PHYSICS LAB NOTES

FOR

MECHANICS, HEAT

AND

SOUND

EXPERIMENTS

PHYSICS 6

Los Angeles Harbor College

- 1 -

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TABLE OF CONTENTS

1. Measurement.................................................................... 12. Acceleration Due to Gravity.............................................. 53. The Addition of Vectors.................................................... 74. Projectile Motion............................................................... 95. Newton’s Second Law......................................................116. Centripetal Force Thistle Tube Method...........................137. The Coefficient of Friction.................................................158. The Conservation of Mechanical Energy..........................179. The Ballistic Pendulum.....................................................21

10. Torque and Center of Mass..............................................2311. Archimedes' Principle.......................................................2712. The Coefficient of Linear Expansion.................................3113. The Heat of Fusion of Ice.................................................3314. Standing Waves on Strings..............................................3515. The Speed of Sound in Air...............................................37

Laboratory Assignment

The Statistics of MeasurementThe Least-Squares Fit to Data

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Experiment 1: MEASUREMENT

PURPOSE:

To determine the precision of measurements made using different devices for measuring length, mass and time, and to learn to report data with the appropriate number of significant Figures.

INTRODUCTION:

The three basic units in the SI system of units are the meter, kilogram, and second.For measurement of length we will use micrometers, vernier calipers, and tape

measures. When using the micrometer, be sure to take account of the zero reading of the instrument. For all the various measuring devices, with the exception of the vernier caliper, estimate to the nearest tenth of a division in order to get the most out of the instrument. For measurement of mass, we will use the double pan balance. If the mass of your object exceeds the capacity of the balance, use a counter mass on the other pan.

The electric stop clock will be used to measure time. The 60-Hertz oscillations assure the accuracy of these devices.

It is good practice to tabulate (put in table form) your data whenever possible.Now to say something about precision and accuracy. Precision is a measure of how

reproducible a measurement is, for example, if one measures an eraser 3 times, using the same ruler, and gets the following readings: 5.2 cm, 5.1 cm, and 5.3 cm, the result can be expressed as 5.2 ± 0.1 cm. The ± 0.1 indicates the precision of the result. The accuracy of a measurement is an indication of how close the measurement is to the true or accepted value.

SUPPLIES & EQUIPMENT :

Tape measure Micrometer Metric rulerVernier caliper Metal cylinder Meter stickWire gauge Wire and nail samples Double pan balanceMetronome Rock samples Electronic balance100-gram slotted mass Electric stop clock

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PROCEDURE :

A. LENGTH

1. Determine the area of the classroom floor in square meters. Make three separate measurements of both the length and width and report your result with the average deviation.

2. Measure the diameter and length of a metal cylinder using the micrometer and a ruler. Then measure it again by using the vernier caliper. Calculate the volume. Observe the rules for the use of significant Figures.

3. Using a wire gauge, measure the diameter of a length of wire. Measure it again, this time with a micrometer. Compare the results, and number of significant Figures that can be recorded in each case.

B. MASS

1. Determine the mass of a 100-gram slotted mass on the balance and record your result with the appropriate uncertainty. Repeat the measurement on the electronic balance.

2. Determine the mass of an irregularly-shaped object such as a rock.

C. TIME

1. With the electric stop clock, time 50 beats of the metronome set at 120. Calculate the beats per second and the beats per minute. Repeat three times and calculate the average value.

2. With the electric stop clock, time 50 beats of your own or your lab partner's pulse. Calculate the beats per second and the pulse rate (beats / min.). Repeat three times for the same person and determine an average value.

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MICROMETER

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VERNIER CALIPER

An example of how to read the vernier caliper when making a measurement:

1. The zero line on the lower or vernier scale points up to 2.1 cm (plus a fraction of a millimeter) on upper or main scale. (Note where the long arrow is pointing on the diagram above.)

2. The 5th line on the vernier scale happens to line up with a main scale line (any line), therefore the last digit is 5. (Note where the short arrow is pointing on the diagram above.)

3. Any line on the vernier scale that lines up with a main scale line is the last digit. Thus, the length of the object is 2.15 cm

WIRE GAUGE

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Experiment 2: ACCELERATION DUE TO GRAVITY

PURPOSE:

In this experiment, the numerical value of the acceleration due to gravity will be determined by a graphical technique.

INTRODUCTION :

If one neglects the effects of air friction, objects relatively close to the Earth's surface undergo uniformly accelerated motion. For our purposes, we will take this value of acceleration to be 9.80 m/s2.

In this experiment, the data are obtained by analyzing a wax paper tape that has a series of spark dots. The apparatus that produces the tape sparks every 1/60 of a second as the free-fall body descends. Thus a time-distance record of the object in free fall is produced and the acceleration due to gravity can be calculated.

By definition, acceleration is the time rate of change of velocity, so a plot of the instantaneous velocity vs. time should yield a straight line, the slope of which is the acceleration. For each spark interval, the average velocity is readily calculated, being the distance the object falls in the interval divided by time it takes to fall that interval distance. Use the fact that the average velocity is equal to the instantaneous velocity at the midpoint in time of the interval.

SUPPLIES & EQUIPMENT:

Demonstration free fall apparatus Meter stick Spark tapePlastic triangle Metric ruler Masking tape

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Average velocity = v = ΔxΔt =

x f − x it f − t i

PROCEDURE:

1. Obtain a spark tape, secure it to the table with masking tape and draw a straight line perpendicular to the long direction of the tape, through every other dot. Start at the third or fourth dot down from the top. You should obtain about ten intervals. Number the perpendicular lines 0 through 10.

2. Measure and record the interval distances between each three successive dots, starting with 0 - 1, then 1 - 2 and so forth. Enter your data in the table.

3. Calculate the average velocity for each of your intervals by dividing the interval distance x by the elapsed time for each interval. The elapsed time is 1/30 second. Plot these average velocities on the y-axis vs the corresponding midpoint in time on the x-axis. Draw the best straight line for the data points by fitting the line so that the line is the closest it can be to all the data points. Note that the line does not necessarily have to pass through any particular point.

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4. Calculate the slope of your straight line. This is done by dividing the rise (change in y) by the run (change in x) for any two points on the line, not necessarily data points, since it is possible that no data points lie on the line. Choose the two points so that they are widely separated. Slope = V/t = a = g (experimental)

5. Calculate the percent error of the value of g you obtain from your graph when compared to the given value of 9.80 m/s2.

% error =

| gexperimental − 9 .80 m/s2 |

9.80 m /s2 X 100 %

Experiment 3: THE ADDITION OF VECTORS

PURPOSE: To establish the condition for equilibrium of a suspended metal object.

INTRODUCTION:

The first condition for equilibrium is that the vector sum of the forces (the net force) acting on an object is zero:

F = 0

in a two-dimensional problem this becomes:

Fx = 0, and Fy = 0.

SUPPLIES & EQUIPMENT:

Force table Slotted masses Electronic balanceMetal cube (brass or iron) Metric ruler Protractor

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50-gram mass holder Circular bubble level

PROCEDURE:

A. ADDING FORCES WITH THE SAME MAGNITUDE BUT DIFFERENT DIRECTIONS.

1. Level the force table using a spirit level.

2. Determine the mass of a metal cube, on the electronic balance.

3. Determine the weight of this metal object. W = mg, where g = 9.80 m/s2.

4. Clamp three pulleys along the edge of the force table as in fig. 1., with A = 10o, B = -10o, and c = 180o (position of cube).

5. Apply forces FA and FB of the same magnitude to balance the weight of the metal cube (at C) by placing masses on the hangers at A and B.

6. Record FA, FB and in data table 1.

7. Repeat steps 4 and 5, with: A = 30o, B = -30o and A = 50o, B = -50o 8. Using the graphical method, add the vectors head-to-tail to determine the resultant FR

of FA and FB. Use a ruler and protractor to draw the vectors to scale and be sure to specify the scale you are using. (for example 1N = 3 cm). Enter the data in data table 1. (See Fig. 2.)

Fig. 1 Fig. 2

For Example : FA = mA* g = ( ________ kg) X (9.80 m/s2) = ____________ N

* Note that mA includes the mass of the mass hanger.

FR

FB

FA

B

AObject

W

(Load)180o 0o

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At Equilibrium: F = FR + (-W) + Frictional Force = 0

| Frictional Force | = | f | = | FR - W |

B. Adding forces of different magnitudes and directions.

1. Balance the weight of the metal cube, W, with FA and FB of different magnitudes and different angles A and B on the force table. See Fig. 3a.

2. Calculate the resultant of FA and FB using the components method. See Fig. 3b which

shows the components of FA.

Fig. 3a Fig. 3b

Experiment 4: PROJECTILE MOTIONPURPOSE:

The object of this experiment is to determine the initial velocity of a projectile from the range and time-of-flight measurements. Also, the equations of motion will be used to predict the point of impact of a projectile.

INTRODUCTION:

A projectile is any object in motion through space, which no longer has a force propelling it. Examples are: thrown balls, rifle bullets, falling bombs and rockets (after the propelling force is gone).

In order to determine the initial velocity of a projectile fired horizontally, one first

makes use of the equation y = ½gt2 to calculate t, the time of flight; where t = √2 y /g  . Then, from a measurement of the range (horizontal distance) the initial velocity, vo , can be determined from the equation s = vot .

For a projectile fired at an angle, the range of a projectile can be determined if the angle of elevation, the initial velocity and the initial height of the projectile above the landing point are known.

SUPPLIES & EQUIPMENT:

FyA

FxA

FA

B

FB

FA

AW

180o 0o

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Ballistic pendulum apparatus Large cardboard InclinometerPlain white and carbon paper Metric ruler Catch boxSpirit level Wooden board for inclined plane "C" clampShort support rod Clamp and rod for inclined plane Plumb bobOne and two meter sticks

Fig. 1, Part A

PROCEDURE:

A. INITIAL VELOCITY

1. Be extremely careful not to hit anybody with a projectile during this experiment.

2. Clamp the gun (not too tightly) to the table, using the inclinometer to orient the gun to fire horizontally and take a trial shot. Tape a large piece of cardboard to the floor centered on the spot where the projectile landed. On top of the cardboard, tape a carbon paper and a plain paper to record the point of impact. Use one of the boxes supplied to catch the projectile (ball).

3. Take six shots. Measure the range of each shot accurately. Record your values for the ranges in the data table.

4. Measure the height from the floor to the bottom of the ball, this is y and is the vertical displacement of the projectile. Use a plumb bob to get the exact vertical direction. Calculate the time of flight from this measurement:

t = √2 Δy / g5. Calculate the range s and the average initial velocity. vo = s/ t .

y

s

vo

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B. PREDICTION OF THE RANGE

1. Clamp the spring gun to a board at an arbitrary angle of between 10o and 20o. Measure this angle precisely with an inclinometer.

2. Measure the height of fall, y (= yf - yi).

3. Calculate the expected range. Fire the projectile and measure the range. Fire the projectile five more times and determine an average measured range.

4. Calculate the percent difference between the measured and calculated range. Compare the results.

Experiment 5: NEWTON'S SECOND LAW

INTRODUCTION:

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to the mass being accelerated. Furthermore, the direction of the acceleration is in the direction of the resultant force.

F = ma (Newton's Second Law)

Using an air track, the acceleration of masses due to an unbalanced applied force will be determined, and compared with the acceleration calculated from the equation of motion for a uniformly accelerated object.

From Newton's 2nd law:

F = (m1 + m2)a m2g = (m1 + m2)a

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Solving for a: a =

m2gm1 + m2

From the equation of motion:

s = vot + ½at2. With vo = 0, a = 2 s

t2 .

SUPPLIES & EQUIPMENT:

Air track and accessories 5 & 10-gram slotted masses Electronic balanceThread and scissors 5-gram mass holder

Fig. 1. Experimental Setup

PROCEDURE:

1. Level the air track by adjusting the leveling feet and balancing glider at the center of the air track. Turn air supply off when this is accomplished. Do not lean on the air track or the table (use another table for writing) during the experiment.

2. Determine the glider's mass m1 on a balance and convert this measurement to kilograms.

3. Place photogate #1 at the position x1 = 80 cm and photogate #2 at the position x2 = 150 cm.

4. Place a 5-gram mass holder at the end of the thread running over the pulley. Add a 5-gram mass onto the mass holder, so now, m2 = 10.0 grams = 0.0100 kg.

5. Set the photogate stop clock to the "pulse" mode. and push the "reset" button. Set the resolution scale to 1ms. Set the “memory” switch to the “on” position. Make sure the air is flowing steadily before you let go of the glider.

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6. Turn on the air supply. Delicately hold the glider as close to the light beam of gate # 1 as possible (just before the LED on top of the gate lights up). Then release glider (do not push or perturb the glider) and record the displayed time.

7. Reset the stop clock and repeat the procedure two more times. Average the three values and record in the data table.

8. Add a 5-gram mass onto the mass holder. Repeat steps #5 and #6. (Remember that m2 equals the mass of the holder plus the mass on the holder, so the total mass for this step is 15 g.)

9. Repeat step #8 for m2 = 20 grams (including hanger). and m2 = 25 grams (including hanger).

10. Calculate the acceleration of the masses by using the equation of motion:

s = vot + at2 , s = | x2 - x1 |

with vo = 0, s = at2 a =

11. Compare this calculated acceleration with the value calculated using Newton's law F = ma.

Experiment 6: CENTRIPETAL FORCE - THISTLE TUBE METHOD

INTRODUCTION:

In this experiment we will study the motion of an object travelling in a circular path. A small object of known mass will be rotated in a circular path. The centripetal force will be determined directly and then calculated from measurements of the radius and the velocity. The following relation will be verified:

Fc = mv2

rSUPPLIES & EQUIPMENT:

Thistle tube String & scissors # 5 Rubber stopperMasking tapeRed felt marker Hooked masses, 50g, 100g & 200gStop clock Meter stick Electronic balance

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PROCEDURE:

1. Determine the mass of a stopper. Tie a 1.5 m length of string to the stopper, then thread it through the thistle tube. Tie a 0.150 kg mass to the other end of the string. The weight of this mass creates the tension in the string that provides the centripetal force on the stopper.

2. To help you maintain the radial distance, use a dot of red ink as a marker at the top edge of contact with the thistle tube.

3. Using the stop clock, measure the total time for 25 revolutions for two different values of radial distance. Try values close to 0.500 m and 0.750 m. The time for one revolution is the total time divided by 25.

4. Maintain a steady horizontal swing.

5. The velocity is given by the equation:

v = =

where r is the radius of the circular path and T is the time for one revolution.

6. Repeat the above procedure for a 0.200-kg mass attached to the string.

7. What factors contribute to error in this experiment?

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Experiment 7: THE COEFFICIENT OF FRICTION

PURPOSE:

The object of this experiment is to demonstrate some of the principles of dry friction and to determine the coefficients of kinetic and static friction for wood-on-wood surfaces.

INTRODUCTION:

In this experiment, we will investigate some of the principles of friction, such as: 1. The coefficient of static friction, s, is usually greater than the coefficient of kinetic friction, k. 2.The frictional force, f, is proportional to the normal force, FN. 3. Friction always acts in a direction opposite to the motion of an object.

SUPPLIES & EQUIPMENT:

Friction board Friction Block Meter stickString & scissors Inclinometer Metric ruler

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Electronic balance Masking tape Clamp & rod for inclined planeSlotted masses Spirit level Clamp-on pulley

PROCEDURE:

A. COEFFICIENT OF STATIC FRICTIONWe will determine the coefficient of static friction by tilting the board at an angle. At

the point where the angle is just enough to cause the block to slip (overcome friction), we have:

Fig.1: Experimental setup for Part A with associated forces shown

s = f / FN

Fx = 0: f + (-mg sin = 0

f = mg sin

Fy = 0: FN + (-mg cos = 0

FN = mg cos

s = mg sin θmg cos θ

s = tan

1. Place the block at the top of the inclined board. Experimentally determine the angle at which the block just breaks loose and starts sliding down the incline, using an inclinometer.

2. Repeat step 1-A five times and calculate an average value for the angle , and then calculate the coefficient of static friction s = tangent

B. COEFFICIENT OF KINETIC FRICTION

The coefficient of kinetic friction will be determined by making use of the fact that the frictional force is proportional to the normal force, f = kFN .

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Fig. 2. Experimental setup for Part B with associated forces shown.

1. Determine the mass of the friction block and record its mass on the data sheet.

2. Level the friction board on the table. Clamp a pulley on one end. Tie a string and mass hanger to the block. Place slotted masses on the hanger until the block starts moving with constant velocity once given a slight push. The force pulling on the block is the applied force to overcome kinetic friction and is equal and opposite to the kinetic friction force. Mark the place on the board with a piece of tape where you start the block in order to start the block at the same place each time.

3. Repeat step 2-B four more times, each time adding 100 additional grams to the top of the block.

4. Plot a graph of the magnitude of the force of friction, | f |, on the y-axis vs. normal force on the x-axis. The slope of the graph can be used to calculate the coefficient of kinetic friction.

Experiment 8: THE CONSERVATION OF MECHANICAL ENERGY

INTRODUCTION:

Though conservation of energy is one of the most powerful laws of physics, it is not an easy principle to verify. If a boulder is rolling down a hill, for example, it is constantly converting gravitational potential energy into kinetic energy (linear and rotational), and into heat energy due to the friction between it and the hillside. It also loses energy as it strikes other objects along the way, imparting to them a certain portion of its kinetic energy. Measuring all these energy changes is no simple task.

This kind of difficulty exists throughout physics, and physicists meet this problem by creating simplified situations in which they can focus on a particular aspect of the problem. In this experiment you will examine the transformation of energy that occurs as an air track glider moves down an inclined track. Since there are no objects to interfere with the motion and there is minimal friction between the track and glider, the loss in gravitational potential energy as the glider moves down the track should be very nearly equal to the gain in kinetic energy. In the form of an equation, we have:

KE = (mgh) = mgh

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where KE is the change in kinetic energy of the glider, KE = ½mv22 – ½mv1

2 and (mgh) is the change in its gravitational potential energy (m is the mass of the glider, g is the acceleration of gravity, and h is the change in the vertical position of the glider).

SUPPLIES & EQUIPMENT:

Air Track & accessory kit Meter stick Electronic balance2 Shim blocks, about 1 cm thick Vernier caliper Photogate timerAccessory photogate timer Glider Air supplyPhotogate timer transformer

PROCEDURE :

PART A:

1. Level the air track as accurately as possible by setting the glider at the middle of the track and adjusting the leveling screws until there is no movement of the glider. Once leveled, do not lean on the table or push down on the glider.

2. Measure D, the distance between the air track support legs. Record the distance above table A to the nearest millimeter.

3. Place a block of known thickness, H, under the support leg of the track. For greater accuracy, the thickness of the block should be measured with a vernier caliper. Record the thickness of the block above table A to the nearest tenth of a millimeter.

4. Set up a photogate timer and an accessory photogate as shown in the figure below.

Fig. 1: Equipment Setup.

5. Measure and record d, the distance the glider moves on the air track from where it first triggers the first photogate, to where it triggers the second photogate. You can tell where the photogates are triggered by watching the LED on top of each photogate. When the LED lights up, the photogate has been triggered. As always when measuring with a metric ruler, your measurement should be to the nearest millimeter.

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6. Measure and record L, the length of the glider. (The best technique is to move the glider slowly through one of the photogates, and measure the distance it travels from where the LED first lights up to where it just goes off.)

7. Measure and record m, the mass of the glider.

8. Set the photogate timer to GATE mode, leave the memory function in the "off" position, and press the RESET button.

9. Hold the glider steady near the end of the air track, then release it, (don't push), so it glides freely through the photogates. Record t1 the time during which the glider blocks the first photogate and t2 the time during which it blocks the second photogate.Notice that t2 = ttotal - t1. (Photogate timer first displays t1 , then ttotal = t1 + t2 , and does not display t2 by itself.)

10. Repeat the measurement four times and record your data in table A. You need not release the glider from the same point on the air track for each trial, but it must be gliding freely and smoothly (minimum wobble) as it passes through the photogate.

PART B:

1. Repeat procedure A with a block of greater thickness, H '. Record data in Table B.

CALCULATIONS:

1. Calculate , the angle of incline for the air track, using the equation = sin-1(h/d). Since sin  = h/d = H/D, you can calculate h = d (H/D), which is the distance through which the glider drops vertically in passing between the two photogates.

2. For each set of time measurements:

a. Divide L by t1 and t2 to determine v1 and v2, the velocity of the glider as it passed through each photogate.

b. Use the equation KE = ½mv2 to calculate the kinetic energy of the glider as it passed through each photogate.

c. Calculate the change in kinetic energy, KE = KE2 - KE1.

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D = distance between supports

d = distance between photogates

H = block thickness (distance air track leg raised)

Fig. 2: Elevations

d. Calculate the average value of KE = KE2 - KE1, and calculate mgh. Find the percent difference between them. A small value of this percent difference is expected from the law of conservation of energy.

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Experiment 9: THE BALLISTIC PENDULUM

In this experiment we will determine the initial velocity of a projectile by using the principles of the conservation of momentum and the conservation of energy.

INTRODUCTION :

A device called a ballistic pendulum will be used in this experiment to determine the initial velocity of a projectile. The device consists of a spring gun that propels a metal ball of mass m into a pendulum bob of mass M. This pendulum-ball combination then swings up onto a rack with a velocity v just after impact. The change in height h through which it rises depends directly on the initial velocity vo of the ball.

In order to derive an expression for the initial velocity vo of the projectile, we can make use of the law of conservation of linear momentum, expressed as:

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Momentum Before Impact = Momentum After Impact

mvo = (m + M) V

vo = (m + M

m )V Eq. 1

The second part of the process involves the pendulum-ball combination emerging with initial velocity v, then rising from h1 to h2. The conservation of energy for this part can be expressed as:

KE1 + PE1 (at h1) = KE2 + PE2 (at h2)

0KE1 - KE2 = PE2 - PE1 ; since v2 = 0

½(m + M)V2 = (m + M)gh2 - (m + M)gh1

½(m + M)V2 = (m + M)gh

½v2 = gh

So

V = √2gΔh Eq. 2

Substituting the expression for V from Eq. 2 into the momentum Eq. 1, we have:

vo = (m + M

m )√2gΔh Eq. 3

SUPPLIES & EQUIPMENT:

Ballistic pendulum apparatus Ruler C-clampElectronic balance Spirit level

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PROCEDURE :

1. Level the apparatus on the lab table using a spirit level. You may need to shim the apparatus. Lightly clamp the apparatus to the table using a C-clamp. Once leveled and clamped, do not lean on the table or otherwise disturb the level of the apparatus.

2. Determine the position (hi) of the center of mass of the stationary pendulum relative to the base plate. The center of mass is indicated by the pointed projection on the side of the pendulum.

3. Determine the mass of the ball and record it on the data sheet.

4. Fire the gun six times, each time recording the number of the notch in which the pendulum comes to rest.

5. Calculate the average notch number. Place the pendulum at this average position and determine the height (hf) from the base plate to the pendulum center of mass. Calculate h = hf - hi.

6. Calculate the velocity of the ball and pendulum just after impact. V = √2gΔh .

7. Calculate the initial velocity of the ball: vo = (m + M

m )V.

8. Calculate the energy loss in Joules. The kinetic energy before impact is ½mvo2, and

immediately after impact the kinetic energy is ½(m+M)V2. What percent of the original kinetic energy was "lost" to non-conservative work? Where did this energy go?

Experiment 10: TORQUE AND CENTER OF MASS

PURPOSE :

The object of this experiment is to use the method of balancing torques to determine the center of mass of a non-homogeneous meter stick, and to determine the unknown mass of an object.

INTRODUCTION :

If a rigid object is in rotational equilibrium, the net torque acting on it, about an axis, is zero. This equilibrium condition can be stated as:

= 0

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where = Fd, F is the applied force, and d is lever arm. The lever arm is the distance from the axis of rotation (the fulcrum) to the point where the downward force is applied. The plus sign {+} corresponds to a counter-clockwise torque and the negative sign {-} corresponds to a clockwise torque.

The center of mass, denoted here by CM, is the point at which the mass of the object can be considered to be concentrated. The position x of the CM of a non-homogeneous meter stick can be determined by balancing the torque of the stick on one side of the fulcrum with the torque of a known mass on the other side of the fulcrum.

Having established the position of the CM and knowing the mass of the stick, the same procedure can be used to determine the unknown mass of another object.

SUPPLIES & EQUIPMENT:

Weighted meter stick Knife edge clamp Scissors Metal cubeElectronic balance Knife-edge stand Hooked masses Light string

PROCEDURE :

A. CENTER OF MASS OF A NON-UNIFORM METER STICK

1. Record the mass of the non-uniform meter stick m1 indicated on the electronic balance.

2. Set up the apparatus as shown in Fig. 1, making sure that the fulcrum is at the midpoint of the stick. Slide m2 in along the stick until the stick is in equilibrium. Record m2 and d2. Be sure to include the mass of the string in the mass of m2.

3. Use Eq. 1 to estimate the lever arm, d1, the distance of the meter stick CM from fulcrum. Then calculate x, the position of the meter stick’s CM relative to the weighted end of the stick. This equation is obtained from the equilibrium condition:

counter-clockwise+ clockwise = F1d1 - F2d2 = 0

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F1d1 = F2d2

d1 =

F2

F 1 d2 =

m2 g

m1 g d2

d1 =

m2 g

m1 g d2 = distance of CM from fulcrum Eq. 1 x = position of CM from weighted end

= fulcrum position minus d1

Fig. 1

4. Move the fulcrum 5.0 cm away from the midpoint, toward the weighted end of the stick as shown in Fig. 2. Slide m2 to establish equilibrium. Record m1 and m2 and the new value of d2, the lever arm measured from the new fulcrum position. Use Eq. 1 to calculate the new value of d1 from the fulcrum position to obtain your second estimate of x. The position of the CM of the stick is x.

Fig. 2

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5. To obtain your third estimate of x, remove m2 and balance the stick on a knife edge clamp. The meter stick is balanced because its CM is resting on the knife-edge clamp which is at the fulcrum of the system. Record x, the position of the CM from the weighted end of the stick.

B. DETERMINATION OF AN UNKNOWN MASS

1. Having calculated the position of the center of mass on the previous page, set up the apparatus as shown in Fig. 1 by moving the fulcrum back to the midpoint of the stick. m2, a metal cube, will be the unknown mass.

2. Using a string, hang the unknown mass on the stick and slide it along the stick to balance.

3. Record the new value of d2. Use Eq. 2 to obtain your estimate of the unknown mass, m2.

  = 0 , so F1d1 + (F2d2) = 0 and F2 =

F1

d2 d1 , giving m2g =

m1g

d2 d1.

m2 =m1

d2 d1 Eq. 2

4. Weigh the metal cube on the electronic balance and find the percent difference between the two measurements of m2.

C. MULTIPLE-TORQUE SYSTEM: FINDING THE MASS OF A METAL CUBE(Use the same m2 as in Part B)

1. The equilibrium condition can be used even when there are several torques involved. Set up the apparatus as shown below:

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Fig. 32. Use Eq. 3 to obtain another estimate of the unknown mass m2.

= 0 , so F1d1 + F2d2 F3d3 - F4d4 = 0 giving F2 =

F3 d3 + F4 d4− F1d1

d2

m2 =

m3 d3 + m4d 4− m1d1d2 Eq. 3

3. Find the percent difference between this measurement and the value obtained directly from the electronic balance.

Experiment 11: ARCHIMEDES' PRINCIPLE PURPOSE: Archimedes' Principle will be used to determine: a) the density of a symmetrically-shaped object; b) the density of an irregularly-shaped object; and c) the specific gravity of a liquid.

INTRODUCTION:

Archimedes' Principle states that an object that is submerged in a fluid is buoyed up by a force that is equal in magnitude to the weight of the fluid displaced by the object. This force is called the buoyant force, or the buoyancy. The buoyant force can be determined experimentally with the following setup:

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Fig. 1 Fig. 2 T1 = Wo (Weight of object in air) T2 = Waw (Apparent weight of object in water)

Wo = mog T2 = Wo FB Waw = Wo FB

Therefore FB = Wo Waw (Eq. 1)

According to Archimedes' principle, the buoyant force, FB = Ww

or FB = mwg

Since mw = wVw then FB = wVwg , and the volume of water displaced by the immersed object can be expressed as

Vw = FB /wg (Eq. 2)Key to symbols:

mo = mass of object (in air) , W o= weight of object in air Vo = volume of objectmaw = apparent mass of object in water (fluid) Waw = apparent weight of object in watermw = mass of water displaced Ww = weight of water displaced

w = density of water = 1000 kg/m3 Vw = volume of water displaced

THE DENSITY OF AN OBJECT

When an object is totally submerged in water (a fluid) , the volume of water displaced is equal to the volume of the object.

(Volume of submerged object) Vo = Vw (Volume of water displaced) (Eq. 3)

Since the volume of an object is Vo = mo / o , and volume of the fluid displaced is Vw = FB /wg., then (Eq. 3) becomes

mo / o = FB /wg

Density of the object can be expressed as

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o =

mo gFB w (Eq. 4)

The buoyant force FB can be determined from the apparent weight loss, FB = (Wo - Waw). It can also be determined from the weight of the water displaced.

SUPPLIES & EQUIPMENT:

Double pan balance150-ml beaker Lab jack600-ml beaker 250-ml graduated cylinder Rock sampleUnknown fluid Vernier caliper HydrometerShort support rod Table clamp Overflow canString & scissors Small paper clips Metal cube

PROCEDURE:

A. DENSITY OF A METAL CUBE

1. Measure the length of one side of the metal cube. Calculate the volume of the cube Vo.

2. Suspend the cube from a beam balance mounted on a support rod as in Figure 1 and determine its mass, mo.

3. Immerse the suspended cube in a beaker of water as in Figure 2. Determine the apparent mass of the cube in water, maw.

4. Determine the buoyant force (FB = Wo Waw) in newtons. (Eq. 1)29

5. Determine the density of the cube from o =

W o

FB w. (Eq. 4)

B. DENSITY OF AN IRREGULARLY-SHAPED ROCK

1. Suspend a rock from the beam balance and determine its mass, mo in kilograms.

2. Immerse the suspended rock in a beaker of water as in Figure 2.

3. Determine the apparent mass of the rock immersed in the fluid, maw in kilograms.

4. Determine the buoyant force, FB = Wo Waw, in newtons (N). (Eq. 1)

5. Determine the density of the rock from o =

mo gFB w. (Eq. 4)

6 Determine the mass of a 150-ml beaker.

7. Place the displacement can on a level surface near the edge of a sink. Fill it with water, and let the excess drain off into the sink.

8. Slowly lower the rock into the water, allowing the displaced water to flow into the small beaker. Weigh the beaker with displaced water, mb+w .

9. Determine the mass of the water displaced, mw = mb+w – mb .

10. Determine the weight of water displaced, Ww= mwg . This is equal in magnitude to the buoyant force FB, according to Archimedes principle.

11 .Determine the density of the rock by applying (Eq.4), o =

mo gFB w.

C. SPECIFIC GRAVITY OF AN UNKNOWN LIQUID .

1 With the same cube used in Part A, determine the buoyant force, FB (fluid) on the metal cube by immersing it in an unknown fluid.

FB (fluid) = Wo Waf. Wo = weight of object in air.FB (fluid) = mog maf g Waf = apparent weight of object in fluid.

2. Calculate the density of the fluid using equation (5).

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In Water: o =

mo g ρwFB =

W o ρwF B(water ) In Fluid: o =

mo g ρfFB =

W o ρfF B( fluid )

Therefore,

W o ρfF B( fluid ) =

W o ρwFB , and f =

F B( fluid ) ρw

FB (water) Eq. 5)

where o = density of metal cube in air, w = density of water and f = density of fluid

3. Calculate the specific gravity, S.G. =

ρ f

ρw .

4. Fill a tall measuring cylinder with the “unknown” fluid. Use a hydrometer to measure the specific gravity of the fluid.

Experiment 12: THE COEFFICIENT OFLINEAR EXPANSION

PURPOSE :

The purpose of this experiment is to measure the coefficient of linear expansion for various metals and to compare the results with the known values.

INTRODUCTION :

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In most cases, when materials are heated or cooled, they undergo expansion or contraction respectively. From the standpoint of materials science, this process must be taken into account when designing structures that are subjected to temperature variations. Otherwise, tensile or compressive stresses might develop which could destroy the structure.

The linear (one-dimensional) coefficient of expansion is defined as the fractional increase in length divided by the temperature change. This coefficient is designated by the Greek letter alpha (), and is found to be almost constant over a wide range in temperature. In equation form, the definition of is:

=

ΔLLoΔT

where L is the change in length, Lo is the original length, and T is the temperature change in degrees Celsius.

In this experiment, the value of the linear coefficient of expansion of several rods of common metals will be determined. The length of the rod is measured at room temperature, then steam is passed over the rod with the resulting temperature increase causing it to expand. The amount of expansion is measured with a dial indicator. The coefficient is then determined using the data gathered.

SUPPLIES & EQUIPMENT:

Linear expansion apparatus Dial indicatorAluminum, copper and steel rods Electric steam generator0 - 100 oC Thermometer GlycerineMeter stick

PROCEDURE :

1. Measure and record the initial length of the rod Lo, to the nearest millimeter. Determine and record the ambient temperature (room temperature).

2. Set up the apparatus as shown in Figure 1. The steam jacket for the rod has an opening for steam, thermometer, and rod ends, and an outlet for the condensed steam. Fill the steam generator about 2/3 full of water and turn on the generator, but do not connect the generator to the expansion apparatus as yet. Insert the rod in the apparatus until it just makes contact with the dial indicator probe and is in firm contact with the screw at the other end.

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Fig. 1. Linear Expansion Apparatus with Associated Equipment

3. Make sure that the dial indicator is firmly screwed onto its holder and that the graduated ring is tightened down. See Fig. 2. Record the initial reading of the dial indicator, to the nearest 0.01 mm (= 0.00001m).

Fig. 2 Dial Indicator (Micrometer Gauge)

READING THE DIAL INDICATOR:

Example:

The gauge to the left indicates 0.07 mm

The gauge below indicates 0.14 mm

4. When the generator is generating steam briskly, connect the steam tube to the inlet on the apparatus. Warning! Be careful not to scald yourself.

5. Allow the steam to warm up the rod to a constant maximum temperature, Tmax. When the rod stops expanding, record the final reading of the dial indicator.Calculate T = (Tmax T ambient).

6. Calculate the change in length, L = Final reading - Initial reading.

7. Calculate the coefficient of expansion and record it on the data sheet. Compare your values with the known values of the coefficient of linear expansion by calculating the percent difference.

8. Repeat the above procedure for two other rods. Be careful not to burn yourself on the hot metal. When finished, dry the equipment thoroughly.

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Experiment 13: THE HEAT OF FUSION OF ICE

PURPOSE: The value of the latent heat of fusion for water will be determined by the of calorimetry.

INTRODUCTION:

When a substance such as water undergoes a change of state from the solid phase to the liquid phase, not all of the heat energy that is added to the system is reflected in a change of temperature of the substance. Some energy is needed to break the bonds between the molecules of the substance and this energy is called the latent heat of fusion of the substance.

In today's experiment the latent heat of fusion will be determined by the method of mixtures and by applying the principle that the heat lost is equal to the heat gained (conservation of energy).

In this experiment, an ice cube is placed into a measured amount of warmed water and is left to melt, cooling the water in the process. By noting the temperatures before and after melting, the heat of fusion is then calculated as follows:

HEAT GAINED:

by ice cube = (heat needed to melt the ice) + (heat for warming the melted ice) Qi = mi Lf + micw(Tf - 0oC)

HEAT LOST:

by water = (mass of water) X (1.00 cal / g.oC) X (temperature change)

Qw = mwcw(To - Tf) cw = Specific heat of water.

by calorimeter = (mass of calorimeter) X (0.22 cal / g.oC) X (temperature change)

Qc = mccc(To - Tf) cc = Specific heat of calorimeter.

CONSERVATION OF ENERGY:

Heat Gained = Heat Lost Qi = Qw + Qc Eq. (1)

mi Lf + micw(Tf - 0oC) = mwcw(To - Tf) + mccc(To - Tf) mi Lf = mwcw(To - Tf) + mccc(To - Tf) - micw(Tf - 0oC) Eq. (2)

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Lf =

mwcw (T o − T f ) + mc cc(T o − T f ) −micw (T f − 0oC )mi Eq. (3)

SUPPLIES & EQUIPMENT:

Double-walled calorimeter Ice cubes Steam GeneratorThermometer Electronic balance BeakerForceps/Tongs

PROCEDURE:

1. Determine the mass of the plastic collar. Slip the collar back on the inner cup.

2. Determine the mass of the inner cup, stirrer and plastic collar of the calorimeter.

3. Fill the inner cup of the calorimeter to about 2/3 full with warm water at about 40o.

4. Re-determine the mass of the inner cup, stirrer, collar, and water. Calculate the mass of water in the cup.

5. Place the cup, stirrer, collar, and water into the outer calorimeter jacket and record the exact temperature just before the ice cube is placed in the water.

6. Wipe any excess water from an ice cube and place it carefully into the calorimeter cup.

7. Stir the contents occasionally while constantly observing the ice cube. As soon as the ice cube is completely melted, record the temperature. This temperature is Tf.

8. Re-determine the mass of the cup, stirrer, collar, and contents. The mass of the ice cube can now be calculated.

9. Compute the heat of fusion of ice and compare this to the accepted value by calculating the percent error.

10. Repeat the experiment. Comment on the reproducibility of the results.

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Experiment 14: STANDING WAVES ON STRINGS

PURPOSE:

In this experiment we will study the relationship between tension in a stretched string and the wavelength and frequency of the standing waves produced in it.

INTRODUCTION:

Standing waves are produced by the interference between two traveling waves with the same wavelength, velocity, frequency and amplitude traveling in opposite directions. The equation for the velocity of propagation of transverse waves on a stretched string is:

v = √ Tμ . (Eq. 1)

where T is the tension in the string and is the linear density (the mass per unit length of the string). The velocity of propagation v, the frequency of vibration f, and the wavelength are related this way:

v = f (Eq. 2)

A stretched string has many modes of vibration. It may vibrate as a single segment, in which case its length is half of a wavelength. It may vibrate in two segments with a node (zero displacement) at the center as well as at each end; then the wavelength is equal to the length of the string. The wavelengths of the many modes of vibration are given by the relation:

L= nλ2 ,

so, λ = 2 L

n (Eq. 3)

where L is the length of the string, is the wavelength, and n is an integer called the harmonic number, indicating the number of segments.

SUPPLIES & EQUIPMENT:

Electric tuning fork 5- rheostat Thick stringStroboscope Ruler Thin stringElectronic balance Meter stick Slotted masses

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Power supply for tuning fork Leads & connectors Table clampRod pulley 50-gram mass hanger Scissors5-gram mass hanger 6-inch "C" Clamp

PROCEDURE:

1. Cut off a piece of the string about 2 meters long and determine its length, mass and linear density.

2. Clamp the apparatus to one end of your table and clamp the pulley to the other end, as shown in Figure 1. Knot the string to one end of the tuning fork and knot the other end to the mass hanger. Suspend the string over the pulley, and adjust the pulley until the string is horizontal. Write down the mass of the hanger.

3. Connect the fork to the rheostat, as your source of current as shown in Figure 1, with the tap on top of the rheostat set very close to the positive end. Use no more than a 6 V setting. Set the fork into vibration by adjusting the contact point screw above and to the left of the two terminals of the tuning fork apparatus. The rheostat may need to be adjusted to create noticeable but not violent vibrations.

4. Measure the frequency of the tuning fork using a stroboscope. Start with the highest strobe frequency possible and lower it until one stationary image of the tuning fork is obtained. When lowering the frequency of the strobe, also observe that a stationary image is obtained when the strobe frequency is ½, ⅓, ¼, etc., times that of the tuning fork. Divide the number that appears on the stroboscope by 60 to get the frequency of the tuning fork in cycles per second (Hertz).

5. Vary the tension of the string by adding masses to the hanger until the string vibrates in five segments with maximum amplitude. Measure the length of one segment from a point vertically over the center of the pulley wheel to a node (zero amplitude). The wavelength will be twice the length of one segment. Record in the data table the added mass in kilograms. Then record the total mass (added mass plus the mass hanger) in the data table. Record the resulting tension T = mg in newtons.

6. Repeat the procedure for 4, 3 and 2 segments by adding more mass to the pulley.

7. Compare the experimental velocity (v = f) with the theoretical velocity (v = √T /μ ) by computing the percent difference.

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Fig. 1: Standing Waves on Strings Apparatus

Experiment 15: THE SPEED OF SOUND IN AIR

PURPOSE:

The speed of sound in air will be determined by means of an adjustable air column resonance tube, driven by a known frequency.

INTRODUCTION:

When a tuning fork is set into vibration over the open end of a tube which is closed at the other end, a series of compressions and rarefactions occur within the length of the tube. If the length of the tube is such that an odd number of quarter wavelengths just fit into the tube, a condition known as resonance occurs and the sound heard emanating from the tube is greatly enhanced.

When resonance occurs, the gas particles just outside the mouth of the open tube are oscillating up and down with their maximum amplitude. This location is called the displacement antinode, and is symbolized in Figure 1 by curved lines showing a maximum displacement from the center of the column (although the actual displacement is vertical, not horizontal). There must be a displacement node at the bottom of the air column, as the water prevents the gas particles from oscillating up and down.

Since resonance occurs at odd multiples of quarter wavelengths, one is able to determine the wavelength, , by noting the length of the tube at which resonance occurs. Thus:

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Fig. 1.

From the above equations, the wavelength () can be calculated as:

= (L3 - L1) (Eq. 1)

= 2(L2 - L1) (Eq. 2)

Once the wavelength is determined, the speed can be calculated from the relationship:

Speed = Wavelength X Frequency

or,

v = f. (Eq. 3)

The theoretical speed of sound in meters per second is given by the relation:

v = 331.5 + 0.607 T. (Eq. 4)

where 331.5 m/s is the speed of sound at 0O C in meters per second and T is the temperature in Celsius degrees.

SUPPLIES & EQUIPMENT:

Resonance apparatus Thermometer 512 Hz tuning fork Beaker480 Hz tuning fork Turkey baster Rubber mallet

PROCEDURE:

1. Adjust the water level in the tube by raising the reservoir until the water level is about 10 cm from the top of the tube. See Figure 2.

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Fig. 2.

2. Strike the fork with the rubber mallet and hold it (horizontally) close to the top of the tube, with the prongs vibrating vertically. Lower the reservoir until the first resonance is heard. Record this position as L1.

3. Determine the lengths for the other two resonance positions as in step 2.

4. Take the average of three readings at each resonance position for calculating the speed of sound in air. Compare this to the theoretical value.

5. Repeat the procedure for another fork of a different frequency.

Physics 6 Laboratory Assignment

Part I.

View the video produced by the Jet Propulsion Laboratory, NASA Space Agency, Pasadena California. The segments that will be shown are:

a) Space Flight Operations Facilityb) Magellan: Exploration of Venusc) Tracking and Data Acquisitiond) L.A. The Moviee) Miranda The Movief) Earth The Movieg) Mars The Movie

Write one or two sentences on each segment. Make sure that your report is neat and legible.

Part II. EXTRA CREDIT

Find an article in a periodical or book (not an encyclopedia ) that is related to satellites, space craft or space technology. You may want to consider using the cumulative index in the library. The following are some examples of the type of literature that you may consider, but are certainly not limited to:

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National Geographic Discover Magazine Popular Science Physics Today Time Magazine Newsweek US News Report Newspapers Scientific American Science Digest Various textbooks Books Etc.

Write a summary of the article. The length of this summary should be about one page of neatly and legibly hand-written text or half page of type-written text.

Attach the article (a Xerox copy is okay) to your report.

This assignment can earn up to 10 points extra credit depending on the quality of the work.

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