THE PHYSICS 11
LAB BOOK
Book 1: Labs 1 – 19
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TABLE OF CONTENTS
MECHANICS AND PROPERTIES OF MATTER
1...... Measurement 1
2...... Vector Addition 7
3...... Topographic Mapping 9
4...... Scientific Method Pendulum 11
5...... Acceleration Due to 13
6...... Simple Machines – Pulleys 15
7...... Simple Machines – Lever, Wheel and Axle, Inclined Plane 19
8...... Newton's Second Law of Motion 21
9...... The Coefficient of Friction 23
10...... Centripetal Force 25
11...... Hooke's Law 27
12...... The Ballistic Pendulum 29
13...... Moments and Center of Mass 33
14...... Archimedes' Principle 37
15...... Boyle's Law 39
HEAT
16...... Heat of Fusion of Ice 41
17...... Heat of Vaporization of Water 43
18...... Specific Heat of Metals 45
19...... The Coefficient of Linear Expansion 49
The Statistics of Measurement
The Least-Squares Fit to Data
Experiment 1
MEASUREMENT
INTRODUCTION
This experiment will involve making various measurements of mass, length, and time using simple laboratory measuring equipment. The system of units we will be using is called the metric system or the Systeme International, hereafter referred to as "SI".
The SI unit of length is the meter. We will be using the meter stick, the vernier caliper, the micrometer, the tape measure and the wire gauge to measure this quantity.
The Meter Stick: The physical size of an object is a fundamental property, and the height, width and depth of an object is measured by its length along each dimension. Examine the meter stick in front of you. The meter stick is slightly longer than a yardstick, and is divided into 100 centimeters. Each centimeter is further divided into 10 millimeters, so there are 1000 millimeters in a meter. The millimeter can be abbreviated as mm, and the centimeter can be abbreviated as cm. Every measurement of length must be followed by its unit.
Whenever a meter stick or metric ruler is used, the result should be expressed to the nearest millimeter. For example, the length of one-third of a meter stick can be expressed as 333 millimeters, 33.3 centimeters or 0.333 meters. The left-hand edge of a meter stick is supposed to be at 0.000 meters, but its edge may be damaged or worn. The correct way to get an accurate measurement is to place the object being measured near the center of the ruler, read the position of the left edge of the object, read the position of the right edge of the object, and subtract one number from the other. For example, if the left edge is at 321 mm and the right edge is at 674 mm, the length of the object is 674 - 321 = 353 mm.
The Vernier Caliper – This device can measure to an accuracy of one-tenth of a millimeter, and all measurements obtained with this device should be quoted to this degree of accuracy. To use this device, the length to be measured is placed in the jaws of the caliper, and the jaws are then closed by pushing on the wheel to the right of the movable window. The measurement is found by reading the ruler visible inside the window of the movable jaw.
This reading is a two-step process:
First, look just below the window of the movable jaw. You should see eleven vernier lines, and for this step you use only the leftmost of these eleven vernier lines. That leftmost line points in between two ruler lines directly above it, seen inside the window. Write down the value of the ruler line on the left. The measurement will begin with this value.
Second, which of the eleven vernier lines has a ruler line directly above it? These vernier lines are numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This number is placed after the value found in the first step. The vernier number 10 is never used.
For example, suppose the vernier caliper has been set as shown:
Performing the first step, the leftmost vernier line (thick arrow) points between the ruler lines 11 mm and 12 mm. The ruler line on the left is 11 mm, so you would write down the value ’11. mm’. Performing the second step, the vernier line 3 (thin arrow) has a line directly above it, and so a 3 is placed after the previous value. The answer is 11.3 mm.
As a second example, suppose the vernier caliper has been set as shown:
Performing the first step, the leftmost vernier line points between the ruler lines 25 mm and 26 mm. The ruler line on the left is 25 mm, so you would write down ’25. mm’. Performing the second step, the vernier line 8 has a line directly above it, and so an 8 is placed after the previous value. The answer is 25.8 mm.
The Micrometer - This device can measure to an accuracy of one-hundredth of a millimeter, and all measurements obtained with this device should be quoted to this degree of accuracy. To use this device, the length to be measured is placed in the jaws of the micrometer, and the barrel is rotated until the jaws have closed. Warning! A large amount of force should not be applied when rotating the barrel, as this will strip the screw inside the barrel and ruin the micrometer. Close the jaws so that they are ‘finger-tight’. That means that when your fingers rotate the barrel with only light pressure applied, your fingers slide along the barrel and it does not rotate any more. Some of the micrometers have a small friction barrel on the right-hand side of the barrel, which will prevent the barrel from rotating when too much force is used. If your micrometer has a friction barrel, use it to close the jaws.
This reading is a two-step process:
First, look at the ruler between the jaws and the barrel. The left edge of the barrel cuts across the ruler, which is measured in millimeters, and shows millimeter lines (on top) and half-millimeter lines (on bottom). Write down the value of the ruler line that is visible to the left of the edge of the barrel.
Second, which of the barrel lines is closest to the horizontal line on the ruler? The two-digit number of that barrel line (from .00 mm to .49 mm) is added to the value found in the first step. If this is confusing, open the jaws slightly until the barrel value is .00 mm, and the measurement is obvious. Then, slowly close the jaws until the barrel has returned to its former position. The correct value will be slightly smaller than the value obtained when the jaws were slightly open.
For example, suppose the micrometer has been set as shown:
Performing the first step, the ruler line 7.00 is the line that is visible to the left of the barrel, so you would write down the value ‘7.00 mm’. Performing the second step, 26 is the barrel line closest to the horizontal line, and so 0.26 mm is added to the previous value. 7.00 + 0.26 = 7.26, so the answer is 7.26 mm.
As a second example, suppose the micrometer has been set as shown:
Performing the first step, the ruler line 6.50 is the line that is visible to the left of the barrel, so you would write down the value ‘6.50 mm’. Performing the second step, 40 is the barrel line closest to the horizontal line, and so 0.40 mm is added to the previous value. 6.50 + 0.40 = 6.90, so the answer is 6.90 mm. Notice that the answer contains a ‘0’ in the last place, to signify that the length has been measured to this level of accuracy.
EQUIPMENT & MATERIALS
Wire and nail samplesMeter stickWooden blockBalance
Vernier caliperRock specimenWooden sphereMetronome
MicrometerTape measureGlass marble Wire gauge
Stop clock
EXPERIMENTAL PROCEDURE
A.LENGTH
1.METER STICK:Measure the dimensions of the top of your student table to an accuracy of the nearest millimeter. Enter all measurements in the laboratory report at the end of this experiment.
Area=length X width.
2.VERNIER CALIPER:Measure the sides of a wooden block, to an accuracy of a tenth of a millimeter. Measure the diameter of a wooden sphere.
3.MICROMETER:Measure the diameter of a glass marble, to an accuracy of a hundredth of a millimeter.
4.TAPE MEASURE:Measure the length and width of the classroom floor in feet and inches, using the 50 ft. tape measure. Convert to decimal feet (3 ft. 4 in. 3.33 ft., for example). Then convert your measurements into the SI system of units; 1 foot = 0.3048 meters. Calculate the area of the floor (length times width) in ft2 and m2. Notice that in the Imperial (English) system you have to convert to decimal feet before multiplying. In the metric system, calculations are easier.
5.WIRE GAUGE: Find the diameter of a small wire or nail by sliding it along the rim of the gauge (measured in inches). Multiply this by 25.4 to convert to millimeters, and check the result using the micrometer.
B.MASS
1.BALANCE:The SI unit of mass is the kilogram. In our lab, the balance is used to measure this quantity. Slide the two scale weights to their zero positions on the left-hand side, then calibrate by rotating the weight on the screw until the needle at the top of the scale is zeroed. The balance works by placing the mass to be measured on the left-hand pan, then sliding the two scale weights to the right until the needle is zeroed again. The mass of the object is the sum of the two scale weights, to an accuracy of one-tenth of a gram.
Determine the mass of three items on the balance such as a block, a sphere and a rock.
C.TIME
1.METRONOME:The SI unit of time is the second. The stop clock we use owes its accuracy to the precise 60 Hz line voltage oscillations that the power company provides. Set the metronome at a reading of 120 by placing the top of the sliding weight just below ‘120’ on the metronome face. Use the stop clock to measure the amount of time the metronome takes to count out 100 beats, to a tenth of a second accuracy. Divide by 100 to get a measured time for 1 beat, to a thousandth of a second accuracy. The nominal time for 1 beat is determined from the ‘named’ value given as 120 beats per minute. This is the given value used in determining the percent difference. The percent difference is given by:
% difference = X 100%
The given value in a calculation of percent difference may be a value that has been determined by very precise experiments, or it may be a value expected from theoretical considerations.
2.PULSE: Time 20 beats of your pulse, to a tenth of a second accuracy. Repeat this four times to give a total of 5 measurements. Calculate the average value of your pulse rate by adding up your five measurements, then dividing that number by 5.
The deviation of each measurement is the measurement minus the average. Some of those deviations will be positive numbers and some will be negative. When you square each deviation, the result must be either zero or a positive number.
Calculate the standard deviation. This is the typical scatter of a single measurement around the average.
Experiment 2
VECTOR ADDITION
INTRODUCTION
A vector is defined as a mathematical representation of a quantity that possesses both magnitude and direction. A scalar quantity has only magnitude. In this experiment we will add a number of forces using a force table and then compare the sum with that obtained by vector addition.
EQUIPMENT & MATERIALS
3 clamp-on pulleys1 sheet of blank paper Slotted massesRuler
Circular (bubble) level3 Mass hangers, 50 gForce table Protractor
EXPERIMENTAL PROCEDURE
1.Place the circular level on top of the force table, and adjust the feet until the force table top is horizontal. Arrange three pulleys with strings on the force table as shown in Figure 1. Two of these will be forces A and B and the third, or equilibrant, will be forceC. The magnitude of the equilibrant will be chosen to balance the forces A and B, creating a total force of zero.
Fig. 1. Force Table, Top View
2.Use masses (slotted masses plus the mass of each hanger) of 200 grams each to create the forces A and B. Place A and B with a small angle of about 40o between them (that is, at +20o and –20o), and balance them with a suitable amount of mass at C. Record the magnitudes and angles for A, B, and C in the laboratory report. The system is balanced when the central pin may be pulled up and the ring released without changing its centered position.
3.Repeat step 2, this time with a larger angle of 60o between them.
4.Repeat step 2 again, using an angle of 90o between them.
5.Repeat step 2 again, using an angle of 140o between them.
6.Draw a labeled free-body diagram to scale on the sheets at the end of this lab for each of the cases in steps 2 - 5. Let 200 grams on the force table be represented by 5.0 cm, so the magnitude of each force can be converted to a length; multiply the number of grams by 0.025 to get the length in centimeters. Using the parallelogram method, add the vectors A and B on the same sheet to find their resultant vector. Draw the equilibrant (Force C) along the negative x-axis. Compare the resultant so obtained with the magnitude and direction of the equilibrant. Are the equilibrant and the resultant exactly opposite and equal to each other?
Shown in Figure 2 is an example of how parallelogram addition works:
We wish to add vectors A and B. We move them so that their tails touch. (Note that one can move a vector so long as the direction is not changed.) Make a parallelogram out of A and B so joined. The diagonal of the parallelogram is called the resultant.
Fig. 2 Parallelogram Method of Vector Addition
- Place 3 unequal forces at unequal angles in equilibrium on the force table. Draw to scale a force polygon on a blank sheet of paper, by placing the tail of arrow B on the head of arrow A and the tail of arrow C on the head of arrow B, as shown in Figure 3. Show the amount by which the polygon does not close by a labeled arrow. Measure its value and indicate this as the resultant error.
Fig. 3 Typical Force Polygon
Experiment 3
TOPOGRAPHIC MAPPING
INTRODUCTION
In this experiment the instructor will give you an overview of how to read topographic maps, which are maps that describe the physical features of part of the Earth’s surface.
EQUIPMENT & MATERIALS
Topographic map360o protractorRuler
String & scissorsPaper
LABORATORY REPORT
Place the answers to the following questions on the blank paper, with your full name printed neatly in the upper-right corner.
1.Name the highest mountain and give its elevation.
2.Which town has the highest elevation?
3.Which mountain has the steepest slope?
4.What is the latitude and longitude (to the nearest tenth of a minute of arc):
(a) of the center of Norton?
(b) of the summit of Bald Peak?
(c) of the summit of White Mountain?
(d) of the mine? (Draw the mine’s line of latitude and line of longitude on the map.)
5.How far is Blue Lake from Norton?
6.Is Dixon or Rockville closer to Norton?
7.How long is the railroad tunnel (use the edge of a sheet of paper to transfer the scale)?
8.How far is Rockville from Norton by highway? Place a length of string along the highway, then straighten it and compare it to the scale.
9.How much farther is this than the straight-line distance (the U.S. average is l5 percent longer)?
10.How long would it take to walk from Rockville to Norton?
11.What direction would you travel from Dixon to Rockville? Directions are measured from true north (0o) through east (90o).
12.Is the trip from Dixon to Rockville uphill or downhill?
13.What is the true direction from White Mt. to Bald Peak?
14.What is the magnetic direction from Summit Mt. to Bald Peak?
15.Starting at the peak of White Mt., you fly horizontally 125o true for 3 minutes at 120mph, turn and fly 270o true for 4 minutes and then turn to 180o true for 1 minute while rising 500 ft. Draw these horizontal motions on your map. What is your final latitude, longitude and height above sea level?
Experiment 4
SCIENTIFIC METHOD
Pendulum
INTRODUCTION
This experiment will use the scientific method to determine what factors enter into the value of the period of a pendulum. The period of a pendulum is the time for one complete swing to and fro, and is given theoretically by the following relation:
where T is the period, L is the length, g is the acceleration due to gravity = 9.80 m/s2 and = 3.14159…
The factors to be investigated as possibly affecting or not affecting the period will include: length of string, mass of the bob, size of the bob, composition of the bob, and amplitude of the swing.
As much as possible in this experiment, each factor will be varied by itself; that is, the other factors will be kept constant while the effect of the one under consideration is studied. Keep the amplitudes of the swings just large enough so that the pendulum will complete the 25 swings. Avoid amplitudes larger than 10o from the vertical.
EQUIPMENT & MATERIALS
Support rodTable clampMetal cubesPendulum clamp
String, scissorsStop clockProtractorMeter stick
BalanceMetal spheresWooden spheres
EXPERIMENTAL PROCEDURE
A.Effect of Length
1.Attach a string to a heavy metal sphere and suspend it from the pendulum support. Start with a long length (75.0 cm measured from the edge of the support to the center of the ball) and measure the time taken for 25 complete swings. Use a stop clock to measure the time. The period will be the total time divided by 25.
2.Repeat step 1 three times, each time shortening the string from the previous time (lengths of 50.0, 40.0 and 30.0 cm will be convenient). Does the length of the string have any effect on the period?