EXPERIMENT NO: DATE: / / 0 THE SCREW GAUGE AIM: To learn to use a Screw Gauge and hence use it to find the dimensions of various regular materials given. APPARUTUS: Given a Screw Gauge, cylindrical glass rod and a cylindrical wire. THEORY: The Least Count of an instrument is the smallest possible measurement accurately possible using that instrument. The lower the value of the least count, the smaller the readings one can take using it. The least count of the commonly used meter scale is mm. Common screw gauges have an LC of 0.0mm. This means that using a SG, we can measure very small length dimensions like the diameter of a small wire. The formula for finding the least count of any instrument that has two scales one running over the other is given by Least Count (LC) = Smallest Value of Main Scale Total number of divisions in the Vernier Scale In the case of the Screw Guage applying the above formula, we get LC of Screw Gauge = mm 00 div = 0.0mm PROCEDURE: Keep the material to be measured between the U shaped metallic frame and tighten the screws to close the gap. Always make sure the turning of the screws must be done while holding on the Ratchet only. When the screw is completely closed, a click sound is heard at the ratchet end. Turn the ratchet further, very gently, to hear more clicks. Look for the reading on the main scale (also known as Head Scale or Pitch Scale). This is the Main Scale Reading (MSR). Note this down in the table with appropriate units. Now, look for the division on the Circular Scale that coincides with the main scale. This would be your Circular Scale Reading (CSR). Tabulate this reading (it has no unit as it is just a division). The Total Reading (TR) is given by TR = MSR + (CSR LC). Repeat the experiment times find the average value of TR. Check the instrument for zero error by keeping the screws closed. At this position, if the zero of the circular scale is above the zero of the mains scale then there is a negative zero error. (eg: divisions). If the zero of the circular scale is below the zero of the mains scale then there is a positive zero error. (eg: + divisions). In this case, each of the 5 TR needs to be corrected using the formula... TR = MSR + [(CSR ZE) LC] Note that the above equations are sign sensitive and so the negative zero error will get added up in the total result and the positive zero error will get subtracted. MSR TR = MSR + (VSR ZE) LC No CSR ZE [mm] [mm] Diamter of the Glass Tube (d ) CALCULATIONS (left side): Average Value of diameter of the glass tube D = mm Average Value of radius of the glass tube Diameter of the Wire (d ) R = D = mm Average Value of diameter of the wire d = mm Average Value of radius of the wire r = d = mm RESULT (right side): The Radius of the given cylindrical glass rod was found to be mm The Radius of the given cylindrical wire was found to be mm
EXPERIMENT NO: DATE: / / 0 VERNIER CALLIPERS AIM: To learn to use the Vernier and hence use it to find the dimensions of given regular materials. APPARUTUS: Given A Vernier Callipers, a Screw Gauge, a hollow cylinder THEORY: Vernier Callipers (VC) and Screw Gauge (SG) are instruments used to measure length dimensions more accurate than the normal mm that is measured using the normal 5 or 0cm scale that we use every day. Both the VC and the SG uses the principle of the Vernier Scale, first described by the French Mathematician Paul Vernier (580 67). The Vernier Scale is any secondary scale that runs over a main (primary) scale; it may be a linear (or straight along a line) secondary scale as in the case of a VC or a circular secondary scale as in the case of the SG. Before understanding how the VC and the SG works, one has to understand the idea of Least Count (LC) of an instrument. The Least Count of an instrument is the smallest possible measurement accurately possible using that instrument. This definition suits any instrument that one may use to measure any physical quantity. The lower the value of the least count, the smaller the readings one can take using it. The least count of the commonly used meter scale is mm. Usually the least count of the VC is 0.mm and that of a SG is 0.0mm although we can have VC and SG much more accurate than these. This means that using a SG, we can measure very small length dimensions like the diameter of a small wire. The formula for finding the least count of an instrument that uses a Vernier scale is given by Least Count (LC) = Smallest Value of Main Scale Total number of divisions in the Vernier Scale In the case of the given VC and SG, applying the above formula, we get LC of Vernier Callipers = mm 0 div = 0.0mm PROCEDURE: = 0.mm AND LC of Screw Gauge = mm 00 div Vernier Callipers: Use the jaws on the upper side of the VC only to measure inner diameter of tubes or other regular shapes; for all other external measurements, use the lower jaws. Keep the material to be measured between the jaws of the VC and close the jaws completely. Look for the reading on the main scale that comes just before the zero marking on the Vernier scale. This is the Main Scale Reading (MSR). Note this down in the table with appropriate units. Now, look for the first division on the Vernier scale that coincides perfectly with any division on the main scale. This would be your Vernier Scale Reading (VSR). Tabulate this reading too (it has no unit as it is just a division). The total Reading (TR) is given by TR = MSR + (VSR LC). Repeat the experiment times and find the average value of TR. TR = MSR + [(VSR ZE) LC] for VC and
Note that the above equations are sign sensitive and so the negative zero error will get added up in the total result and the positive zero error will get subtracted. TABLE: No MSR [cm] VSR ZE Outer Diameter of the Hollow Cylinder (R) TR = MSR + (VSR ZE) LC [cm] 0 Inner Diameter of the Hollow Cylinder (r) 0 Height (or length) of the Hollow Cylinder (h) 0 Average Value of Outer Diameter R = cm Average Value of Inner Diameter r = cm Average Value of Height h = cm CALCULATIONS: The Volume of the given Hollow cylinder is given by the formula V = πr h πr h = πh(r r )cm The Volume of the given Hollow cylinder was found to be cm
EXPERIMENT NO: DATE: / / 0 THE SIMPLE PENDULUM AIM: To find the value of acceleration due to gravity using a simple pendulum. APPARATUS: Given a bob attached to a mass less string, a meter scale, a stop clock and a stand. Least Count of the clock is seconds; Least count of the metre scale is m. FORMULA: T = π L g T = 4π L g g = 4π L 4π T g = S PROCEDURE: Set the Simple pendulum for a convenient length (say 40 cm) and calculate the time that it takes to make 0 oscillations (0T, where T is the time period). Care must be taken to ensure that the angle of oscillation from the mean position is as small as possible. Care must also be taken in order to ensure that no initial velocity is given to the pendulum. It must be allowed to fall freely from the displaced position. After the time reading for 0T is taken, do not stop the oscillation. Note down the value of time then, reset the watch and as the pendulum continues to oscillate, take the value for 0 T once more. Note this down too in the tabular column. Now, change the value of length (to say 60 cm) and repeat the whole experiment for 4 more values of length. Spread out the values of L as much as possible. In each of the tabulated values, find T and T and note it in the tabular column. From the above formulae we have Once the table is filled, plot a graph of L versus T (L on the x axis and T on the y axis) and it is expected to be a straight line. All the points that plotted may not fall on a straight line draw a LINE OF BEST FIT. (The line may even be drawn in a manner that none of the points plotted falls exactly on the line itself. This would still be the correct way of drawing the graph). From the line of best fit, take any two points (x, y ) and (x, y ) and hence find the slope of the line. T = 4π L g T = 4π L g No L [cm] 40 60 0T [s] T [s] Average T [s] T [s ] S = y y x x = 4π g Notice that g and 4π are constants. Knowing the value of slope S, find the value of acceleration due to gravity from the equation, g = 4π S 80 4 00 The value of acceleration due to gravity was found to be m/s
EXPERIMENT NO: 4 DATE: / / 0 SPHEROMETER AIM: To find the radius of curvature of a given spherical surface. APPARUTUS: Given, a 5cm scale, spherometer, plane mirror and a spherical surface. Least count of the Spherometer is cm FORMULA: LC = Pitch No of divs on the circular scale No MSR [mm] CSR TR = MSR + (CSR LC) [mm] R = l 6h + h R = Radius of the spherical surface [cm] l = Distance between legs of spherometer [cm] h = depth measured by spherometer [cm] 4 PROCEDURE:. Determine the pitch and least count of the spherometer using the formula. Place the spherometer on the page of the observation book and make the impression of its legs and then measure the distance between the legs using a scale (l). Place the spherometer on the plane glass surface and turn the screw till the middle leg just touches the surface. Note the reading on the spherometer to make note of zero error if any. 4. Place the spherometer on the spherical surface and find the depth (h) of the spherical surface. Note that readings are taken just like a screw gauge 5. Find the value of Radius of curvature using the formula. 6. Repeat the experiment by placing the spherometer at different places on the spherical surfaces. 7. Find the average radius of curvature. The Radius of curvature of the given spherical surface is found to be cm
EXPERIMENT NO: 5 DATE: / / 0 INCLINED PLANE FINDING MASS OF ROLLER AND PAN AIM: To study Newton s second law of motion in dimension and to find the mass of roller and pan in an inclined pane setup. APPARUTUS: An inclined plane, a roller, a mass pan, a string and a weight box. Least Count of the weight box is g; Least count of the inclined plane is degree THEORY: Let the mass of the roller be M, the mass of the pan be x and the included mass on the pan be m. Set it up as shown in the diagram. When the roller just starts to move, T = Mg sin θ = (m + x)g M sin θ = (m + x) m = M sin θ x which is of the form y = mx + c PROCEDURE: Fix the inclined plane at 45. Tie the string on one side to the pan and the other side to the roller. Pass it through the pulley at the edge of the inclined plane. Keep adding mass on the pan till the roller just starts to move. Note the mass included in the tabular column under the loading mass column. Now take out the mass one by one till the roller falls back to original position. When this happens, note the mass in the pan under the unloading mass column in the table. Find the mean value of the loading and unloading mass and note it down in the table. Repeat the experiment for different values of angle of inclination. Plot a graph of mean mass versus sin θ. Find the slope of the graph to get the mass of the roller and the y intercept to find the mass of the pan. TABLES: No θ sin θ 45 40 5 4 0 5 5 Mass (m) [g] Loading Unloading Mean Mass of the roller is found to be g Mass of the pan is found to be g
EXPERIMENT NO: 6 DATE: / / 0 INCLINED PLANE: FRICTION AIM: To find the coefficient of static friction between several pairs of surfaces. APPARUTUS: An inclined plane with adjustable angle made of a glass surface, Rubber sheet and several other materials to make pairs of surfaces. Least Count of the inclined plane is degree. THEORY: The coefficient of static friction depends only on the surfaces on contact only. In the figure, all the forces balance perfectly. The angle of inclination is θ. Mass of the material used is M, the coefficient of static friction is µ s and the acceleration due to gravity is g. We apply Newton s second law along the direction of the surface of the inclined plane, to get Mg sin θ = μ s N = Mg cos θ which reduces to μ s = tan θ PROCEDURE: First, the experiment is done with the glass surface of the inclined plane. Place any of the given material on the glass surface and slowly increase the angle. When the material just starts to fall off, note down the angle. Find the tangent of this angle to find the coefficient of static friction of this surface and the material. Repeat this with other materials too. The experiment is then repeated by placing a rubber sheet on the incline plane. Material Material θ μ s = tan θ The coefficient of static friction for various pairs of surfaces were found and tabulated.
EXPERIMENT NO: 7 DATE: / / 0 HOOKE S LAW & SPRING CONSTANT AIM: To study Hooke s Law and find the spring constant of the given spring. APPARUTUS: Give a spring, a stand, a metre scale and weights. Least count of the weights is g. Least count of the metre scale is cm THEORY: Hooke s Law states that the restoring force on a spring is directly proportional to the negative of the displacement from its mean position. Mathematically, F x F = kx, where k is the spring constant. When mass is hung from a spring, the displacement from its mean position will change proportional to the weight of the mass. <Draw a diagram showing the experimental set up in the record book> PROCEDURE:. Set up the spring system on the stand vertically.. Fix the meter scale vertically parallel to the spring.. Hang the weight holder on the spring and note this position as the mean position of the spring. 4. Note the reading on the scale. 5. Add masses one by one and in each case, find the reading on the scale and note it down. 6. Draw a graph of x versus F. 7. The slope of the graph will give the spring constant. TABLES: No x [ 0 m] m [ 0 kg] F = m 9. 8 [ 0 N] The spring constant of the given spring was found to be <units>
EXPERIMENT NO: 8 DATE: / / 0 SPRING OSCILLATIONS AIM: To study find the spring constant of the given spring. APPARUTUS: Give a spring, a stand, stop watch. Least count of weights is g. Least count of stop watch is cm THEORY: Hooke s Law states that the restoring force on a spring is directly proportional to the negative of the displacement from its mean position. It can be shown that the time of oscillation for a spring mass system is given by the formula T = π m k PROCEDURE: T = 4π m k k = 4π m 4π T k = T m. Set up the spring system on the stand vertically.. Hang the weight holder and enough weights so that the spring mass system is able to oscillate freely.. Start the oscillations and note the time taken for 0 oscillations. Note this down in the table under 0T for Trial. Repeat this again and write the time under trial. Find the mean of both values and note it in the table. 4. Repeat step for different masses. 5. Plot a graph of T versus m. 6. Find the Slope S of the graph. 7. The spring constant of the given spring can be found by the formula k = 4π S TABLE: No m [ 0 kg] 0T [s] Trial Trial Mean T [s] T [s ] 4 5 The spring constant of the given spring was found to be <units>
EXPERIMENT NO: 9 DATE: / / 0 NEWTON S LAW OF COOLING AIM: To study the Law of cooling and to study the relation between Celsius Scale and Fahrenheit Scale of temperatures. This experiment has to be done in a group of. One person reads the Celsius thermometer, one person reads the Fahrenheit thermometer, one person reads the stop clock and writes down the readings. APPARUTUS: A Celsius thermometer, a Fahrenheit thermometer, Bunsen burner, beaker of water, stand and a stop clock. Least count of the Celsius thermometer is ; Least count of the Fahrenheit thermometer is THEORY: Suppose we have an object that can exchange heat with its surroundings. If it is initially at a temperature higher than the environment temperature, then it will expel hear and cool off approaching equilibrium. This experiment is about that approach to equilibrium and it illustrates an empirical rule about the rate of cooling that was originally suggested by Newton. PROCEDURE: Place the Beaker on the stand and over the Bunsen burner and let the water reaching boiling point. When the water starts to boil, gently place both the thermometers inside the beaker and wait for the readings in the thermometers to become steady. When both the thermometers show a steady value, note it down in the tabular column. Switch of the burner and immediately take down the value of temperature. Now take down the values of temperature as time goes by first for every 0 seconds for 5 minutes and after that for every one minute. Convert the Celsius reading to Kelvin. Plot the following graphs (i) F v/s C (ii) C v/s t & (iii) log K v/s log t Determine the slope of the F v/s C graph. CALCULATIONS: Slope of the F v/s C graph is = The intercept of the F v/s C graph is = The slope of the F v/s C graph is found to be The intercept of the F v/s C graph is = Newton s law of cooling has been verified experimentally verified Time [min] 0 00 0 0 0 40 00 0 40 00 0 40 00 0 40 4 00 4 0 4 40 5 00 6 7 8 9 0 4 5 6 7 8 9 0 4 5 6 7 8 9 0 Temperature [ C] [ F] [K]