Physics 101 (lab 3) Ivan Branov

Physics 101 (General Physics-1) Laboratory Exercise (3) The size of things and use of measurement instruments Your Name: Ivan Branov Lab partners name: Student ID:6468781 Date: 02/08/2022 Introduction: Physics is a quantitative experimental science and as such is largely a science of measurement. Over time, instruments of great accuracy have been devolved to help scientist make better measurements. Common laboratory measurements involve the determination of the fundamental properties of mass, length, volume density. Most people are familiar with the use of scales and rulers or meter stick. However, for more accurate and precise measurements laboratory balance and Vernier calipers or micrometer calipers are often used for smaller object measurements. In this lab, the dimensions of various objects will be measured using a meter stick, Vernier caliper, and micrometer. You will also get a chance to compare the British and metric system of units. With the use of an electric scale, the mass of some objects will be measured and from this, the density will be calculated. Objectives: The object of this lab is to (1) Learn how to use these instrument and what advantages they offer. (2) Learn how to measure small objects using Vernier calipers and micrometer calipers. (3) How to experimentally determine densities of several materials and (4) Distinguish between mass and density, and calculate % error between densities of different materials with the known densities. Equipment needed: Laboratory balance, Vernier caliper, Micrometer caliper, Meter stick, Graduated cylinder, Cylindrical metal rods, Some metal or glass sphere, Short piece of solid copper wire, Rectangular piece of metal sheets, Irregularly shaped metal objects. Theory: Using the proper instrument is extremely important for making accurate measurements of physical properties. The easiest way to measure length is to use a meter (or English yard) stick. For normal everyday measurements, a visible comparison between the object of interest and the scale is all that is needed. To make precise measurements, the scale must be very accurately made and must be read to a fraction of its smallest scale division. When an instrument is used to the limit of its precision, certain errors occur that cannot be eliminated. These errors are called random errors. When you make a series of measurements of a physical quantity, the individual results usually differ among

themselves because of the random errors involved. The best value of the quantity measured is then the average of the values obtained. The precision of measurements can usually be increased by using more accurate and complex equipment and by being careful to eliminate errors as much as possible. No matter what type of instrument you are using, you should always try to make measurements with the greatest accuracy attainable. Some of the instruments that will be using in this lab for accurate measurements are (a) electronic balance, (b) Vernier calipers and (c) micrometer calipers (a) Different types of Laboratory balance: Mechanical balance: are used to balance the weight of an unknown mass m against that of a known mass m 1 so that mg=m 1 g or m 1 =m. The mass of the unknown is then read directly in mass units. The weight W of an object is W=mg (where g=9.8 m/s 2 ) Double beam-double platform balance or equal arm balance: In this balance a set of known masses is used to balance an unknown mass A single platform triple beam balance: On a triple beam balance, the riders on the beams are used to balance the unknown mass on the platform. The common laboratory balance is calibrated in grams. In this case the least count is 0.1 gram and a reading can be estimated to 0.01 g. High form beam balance: In this balance on the left has a dial mechanism that replaces the lower mass beams. Digital balance: The balances with digital readouts are common and have the advantages of accuracy and ease of operation. However, these balances are much more delicate. Some electronic balances have auto calibration and other have key pad for calibration by the user. Most digital balances are zeroed by pressing a button and then when the material is added to the dish, the balance displaces the mass of the content alone. (b) Vernier calipers: In 1963 French instrument maker, Pierre Vernier invented the Vernier calipers in order to improve the precision of length measurements. This scale consists of two parts: A ruler with a main engraved scale and a movable jaw. The span of the lower jaw is used to measure the length and is particularly convenient for measuring the diameter of a cylindrical object. The span of the upper jaw is used to measure the distances between two surfaces, such as inside diameter of a hollow cylindrical surfaces.

Shape Volume parameter Sphere V=1/6 D π 3 D=diameter Rectangular block V=L 1 xL 2 xL 3 L=length, width, thickness Cylinder V=1/4 D π 2 x h D=diameter, h=height Cylindrical wire V=1/4 D π 2 x L D=diameter, L =length Volume by displacement method: This can be done by immersing it in water (or some other liquid) in a graduated cylinder. Since the object will displace a volume of water equal to its own volume, the difference in container readings before and after immersion is the volume of the object. Cylinders commonly have scale divisions of milliliters (mL) and 1 mL=1cm 3 (cubic centimeter). Experimental procedure: (a) Determine the least count of an instrument scale: Determine the least count and estimated fraction of all the different instruments for measurements. Where least count of any measuring equipment is the smallest quantity that can be measured accurately using that instrument and an estimated fraction is a "guesstimate," that is an approximation after the least count number. (b)Density determination: Measure the volume of different object from diameter and length and width measurements. Also calculate mass measurements using electronic or triple beam balance and then measure density which is given by density = mass/volume (c) Percent error calculation: Calculate % error between actual value and experimental value Data Table (1): Least count of an instrument scale Instrument Least count (mm) Estimated Fraction (Fractional value) Meter stick 1 0.5 Vernier Calipers 0.02 0.01 Micrometer Calipers 0.01 0.005 Balance 0.2 0.1 Graduated Cylinder 1ml 0.5

Data Table (2): Length, width, diameter and thickness measurements Type Rod Wire Sphere Rectangular sheet Instrument used Micrometer Caliper Ruler Micrometer Calipers Ruler Vernier Ruler Ruler Ruler Reading Diameter Length Diameter Length Diameter L W H 1 1.30 9.10 0.60 12.1 2.3 5.5 5.5 0.531 2 1.30 9.10 0.58 12 2.63 5.5 5.0 0.530 3 1.29 9.10 0.59 12.1 2.58 5.45 4.95 0.5285 4 1.29 9.10 0.61 12 2.57 5.5 5.40 0.528 Average 1.295 9.10 0.595 12.05 2.52 5.4875 5.2125 0.529375 Data Table (3): Mass, volume and density measurements (also % error calculation) Object Mass Volume Accepted density Exptal. Density (g/cm 3 ) % error Rod Type of Material (Tin Sn) 29.06 11.9855 7.28 2.4246 66.695% Wire Type of Material (Copper Cu) 0.85 3.3504 8.97 0.2537 97.17% Sphere Type of Material (Iron Fe) 66.8 8.379 7.87 7.9723 1.27% Rectangular sheet Type of Material (Aluminum Al) 6.135 15.1420 2.7 0.4194 84.47% Irregular shaped object Type of Material (Alloy) 8.01 8 5.0 0.9986 80.03%

Post lab question: (answer the following question) Q(1): Explain the probable source of error in the experimental determination of the thickness and volume measurements? Could be several sources of probable source of error such as the following: 1. Instrument defective 2. Careless measurement 3. Zero error in instrument 4. Variance in Temperature and Pressure 5. Vibration Q (2): What is the function of Vernier scale in a Vernier calipers? Does it extend accuracy or precision? Explain. Vernier calipers increase accuracy of measurements because its measurements have higher number of significant digits which leads to accuracy. It gives more significant numbers because the vernier scale on the vernier caliper is there to do that function. Q (3): Find the density of a 5 kg solid cylinder that is 10 cm tall with a radius of 3 cm volume of cylinder is given by r π 2 h. V=Pi/4*D^2*L=(3.1415/4)*(3*2)^2*10=282.735 P=M/V=5/282.735=0.0176844g/cm^3 Q (4): How will you measure the mass of an object which exceeds the mass of the triple beam balance? You will start by placing the object on the balance pan and allow it to settle. If the beam is pointing up start moving the 100g beam until it goes down. If it starts going down on the 300g mark than move it to the previous one and let it settle. Once it is settled on the 200g mark move to the second balance beam (the 10g) and start moving it slowly while allowing it to settle. Once it starts going down lets say at 80g mark move it one back at the 70g. Once it is settle move on to the third beam or the 1g beam. Move it slowly 1g by 1g with couple of seconds of pause to give the beam time to settle. Eventually you will find the

sweet spot lets say5g where all three beams will be levelled. Add all three values (200g+70g+5g=275g) and that will be the weight of the object. If the object is too large and heavy you would need another instrument to measure it. Summary and conclusion: