. Add weights in the hangers such that the junction of the threads is in equilibrium in the lower half of the paper.
Make sure that neither the weights nor the threads touch the board or the table. Bring the knot of the three threads to position of no-friction.
For this, first bring the knot to a point rather wide off its position of no-friction. On leaving there, it moves towards the position of no-friction because it is not in equilibrium. While it so moves, tap the board gently. The point where the knot thus come to rest is taken as the position of no-friction, mark this point.
Repeat the procedure several times. Each time let the knot approach the position of no-friction from a different direction and mark the point where it comes to rest. Find by judgement the centre of those points which are close together. Mark this centre as O. To mark the direction of the force acting along a string, place a mirror strip below the string on the paper.
Adjust the position of the eye such that there is no parallax between the string and its image. Mark the two points A1 and A2 at the edges of the mirror where the image of the string leaves the mirror [Fig E 5.
Remove the hangers and note the weight of each hanger and slotted weights on them. Place the board flat on the table with paper on it. Join the three pairs of points marked on the paper and extend these lines to meet at O. These three lines represent the directions of the three forces.
Choose a suitable scale, say 0. Ensure that the scale chosen is such that the parallelogram covers the maximum area of the sheet. Join points O and C. The length of OC will measure the weight of the given body. See whether OC is along the straight line XO. If not, let it meet BC at some point C. Measure the angle COC. Repeat the steps 1 to 9 by suspending two different sets of weights and calculate the mean value of the unknown weight. Table E 5. Board of Gravesand's apparatus is perpendicular to table on which it is placed, by its construction.
Check up by plumb line that it is vertical. If it is not, make table top horizontal by putting packing below appropriate legs of table. Take care that pulleys are free to rotate, i. Friction at the pulleys may persist even after oiling. Slotted weights may not be accurate. Slight inaccuracy may creep in while marking the position of thread.
The Gravesand's apparatus can also be used to verify the parallelogram law of vector addition for forces as well as triangle law of vector addition. This can be done by using the same procedure by replacing the unknown weight by a standard weight. The method described above to find the point of no-friction for the junction of three threads is quite good experimentally. If you like to check up by an alternative method, move the junction to extreme left, extreme right, upper most and lower most positions where it can stay and friction is maximum.
The centre of these four positions is the point of no-friction. What is the effect of not locating the point of no-friction accurately? In addition to the three forces due to weight, there is a fourth force due to friction. These four are in equilibrium. Thus, the resultant of P and Q may not be vertically upwards, i.
It is advised that values of P and Q may be checked by spring balance as slotted weights may have large error in their marked value.
Also check up the result for X by spring balance. State parallelogram law of vector addition. Given two forces, what could be the a Maximum magnitude of resultant force. In which situation this parallelogram can be a rhombus. If all the three forces are equal in magnitude, how will the parallelogram modify? When the knot is in equilibrium position, is any force acting on the pulleys? Interchange position of the body of unknown weight with either of the forces and then find out the weight of that body.
Keeping the two forces same and by varying the unknown weight, study the angle between the two forces. Suggest suitable method to estimate the density of material of a given cylinder using parallelogram law of vectors. Implement parallelogram law of vectors in the following situations: a Catapult d Kite. As the names suggest, these have the provision to start or stop their working as desired by the experimenter. It has two circular dials, the bigger one for a longer seconds hand and the other smaller one for a shorter minutes hand.
The seconds dial has 30 equal divisions, each division representing 0. Before using a stop-watch you should find its least count. In one rotation, the seconds hand covers 30 seconds marked by black colour then in the second rotation another 30 seconds are covered marked by red colour , therefore, the least count is 0.
The least count of a stop-watch is generally about 0. Digital stop-watches are also available now. These watches may be started by pressing the button and can be stopped by pressing the same button.
Second's pendulum: It is a pendulum which takes precisely one second to move from one extreme position to other. Thus, its times period is precisely 2 seconds. Simple pendulum: A point mass suspended by an inextensible, mass less string from a rigid Fig. Place the clamp stand on the table. Tie the hook, attached to the pendulum bob, to one end of the string of about cm in length.
Pass the other end of the string through two half-pieces of a split cork. Clamp the split cork firmly in the clamp stand such that the line of separation of the two pieces of the split cork is at right angles to the line OA along which the pendulum oscillates [Fig. Mark, with a piece of chalk or ink, on the edge of the table a vertical line parallel to and just behind the vertical thread OA, the position of the bob at rest.
Take care that the bob hangs vertically about 2 cm above the floor beyond the edge of the table so that it is free to oscillate. Measure the effective length of simple pendulum as shown in Fig. Displace the bob to one side, not more than 15 degrees angular displacement, from the vertical position OA and then release it gently.
In case you find that the stand is shaky, put some heavy object on its base. Make sure that the bob starts oscillating in a vertical plane about its rest or mean position OA and does not i spin about its own axis, or ii move up and down while oscillating, or iii revolve in an elliptic path around its mean position.
Keep the pendulum oscillating for some time. Count it as zero oscillation. Keep on counting oscillations 1,2,3,, n, everytime the bob crosses the mean position OA in the same direction from left to right. For better results, n should be chosen such that the time taken for n oscillations is 50 s or more.
Read, the total time t taken by the bob for n oscillations. Repeat this observation a few times by noting the time for same number n of oscillations. Take the mean of these readings. Compute the time for one oscillation, i. Change the length of the pendulum, by about 10 cm.
Repeat the step 6 again for finding the time t for about 20 oscillations or more for the new length and find the mean time period. Take 5 or 6 more observations for different lengths of penduLum and find mean time period in each case. Record observations in the tabular form with proper units and significant figures. Take effective length L along x-axis and T 2 or T along y-axis, using the observed values from Table E 6. Choose suitable scales on these axes to represent L and T 2 or T. Plot a graph between L and T 2 as shown in Fig.
What are the shapes of L T 2 graph and L T graph? Identify these shapes. Table E 6. Length of the Effective No. Plot a graph between L versus T from observations recorded in Table E 6. You will find that this graph is a curve, which is part of a parabola as shown in Fig. You will find that the graph is a straight line passing through origin as shown in Fig. ESULT 1. The graph L versus T is curved, convex upwards. The graph L versus T 2 is a straight line.
The effective length of second's pendulum from L versus T 2 graph is Note : The radius of bob may be found from its measured diameter with the help of callipers by placing the pendulum bob between the two jaws of a ordinary callipers, or b Ver nier Callipers, as described in Experiment E 1.
It can also be found by placing the spherical bob between two parallel card boards and measuring the spacing diameter or distance between them with a metre scale. The accuracy of the result for the length of second's pendulum depends mainly on the accuracy in measurement of effective length using metre scale and the time period T of the pendulum using stop-watch. As the time period appears as T 2 in Eq. A stop-watch with accuracy of 0.
Some personal error is always likely to be involved due to stop-watch not being started or stopped exactly at the instant the bob crosses the mean position. Take special care that you start and stop the stop-watch at the instant when pendulum bob just crosses the mean position in the same direction. Sometimes air currents may not be completely eliminated. This may result in conical motion of the bob, instead of its motion in vertical plane. The spin or conical motion of the bob may cause a twist in the thread, thereby affecting the time period.
Take special care that the bob, when it is taken to one side of the rest position, is released very gently. To suspend the bob from the rigid support, use a thin, light, strong, unspun cotton thread instead of nylon string. Elasticity of the string is likely to cause some error in the effective length of the pendulum.
The simple pendulum swings to and fro in SHM about the mean, equilibrium position. Remember that this relation is based on the assumption that sin , expressed in radian holds only for small angular displacement. Buoyancy of air and viscous drag due to air slightly increase the time period of the pendulum. Interpret the graphs between L and T 2, and also between L and T that you have drawn for a simple pendulum. Examine, using Table E 6. How can you determine the value of 'g', acceleration due to gravity, from the T 2 vs L graph?
To determine ' g', the acceleration due to gravity, at a given place, from the L T 2 graph, for a simple pendulum.
Studying the effect of size of the bob on the time period of the simple pendulum. Keep the length of the pendulum the same for each case.
Clamp the bobs one by one, and starting from a small angular displacement of about 10o, each time measure the time for 50 oscillations. Find out the time period of the pendulum using bobs of different sizes. Compensate for difference in diameter of the bob by adjusting the length of the thread. Does the time period depend on the size of the pendulum bob? If yes, see the order in which the change occurs. Studying the effect of material density of the bob on the time period of the simple pendulum.
Find out, in each case starting from a small angular displacement of about 10, the time period of the pendulum using bobs of different materials, Does the time period depend on the material density of the pendulum bob?
If not, then do you see an additional reason to use the pendulum for time measurement. Studying the effect of mass of the bob on the time period of the simple pendulum. Keep the length of the pendulum same for each case. Starting from a small angular displacement of about 10 find out, in each case, the time period of the pendulum, using bobs of different masses.
Does the time period depend on the mass of the pendulum bob? If yes, then see the order in which the change occurs. If not, then do you see an additional reason to use the pendulum as a time measuring device. Studying the effect of amplitude of oscillation on the time period of the simple pendulum. For measuring the angular amplitude, make a large protractor on the cardboard and have a scale marked on an arc from 0 to 90 in units of 5. Fix it on the edge of a table by two drawing pins such that its 0- line coincides.
Start the pendulum oscillating with a very large angular amplitude say 70 and find the time period T of the pendulum. Change the amplitude of oscillation of the bob in small steps of 5 or 10 and determine the time period in each case till the amplitude becomes small say 5.
Draw a graph between angular amplitude and T. How does the time period of the pendulum change with the amplitude of oscillation? Find at what amplitude of oscillation , the time period begins to vary? Determine the limit for the pendulum when it ceases to be a simple pendulum. Studying the effect on time period of a pendulum having a bob of varying mass e. The length of this simple pendulum will be same as that of a solid sphere same size or that of the hollow sphere filled completely with sand solid sphere.
Drain out some sand from the sphere. The situation is as shown in Fig. The CG of bob now goes down to point say A. The effective length further increases, increasing T. The process continues and L and T change in the same direction increasing , until finally the entire sand is drained out. The bob is now a hollow sphere with CG shifting back to centre C. The time period will now become T0 again.
AIM To study the relation between force of limiting friction and normal reaction and to find the coefficient of friction between surface of a moving block and that of a horizontal surface. Static Friction: It is the frictional force acting between two solid surfaces in contact at rest but having a tendency to move slide with respect to each other. Limiting Friction: It is the maximum value of force of static friction when one body is at the verge of sliding with respect to the other body in contact.
Kinetic or Dynamic Friction: It is the frictional force acting between two solid surfaces in contact when they are in relative motion. Thus, the ratio of the magnitude of the limiting friction, F L, to the magnitude of the normal force, R, is a constant known as the coefficient of limiting friction L for the given pair of surfaces in contact.
Thus, the slope of the straight-line graph between F l along Yaxis and R along Xaxis will give the value of coefficient of limiting friction L. The wooden block is made to slide over a horizontal surface say glass or a laminated surface Fig.
Find the range and least count of the spring balance. Measure the mass M of the given wooden block with hooks on its sides and the scale pan m with the help of the spring balance. Place the glass or a laminated sheet on a table and make it horizontal, if required, by inserting a few sheets of paper or cardboard below it.
To ensure that the table-top surface is horizontal use a spirit level. Take care that the top surface must be clean and dry. Fix a frictionless pulley on one edge of table-top as shown in Fig. Lubricate the pulley if need be. Tie one end of a string of suitable length in accordance with the size and the height of the table to a scale pan and tie its other end to the hook of the wooden block. Place the wooden block on the horizontal plane and pass the string over the pulley Fig.
Ensure that the portion of the string between pulley and the wooden block is horizontal. This can be done by adjusting the height of the pulley to the level of hook of block. Put some mass q on the scale pan. Tap the table-top gently with your finger. Check whether the wooden block starts moving. Keep on increasing the mass q on the scale pan till the wooden block just starts moving on gently tapping the glass top.
Record the total mass kept on the scale pan in Table E 7. Place some known mass say p on the top of wooden block and adjust the mass q on the scale pan so that the wooden block alongwith mass p just begins to slide on gently tapping the table top. Record the values of p and q in Table E 7. Repeat step 9 for three or four more values of p and record the corresponding values of q in Table E 7. A minimum of five observations may be required for plotting a graph between FL and R.
Table E 7. RAPH Plot a graph between the limiting friction FL and normal force R between the wooden block and the horizontal surface, taking the limiting friction F L along the y-axis and normal force R along the xaxis. Draw a line to join all the points marked on it Fig. Some points may not lie on the straightline graph and may be on either side of it. Extend the straight line backwards to check whether the graph passes through the origin.
The slope of this straight-line graph gives the coefficient of limiting friction L between the wooden block and the horizontal surface. To find the slope of straight line, Fig.
E normal reaction, R 7. Draw a line parallel to x-axis through point A and another line parallel to y-axis through point B. Let point Z be the point of intersection of these two lines. Then, the slope L of straight line graph AB would be.
The friction depends on the roughness of the surfaces in contact. If the surfaces in contact are ideally perfactly smooth, there would be no friction between the two surfaces.
However, there cannot be an ideally smooth surface as the distribution of atoms or molecules on solid surface results in an inherent roughness. In this experimental set up and calculations, friction at the pulley has been neglected, therefore, as far as possible, the pulley, should have minimum friction as it cannot be frictionless.
The presence of dust particles between the wooden block and horizontal plane surface may affect friction and therefore lead to errors in observations. Therefore, the surface of the horizontal plane and wooden block in contact must be clean and dust free. The presence of water or moisture between the wooden block and the plane horizontal surface would change the nature of the surface. Thus, while studying the friction between the surface of the moving body and horizontal plane these must be kept dry.
Elasticity of the string may cause some error in the observation. Therefore, a thin, light, strong and unspun cotton thread must be used as a string to join the scale pan and the moving block. The portion of string between the pulley and wooden block must be horizontal otherwise only a component of tension in the string would act as the force to move the block. It is important to make a judicious choice of the size of the block and set of masses for this experiment.
If the block is too light, its force of limiting friction may be even less than the weight of empty pan and in this situation, the observation cannot be taken with the block alone. Similarly, the maximum mass on the block, which can be obtained by putting separate masses on it, should not be very large otherwise it would require a large force to make the block move.
The additional mass, p, should always be put at the centre of wooden block. On the basis of your observations, find the relation between limiting friction and the mass of sliding body. Why do we not choose a spherical body to study the limiting friction between the two surfaces? Why should the horizontal surfaces be clean and dry? Why should the portion of thread between the moving body and pulley be horizontal?
Why is it essential in this experiment to ensure that the surface on which the block moves should be horizontal? Comment on the statement: The friction between two surfaces can never be zero. In this experiment, usually unpolished surfaces are preferred, why? What do you understand by self-adjusting nature of force of friction? In an experiment to study the relation between force of limiting friction and normal reaction, a body just starts sliding on applying a force of 3 N.
What will be the magnitude of force of friction acting on the body when the applied forces on it are 0. To study the effect of the nature of sliding surface.
Or repeat the experiment after putting oil or powder on the surface. To study the effect of changing the area of the surfaces in contact. Discuss whether the readings and result of the experiment are same. To find the coefficient of limiting friction by sliding the block on an inclined plane.
Pulley M1 Mass, M3. Here a roller of mass M1 has been placed on an inclined plane making an angle with the horizontal. An upward force, along the inclined plane, could be applied on the mass M1 by adjusting the weights on the pan suspended with a string while its other end is attached to the mass through a pulley fixed at the top of the inclined plane.
Assuming there is no friction between the pulley and the string. Arrange the inclined plane, roller and the masses in the pan as shown in Fig. Ensure that the pulley is frictionless. Lubricate it using machine oil, if necessary.
To start with, let the value of W be adjusted so as to permit the roller to stay at the top of the inclined plane at rest. Start decreasing the masses in small steps in the pan until the roller just starts moving down the plane with a constant velocity. Note W and also the angle. It should be a straight line. ESULT Therefore, within experimental error, downward force along inclined plane is directly proportional to sin , where is the angle of inclination of the plane.
Ensure that the inclined plane is placed on a horizontal surface using the spirit level. Pulley must be frictionless. The weight should suspend freely without touching the table or other objects.
Roller should roll smoothly, that is, without slipping. Weight, W should be decreased in small steps. Error may creep in due to poor judgement of constant velocity. Pulley may not be frictionless. It may be difficult to determine the exact point when the roller begins to slide with constant velocity. Weights in the weight box may not be standardised. When we increase the angle still further, net tension in the string is required to balance mg sin f r or otherwise the roller will accelerate downwards.
It is difficult to determine exact value of W. Give an example where the force of friction is in the same direction as the direction of motion.
How will you use the graph to find the co-efficient of rolling friction between the roller and the inclined plane? What is the relation between downward force and angle of inclination of the plane? Allow the roller to move up the inclined plane by adjusting the mass in the pan. Interpret the graph between W and sin where W is the mass in pan added to the mass of the pan required to allow the roller to move upward with constant velocity.
A spirit level is supported on a rigid crossbar frame which rests on the tip of a micrometer screw C at one end and a fixed knife edge K at the other. Screw C can be moved vertically. The micrometer screw has a disc having equal divisions along its circumference. On the side of it is a linear scale S, attached vertically. If there is any relative displacement between the two frames, P and Q, the spirit level no longer remains horizontal and the bubble of the spirit level is displaced from its centre.
The crossbar can again be set horizontal with the help of micrometer screw and the spirit level. The distance through which the screw has to be moved gives the relative displacement between the two frames. The frames are suspended by two identical long wires of the same material, from the same rigid horizontal support.
Wire B is called the experimental wire and wire A acts as a reference wire. The frames, P and Q, are provided with hooks H 1 and H 2 at their lower ends from which weights are suspended. The hook H 1 attached to the reference wire carries a constant weight W to keep the wire taut. To the hook H2 is attached a hanger on which slotted weights can be placed to apply force on the experimental wire. Suspend weights from both the hooks so that the two wires are stretched and become free from any kinks.
Attach only the constant weight W on the reference wire to keep it taut. Measure the length of the experimental wire from the point of its support to the point where it is attached to the frame. Find the least count of the screw gauge. Determine the diameter of the experimental wire at about 5 places and at each place in two mutually perpendicular directions.
Find the mean diameter and hence the radius of the wire. Find the pitch and the least count of the miocrometer screw attached to the frame. Adjust it such that the bubble in the spirit level is exactly in the centre. Take the reading of the micrometer. Place a load on the hanger attached to the experimental wire and increase it in steps of 0. For each load, bring the bubble of the spirit level to the centre by adjusting the micrometer screw and then note its reading. Take precautions to avoid backlash error.
Take about 8 observations for increasing load. Decrease the load in steps of 0. Least count L. Table E 9. Load on experimental No. Draw a graph with load on the x-axis and extension on the y-axis. Find the variation in M for each slotted weight of equal mass say M1 and M2.
Find the mean of these M. This is the uncertainity M in M. L the least count of the scale used for measuring L. Measure the diameter of the wire at different positions, check for its uniformity. The diameter of the wire may alter while loading.
Backlash error of the device used for measuring extension. The nonuniformity in thickness of the wire. If the length of the wire used is reduced what will be its effect on a extension on the wire and b stress on the wire. Use wire of different radii r1, r2, r 3 but of same material in the above experimental set up. Is there any change in the value of Youngs modulus of elasticity of the material? Discuss your result.
Change the length of the experimental wire, of same material and study its ef fect on the Youngs modulus of elasticity of the material. AIM To find the force constant and effective mass of a helical spring by plotting T 2 - m graph using method of oscillation. Thus, spring constant is the restoring force per unit extension in the spring. Its value is determined by the elastic properties of the spring.
A given object is attached to the free end of a spring which is suspended from a rigid point support a nail, fixed to a wall. If the object is pulled down and then released, it executes simple harmonic oscillations. The time period T of oscillations of a helical spring of spring constant K is given by the relation T, m where m is the load that is the mass of the object. The time period of a stiff spring having large spring constant is small.
One can easily eliminate the term mo of the spring system appearing in Eq. Using Eq. Suspend the helical spring SA having pointer P and the hanger H at its free end A , from a rigid support, as shown in Fig. Set the measuring scale, close to the spring vertically. Take care that the pointer P moves freely over the scale without touching it.
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