Mechanics Labmanual

UTAR FHSC1014 Mechanics Trimester 1

39

LABORATORY MANUAL

FHSC1014 MECHANICS

FOUNDATION IN SCIENCE (P) TRIMESTER 1

UNIVERSITY TUNKU ABDUL RAHMAN CENTRE FOR FOUNDATION STUDIES


1. Making measurements

Physics is a field of science, which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regarded as estimations. The precision of the final result of an experiment cannot be better than the precision of the measurement made during the experiment, so the aim of the experiment is to make estimations as good as possible. Therefore, should be repeated at least once

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument used, or to a combination of both.

Errors have a special meaning in science. Errors have a dmistakes where errors cannot be avoided in measurements. Students doing experiments MUST record the uncertainties and errors in their measurement. Students MUST take errors and uncertainties into account when calculating and presentintheir results in laboratory reports.

2. Scrutinize and inscribe the readings

(i) Vernier caliper

Both the main scale and the vernier scale readings are taken into account while making measurement. The main scale is the first reading on the main scale

Parts of a vernier caliper:

1. Outside jaws2. Inside jaws3. Depth probe4. Main scale5. Main scale6. Vernier7. Vernier8. Retainer

measurement

Introduction

Making measurements

Physics is a field of science, which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regarded as estimations. The precision of the final result of an experiment cannot be better than

recision of the measurement made during the experiment, so the aim of the experiment is to make estimations as good as possible. Therefore, should be repeated at least once to increase its precision and accuracy.

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument used, or to a combination of both.

Errors have a special meaning in science. Errors have a different meaning from mistakes where errors cannot be avoided in measurements. Students doing experiments MUST record the uncertainties and errors in their measurement. Students MUST take errors and uncertainties into account when calculating and presentintheir results in laboratory reports.

Scrutinize and inscribe the readings


nier caliper:

Outside jaws: used to measure external lengths Inside jaws: used to measure internal lengths Depth probe: used to measure depths Main scale (cm) Main scale (inch) Vernier (cm) Vernier (inch) Retainer: used to block movable part to allow the easy transferring a measurement

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Physics is a field of science, which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regarded as estimations. The precision of the final result of an experiment cannot be better than

recision of the measurement made during the experiment, so the aim of the experiment is to make estimations as good as possible. Therefore, measurement

to increase its precision and accuracy.

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument

ifferent meaning from mistakes where errors cannot be avoided in measurements. Students doing experiments MUST record the uncertainties and errors in their measurement. Students MUST take errors and uncertainties into account when calculating and presenting


: used to block movable part to allow the easy transferring a


immediately to the left of the zero of the vernier scale while the vernier scale reading is mark on the vernier scale which exactly coincides or aligns with a mark on the main scale.

Example:

(ii) Micrometer screw gauge

In order to measure an object, the object is placed between the anvil and spindle (jaws). The thimble is rotated using the ratchet gripped. DO NOT OVER TIGHTEN! Note that the THIMBLE) should be used to secure the object firmlyotherwise the instrument could be damaged or give an inconsistent reading.recommended 3 clicks of the ratchet are obtained before taking the reading.

Procedure on how to read the scale on micrometer screw gauge is shown in the figure below.

immediately to the left of the zero of the vernier scale while the vernier scale reading is mark on the vernier scale which exactly coincides or aligns with a mark on the main

Micrometer screw gauge

In order to measure an object, the object is placed between the anvil and The thimble is rotated using the ratchet until the object is lightly

. DO NOT OVER TIGHTEN! Note that the ratchet (NOT THE THIMBLE) should be used to secure the object firmly between the jaws, otherwise the instrument could be damaged or give an inconsistent reading.

licks of the ratchet are obtained before taking the reading.

Procedure on how to read the scale on micrometer screw gauge is shown in the figure

2.4 cm + 0.07 cm = 2.47 cm

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immediately to the left of the zero of the vernier scale while the vernier scale reading is mark on the vernier scale which exactly coincides or aligns with a mark on the main

In order to measure an object, the object is placed between the anvil and until the object is lightly

ratchet (NOT THE between the jaws,

otherwise the instrument could be damaged or give an inconsistent reading. It is licks of the ratchet are obtained before taking the reading.

Procedure on how to read the scale on micrometer screw gauge is shown in the figure

0.07 cm = 2.47


3. Data and error analysis

Performing the experiment and collecting data is process of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results in a clear concise manner completes the experiment. This overprocess is as valid in an instructional laboratory course as in a research environment. You will not have learned any physics if you did not understand the experiment.

Data analysis should not be delayed until all of the data is recoa quick analysis and plot as the data is being collected. This will help to avoid the problem of spending a long time collecting bad data because of a mistake in experimental procedure or an equipment failure.

Data analysis means understathe data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the world a bit better. Your understandingeach stage being a refinement.

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons for this apparent failure of the physical laws. Do NOT simply blame the equipments. Try to explain what went wrong or what competing effects have come into play.

The quality of the data, determines to a great extent, what conclusions can be reached from them. If youand the uncertainties in your data is 2 mm then you really cannot make any solid conclusion. A measurement of experimental results is of little value if nothing is known about the probable size o

Data and error analysis

Performing the experiment and collecting data is only the beginning of the process of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results in a clear concise manner completes the experiment. This overview of the complete process is as valid in an instructional laboratory course as in a research environment. You will not have learned any physics if you did not understand the experiment.

Data analysis should not be delayed until all of the data is recoa quick analysis and plot as the data is being collected. This will help to avoid the problem of spending a long time collecting bad data because of a mistake in experimental procedure or an equipment failure.

Data analysis means understanding what your results mean. When you analyze the data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the world a bit better. Your understanding of your results probably occurs in stages, with each stage being a refinement.

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons

arent failure of the physical laws. Do NOT simply blame the equipments. Try to explain what went wrong or what competing effects have come into play.

The quality of the data, determines to a great extent, what conclusions can be reached from them. If you are looking for a small effect, say a total change of 1 mm, and the uncertainties in your data is 2 mm then you really cannot make any solid conclusion. A measurement of experimental results is of little value if nothing is known about the probable size of its error.

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only the beginning of the process of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results

view of the complete process is as valid in an instructional laboratory course as in a research environment. You will not have learned any physics if you did not understand the experiment.

Data analysis should not be delayed until all of the data is recorded. Try to do a quick analysis and plot as the data is being collected. This will help to avoid the problem of spending a long time collecting bad data because of a mistake in

nding what your results mean. When you analyze the data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the

of your results probably occurs in stages, with

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons

arent failure of the physical laws. Do NOT simply blame the equipments. Try to explain what went wrong or what competing effects have come into play.

The quality of the data, determines to a great extent, what conclusions can be are looking for a small effect, say a total change of 1 mm,

and the uncertainties in your data is 2 mm then you really cannot make any solid conclusion. A measurement of experimental results is of little value if nothing is


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The quality of a measurement depends on the precision and accuracy of the measurement. A good measurement must be close to the true value and be reproducible.

(i) Quantifying the uncertainty

All measurements have uncertainties or errors. The uncertainty given in any measurement indicates the type of instrument used for the measurement as well as the possible range of value measured. Basically, for analogue measuring instruments, except for vernier caliper and micrometer screw gauge, the uncertainty is half of the smallest division of the scale. For digital instruments, the uncertainty is given by the smallest different in the reading.

(ii) Error propagation rules

The Absolute Error of a quantity Z is given by (Z), always 0.

The Relative Error of a quantity Z is given by ( )ZZ

, always 0.

To determine the error in a quantity Z that is the sum of other quantities, add the absolute errors of those quantities (Rules 2 below). To determine the error in a quantity Z that is the product of other quantities, add the relative errors of those quantities (Rules 3, 4, 5 below).

Relation Error 1. Z = cA ( ) ( )AcZ =

(Use only is A is a single term, i.e. Z = 3x) 2.

Z = A B C

( ) ( ) ( ) ( ) ...+++= CBAZ 3.

Z = A B C

( ) ( ) ( ) ( ) ZCC

BB

AAZ

+

+

+

= ...

4.

CABZ = ( ) ( ) ( ) ( ) Z

CC

BB

AAZ

+

+

+

= ...

5.

zyx CBAZ =

( ) ( ) ( ) ( ) ZCC

zBBy

AA

xZ

+

+

+

= ...

a, b, c, ..., z represent constants. A, B, C, ..., Z represent measured or calculated quantities (A), (B), (C), , (Z) represent the errors in A, B, C, ..., Z respectively.

(iii) Percentage error and percentage difference

In several of the laboratory exercises, the true value of the quantity being measured will be considered to be known. In those cases, the accuracy of the experiment will be determined by comparing the experimental result with the known value. Normally this will be done by calculating the percentage error of your


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measurement compared to the given known value. If E stands for the experimental value, and K stands for the known value, then the percentage error is given by

% 100

=

KKE

error Percentage

In other cases we will measure a given quantity by two different methods. There will then be two different experimental values, E1 and E2, but the true value may not be known. For this case, we will calculate the percentage difference between the two experimental values. Note that this tells nothing about the accuracy of the experiment, but will be a measure of the precision. The percentage difference between the two measurements is defined as

% 1002 21

12 +

=

EEEE

difference Percentage

4. Graphical representation and analysis of uncertainties in slopes and intercepts

In the physical sciences, it is helpful to represent data in the form of a graph when interpreting the overall trend of the data. Data analysis graphs are useful to determine the relationships exist between various quantities, how the data is distributed, and so forth, which may be hard to figure out merely by speculating the tabulated values only.

There are a few essential aspects when plotting a graph:

Choice of scale Choose a scale for each of the axes with the main divisions on the graph paper

that are easily subdivided and such that the entire range of values may be in included. If the values to be plotted are exceptionally large or small, use some multiplying factor that permits using a maximum of two or three digits to indicate the value of the main division.

Label the title, and naming the abscissa scale (X-axis) and the ordinate scale (Y-axis) After you have decided which variable is to be plotted on which axis, neatly

letter the name of the quantity being plotted together with the proper unit. Abbreviate units in standard form, e.g. meters (m). Students should always ensure that the correct units are used in the experimental work.

(i) Plotting and drawing the graph the best-fit line

In drawing the graph, it is not always possible to make all the points lie on a smooth curve. In such cases, a smooth curve should be drawn through the series of points to follow the general trend and thus represent an average.


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Before plotting a linear graph, its important to determine the centroid point of the data set. Centroid is the point, which shows the mean of X-values and Y-values. The function of centroid is to reduce the effect of data scattering.

Centroid, ( )

++++++=

NYYY

NXXX NN ...

,

... 2121y,x

Add centroid point to linear graph and circle the centroid so as to differentiate it from other points. Then, draw the best straight line which must pass through the centroid.

(ii) Linear Least Squares Fits

Often measurements are taken by changing one variable (call it x) and measuring how second variable (call it y) changes as a function of thr first variable. In many case of interest it is assumed that there exists a linear relationship between the two variables. In mathematical terms one can say that the variables obey an equation of the form

cmxy += (Eq. 1)

where m and c are constants. This also implies that if a graph is made with x as the horizontal axis and y as the vertical axis, it will be a straight line with m equal to the slope (y/x) and c equal to the y intercept (the value of y at x = 0).

The question is how to best verify that the data do indeed obey Equation 1. One way is to make a graph of the data, and then try to draw the best straight line possible through the data points. This will give a qualitative answer to the question, it is possible to give a quantitative answer to the question by process described below.

The measurements are repeated measurements in the sense that they are to be considered together in the attempt to determine to what extent the data obey Equation 1. It is possible to generalize the idea of minimizing the sum of squares of the deviations. The result of the generalization to two-variable linear data is called a linear least squares fit to the data. It is also sometimes referred to as a linear regression.

The aim of the process is to determine the values of m and c that produce the best straight-line fit to the data. Any choice of the values for m and c will produce a straight line, with values y determined by the choice of x. For any such straight line (determined by a given m and c) there will be a deviation between each of the measured ys and the ys from the straight-line fit at the value of the measured xs. The least squares fit is that m and c for which the sum of the squares of these deviations is a minimum sum of the squares of the deviations are given by the following equations:

2

11

2

11 1

=

n

i

n

i

n

i

n n

iii

xxn

yxyxnm (Eq. 2)


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2

11

2

111

2

1

=

n

i

n

i

n

i

n

ii

n

i

n

i

xxn

xyxxyc (Eq. 3)

Here n is the number of data points, xi and yi are the measured values, and the n

1

stands for the summation from i = 1 to i = n.

We can find the best values for the gradient and the intercept of a line through a set of x-y data using Equations 2 and 3. However, it is not possible to decide how many figures m and c should be quoted to until the uncertainties in m and c, which we will write as m and c respectively, have been calculated.

There are a number of mathematical steps required before we can arrive at explicit equations for m and c. We will not go through the steps here, but simply quote the results:

21

2

11

2

21

=

n

i

n

i

m

xxn

n

(Eq. 4)

21

2

11

2

21

1

2

=

n

i

n

i

n

i

c

xxn

x

(Eq. 5)

where is the uncertainty in each y-value of the data point. It is usual, when fitting a line to data in which the uncertainty in each point is constant, to make this uncertainty to be standard deviation of the distribution of the y-value about the fitted line. This is given by

21

1

2)(2

1

= n

ii cmxyn

(Eq. 6)


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Example

In an experiment to study the behavior of the silicon diodes when cooled, the voltage across a diode was measured as a function of the diode temperature. Table 1 shows the data gathered for the application of linear square fits method in plotting a straight-line graph.

Table 1: Columns required for fitting a line to data using the method of least squares.

xi (K) yi (V) xi yi (KV) xi2 (K2) 300 0.630 189.00 90000 290 0.653 189.37 84100 280 0.670 187.60 78400 270 0.678 183.06 72900 260 0.695 180.70 67600 250 0.705 176.25 62500 240 0.735 176.40 57600 230 0.748 172.40 52900

xi = 2120 yi = 5.514 xi yi = 1454.42 (xi2) = 566000

Now use Equation 2 to find the gradient of the line

132 VK10616.133600

32.54)2120()566000(8

)514.5)(2120()42.1454(8=

=

=m

and use Equation 3 to find the intercept of the line on the y-axis

V1176.133600

6.37553)2120()566000(8

)42.1454)(2120()514.5(5660002 ==

=c


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Practical 1 _____________________________________________________________________

The Use of Vernier Caliper and the Micrometer Screw Gauge

Objective: To determine the density of oil, copper and PVC.

Apparatus and Materials: 1. Measuring cylinder 2. Copper wire 3. PVC tube 4. Micrometer screw gauge 5. Vernier caliper 6. Oil

Equipment: 1. Electronic balance

Part 1: Determination of the density of oil Procedure: 1. Measure the mass of an empty measuring cylinder. 2. Fill the measuring cylinder with 100 cm oil. 3. Measure the mass of the measuring cylinder filled with oil. 4. Calculate the density of oil.

Part 2: Determination of the density of copper Procedure: 1. Measure the length of a copper wire provided. 2. Using a micrometer screw gauge, measure the diameter of the copper wire at

several places. Determine the average diameter of the copper wire. 3. Measure the mass of the copper wire using an electronic balance. 4. Calculate the volume of the copper wire. 5. Calculate the density of copper.

Part 3: Determination of the density of PVC Procedure: 1. Measure the external and internal diameter of the PVC tube. 2. Measure the length of the PVC tube. 3. Calculate the volume of the PVC tube. 4. Measure the mass of the PVC tube using an electronic balance. 5. Calculate the density of PVC.


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Practical 2 _____________________________________________________________________

To investigate the vector addition

Objective: To verify the parallelogram law of forces.

Apparatus and Materials: 1. Pulley 2. Slotted mass 3. Cardboard 4. White paper 5. Pin 6. Retort stands 7. Metre rule 8. Protractor

Setup: 1. A piece of cardboard, white paper, string and slotted masses are setup as in

Figure 2.1.

X Y

O P

R

Q

O

Pr Q

r

QPRrrr

+=

Pulley

String

Slotted mass

White paper

Thumb tack

Cardboard Note: Ensure that the masses P, Q and R are not in contact with the cardboard to avoid friction.

Figure 2.1


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Theory: Forces which has a magnitude and direction is called vector quantity. The additions of two or more forces called resultant forces. The magnitude and direction of the resultant is obtained using the parallelogram law as shown in figure. If P

r and Q

r are

two forces added together and , is the angle between them, then the resultant R obtained is the diagonal of the parallelogram constructed by P

r and Q

r.

Figure 2.2

Using the cosine rule: ( )+=+ oQPQPQP 180cos222 rrrrrr

cos222 QPQPR

rrrrr++=

From the equations above, if the angle between two forces is known then the magnitude of the resultant can be determined.

Procedure: 1. Place suitable masses at point P, Q and R until equilibrium is reached. 2. Mark the positions O, X, and Y of the string on the white paper using some

pins. Measure the angle made by the strings. 3. Repeat step (1) and (2) by using different masses for P, Q and R for eight (8)

sets of readings. State the weight of slotted mass in Newton. 4. Tabulate: P, Q, R and angle in Table 1. 5. Using an appropriate scale, draw a parallelogram in the graph paper to

represent each set of forces P, Q, R and the angle . 6. For each set of force P and Q the magnitude of the resultant R can be obtained

by three methods. First, directly from Table 1; second from the diagonal of the parallelogram formed by P and Q; and third, using the Cosine Rule.

7. Record the result for all the three method in Table 2. 8. From table compare the results of the three methods and give your comments. 9. Does your result verify the parallelogram law of forces? Give comment on

your answer. 10. When will P2 + Q2 = P + Q2 ?

Pr

Qr

QPRrrr

+=


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Practical 3 _____________________________________________________________________

To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal

Objective: To investigate the trajectory of a two dimensional motion.

Apparatus and Materials: 1. Ramp 2. Wooden block 3. Pendulum bob 4. Plumb line 5. Steel ball 6. Wooden board 7. Carbon paper 8. Meter rule 9. Plasticine

Setup: 1. A ramp has been set up at the edge of a bench as shown in the Figure 3.1. 2. Suspend a plum-line from the edge of the bench as shown in Figure 3.2. 3. Mount a wooden board horizontally using two clamps so that the board is

situated about the bottom of the ramp. 4. Place a sheet of blank paper on top of the board. 5. Place a piece of carbon paper on the top of the blank paper. The ink-side of the

carbon paper should be facing down. 6. When a ball is released at the top of the ramp, the ball will travel through a

trajectory as shown in Figure 3.2.

Figure 3.1

Figure 3.2

x


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Theory: Let:

g = 9.80 ms-2 u = speed of the ball as it leaves the ramp k = constant y = vertical distance (between the bottom of the ramp and the top of the board) x = horizontal distance (between the plum-line and mark on the paper]

The equation which relates x and y is

ku

xkgx

y+

+=

2) 1(

Procedure: 1. Position the ball at the top of the ramp. Release the ball so that it rolls down

the ramp and onto the board below. 2. Remove the carbon paper and observe that the ball makes a small mark on the

blank paper. 3. Measure and record the vertical distance y and the horizontal distance x. 4. Reduce the value of y and repeat the steps above to obtain eight (8) sets of

values of x and y.

5. Tabulate: y, x, andx

y.

6. Plot a graph of y/x against x. 7. Determine the gradient and y- intercept of the graph. 8. Use your answer from [7] to determine values of k and u.


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Practical 4 _____________________________________________________________________

To find the force constant of a spring

Objectives: To study the application of Hookes Law. To study the forces in equilibrium. To study the resolution of vector quantities.

Apparatus and Materials: 1. Spring 2. Plumb-line 3. Protractor 4. Slotted masses 200g with hanger 5. Thread 6. Retort stand 7. Nail or pin

Setup: 1. Set up the apparatus as shown in Figure 4.1 below. 2. Adjust the spring, so that it stretches horizontally. 3. The angle between the plumb-line and the section AB is . 4. The mass of the load is m, its weight is mg.

Figure 4.1

m=200g


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Theory Let: g = 9.80 ms-2 m = mass of the load = angle between the plumb-line and the section AB x = extension of the spring k = force constant of the spring l = stretched length of the spring lo = unstretched length of the spring

When the system is in equilibrium, the forces acting at the point B are in equilibrium

Vertically: mg = T cos . (1)

Horizontally: kx = T sin ... (2)

Therefore: kx = mg tan

kmg

xtan

=

A graph of x against tan will yield a straight line.

The gradient is equal tok

mg.

Procedure: 1. Measure the unstretched length, lo of the spring before setting up the apparatus. 2. Adjust the spring, so that it stretches horizontally. 3. Measure the angle between the plumb-line and the section AB. 4. Measure the new length, l of the spring. 5. Calculate the extension, x of the spring. [where x = l lo] 6. Pull the spring side way to vary the length l to obtain six (6) sets of values of

and x. {Note: before taking the value of the angle , make sure that the spring is horizontal.}

7. Tabulate: x, , tan . 8. Determine the gradient of the graph. 9. Determine the force constant, k of the spring.


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Practical 5 _____________________________________________________________________

To determine the coefficient of static friction between two surfaces

Objectives: To determine the relationship between the mass of load and the length of spring. To determine the coefficient of static friction between two surface.

Part 1: The relationship between the mass of load and the length of spring

Apparatus and Materials: 1. Retort stand 2. Spring 3. Slotted masses 200g with hanger 4. Meter rule

Setup:

Figure 5.1

Procedure: 1. Hook one end of the spring on the retort stand. 2. Hang the hanger with a 20g slotted mass at the other end. 3. Measure the length l1 of the spring, record the mass m1 of the load. 4. Increase the mass m1, measure the corresponding length l1 of the spring. 5. Tabulate l1 and m1. 6. Plot a graph of l1 against m1.


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Part 2: The coefficient of friction between two surfaces

Apparatus and Materials: 1. A smooth plank as inclined plane 2. Retort stand 3. Wooden blocks 4. Electronic balance 5. Spring 6. Protractor 7. Pendulum bob 8. Thread 9. Plasticine

Setup:

Figure: 5.2


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Theory: If the wooden block is being displaced down the inclined plane, the block will return to its original position when released because the net force up the plane exceeds the limiting friction down the plane. The downward displacement is being reduced gradually until a stage where the block stays stationary when released. At this point, the force up the plane equalized the limiting friction down the plane.

If T is the tension of the spring, F is the limiting friction, and is the coefficient of static friction, then

T- mg sin = F T- mg sin = mg cos

If T = mg, where m = mass equivalent to tension T, then

mg mg sin = mg cos m = m( cos + sin )

Procedure: 1. Weigh the mass of wooden block with a smooth surface. Record down the

mass. 2. Adjust the retort stand, to adjust the angle of inclination of the plank, such that

the wooden block can slide down the plane freely. 3. Measure and record the angle of inclination of the plank. 4. Set up the apparatus as shown in Figure 5.2. 5. Start with one wooden block attached to the lower end of the spring. 6. Displace the block downward and released, so that the block will be pulled up

by the tension in the spring. 7. Repeat step [6] with a smaller displacement until a stage that the wooden block

stays stationary upon released. Measure and record the length l2 of the spring. 8. From the graph of l1 against m1 in Part 1, obtain the corresponding mass, m for

the length l2. 9. The mass of the wooden block could be increased by adding another wooden

block on top of the first, weigh the new combined mass of the block. Repeat steps [6] to [8].

10. Tabulate: m, l2 and m. 11. Plot a graph of m against m. 12. Calculate the gradient of the graph of m against m. 13. Hence, determine the coefficient of static friction, .


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Practical 6 _____________________________________________________________________

To verify the conservation of spring and gravitational potential energy

Objective: To verify the law of conservation.

Apparatus and Materials: 1. Spring 2. plastic / rubber ball 3. Spring holder 4. Metre rule

Equipment: 1. Electronic balance

Setup:

Figure 6.1

h Compress

Metre ruler

Release


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Theory:

When spring is compress, the spring store potential energy:

2

21 kxPE spring =

The total energy E of a simple mechanical system is the sum of the potential energy PE and the kinetic energy KE. In the absence of friction the total energy E of the system is a conserved quantity so that E = KE + PE. In the absence of friction, if the KE and PE change, they must change so that their sum is equal to the total energy E. In this experiment several simple mechanical systems will be examined for this property.

As the spring been release, the potential energy of the spring is converted to kinetic energy and after the ball reach the maximum high, the kinetic energy is equal to zero and transform to Gravitational Potential Energy.

PEKEPEspring +=

at maximum height:

mghkx += 021 2

Procedure: 1. Measure the mass of the ball, m. 2. Compress the spring downward, record the vertical distance of spring as x and

let it go. 3. Measure the maximum height, h the ball can achieve. 4. Repeat the step [2] and [3] to obtain eight (8) sets of data. 5. Tabulate: x, h and x2. 6. Plot a graph of x2 against h. 7. Determine the gradient of the graph. 8. Use your answer from [7] to determine values of spring constant, k.


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Practical 7 _____________________________________________________________________

To Design a Roller Coaster via PhET Energy Skate Park Simulation

Objectives: To understand the conservation of energy in real-world applications To design a roller coaster (via simulation) and observe the physics concepts

used in the design

Apparatus and Materials:

http://phet.colorado.edu/en/simulation/energy-skate-park

Online Simulation Lab ROLLER COASTER PHYSICS Purpose: The purpose of this simulation lab is to strengthen your understanding of energy conservation in real-world applications. You will use a skateboarder and his park to represent the roller coaster and its track. You will observe many other physics concepts at work as well.

Note: This exercise is authored by Scott McCurdy. The copy is available at: http://phet.colorado.edu/en/contributions/view/3027

Pre-Lab Inquiry What Do You Think? You are asked to design a new roller coaster. It is totally up to you to determine what the riders will experience. The only rule is that the coaster obeys the laws of physics. Take a minute and brainstorm about a design you would like.

1. Name three adjectives that will describe your roller coaster.

2. Describe three features your roller coaster will have that will attract riders.

3. Name three variables that will affect the type of experience a rider will have. EXPLAIN.


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4. Name three concepts of physics that the roller coaster must obey in order to be successful. EXPLAIN.

5. Draw a side-view sketch of your roller coaster design below.

Concept Review Write out an explanation for each question below.

6. Define potential and kinetic energy.

7. Describe when potential and kinetic energy are at their highest on a roller coaster.

8. How does conservation of energy apply to roller coasters?

9. How does friction affect a roller coaster?

10. What is responsible for the apparent change in weight that riders experience on coasters?


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Internet Lab Activity

Open up the University of Colorado, PhET Energy Skate Park simulation: 1. Go to http://phet.colorado.edu/ 2. Click Play with Sims> 3. Click the Energy Skate Park icon 4. Click Run Now! 5. Spend ONE MINUTE to explore the simulation and familiarize yourself with

the controls. 6. Click the Reset button in the top-right corner. Begin the exploration below.

Exploration Questions Use the simulation to answer the questions below.

1. Does the skater hit the same height on the opposite sides of the track? (Checkmark the Show Grid button to help you determine this!)

a. What must be true about the system for this to be possible?

b. Click the Track Friction >> button to adjust the friction settings. What do you observe about the skater as you adjust the setting?

2. Now, turn on the energy Pie Chart and Bar Graph. (You may need to move things around a little to see everything.)

a. On the visual aids, what color represents potential energy and which is kinetic energy?

b. When does the skater have the highest amount of kinetic energy? Potential energy?

c. When does the skater have the lowest amount of kinetic energy? Potential energy?

d. Describe how the bar graph changes as the skater moves along the track.


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e. Explain which visual aid (pie chart or bar graph) helps you understand conservation of energy better, and why.

f. Keep your preferred visual aid open for the remainder of the investigation.

Build Your Roller Coaster Use the simulation to build and test your roller coaster design from the Pre-Lab Inquiry.

1. If you made any changes during the Exploration Questions, click Reset again.

2. Right-click the track and select Roller Coaster Mode. This keeps the skater attached.

3. Notice that you can zoom out to give yourself a wider view. You may want to do this as you build your coaster.

4. Drag in new pieces of track and manipulate the curves until you closely match your pre-lab sketch.

5. Drag and drop the rider to the location of the beginning and observe. DO NOT MAKE CHANGES YET.

a. The ride probably was not successful on the first attempt. If not, what physics concept(s) was violated?

b. Identify several adjustments you need to make.

6. After making the initial adjustments, try the ride again. Continue making adjustments until the ride becomes successful (rider makes it from one end to the other completely does not have to make it back through).

7. Raise your hand and show the teacher your successful design. 8. Draw a side-view sketch of your successful design below.


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9. Label the points of acceleration on your sketch. a. Down arrow = slowing down b. Up arrow = speeding up c. Circle arrow = changing direction

10. Click the Track Friction >> button and adjust the setting. 11. Run the rider through your track again and observe the changes.

a. Did the rider make it to the end?

b. What do you notice differently about the pie chart and/or bar graph?

12. Describe the changes you need to make to your design, as a result of the presence of friction.

13. Make the necessary adjustments until you achieve a successful ride with friction.

14. Raise your hand and show the teacher your friction-savvy coaster. 15. Draw a side-view sketch of your friction-savvy coaster below.


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Post-Lab Questions:

1. List and explain the differences between each of your sketches.

2. At the top of a hill on the ride, most of the energy is _______________ and at the bottom of the hill, most of the energy is converted into _________________.

3. What are the equations for potential and kinetic energy?

4. If you were an engineer of an actual roller coaster, what information would you need to know in order to ensure that your coaster would be safe?

5. Would it be possible to predict the speeds that a coaster will reach before its ever placed on the track? How?

6. The most thrilling roller coasters usually contain vertical loops. What keeps the riders in their seats when they go upside-down?

7. Consider going around a horizontal turn to the right. If the coaster suddenly slipped off the track, what path would it follow? Draw a top-view sketch below.

8. You should have drawn the coaster following a straight line after it slipped off the track. Since that is the path it would take without the track, there must be an unbalanced force causing it to accelerate (turn) around the bend. What direction is that force pointing? Draw a top-view sketch of the force vectors below.


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Practical 8 _____________________________________________________________________

To determine the moment of inertia of a flywheel

Objective: To study the moment inertia of a flywheel.

Apparatus and Materials: 1. Flywheel 2. Digital stop watch 3. Slotted masses with hanger 4. Meter rule 5. G clamp 6. Thread 7. A soft board to absorb the impact when the slotted masses hit the ground 8. Vernier caliper

Setup: 1. Clamp the flywheel to the side of the bench. 2. One end of the thread is fixed to the flywheel. The other end is tied to the mass

hanger. 3. Roll the thread round the axle of the flywheel. 4. The distance between the base of the hanger and the floor is, h. 5. When you release the masses, the masses will accelerate downward, and

flywheel will have an angular acceleration.

Figure 8.1


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Theory: Let:

T = tension in the string m = mass of the load a = acceleration of the load = angular acceleration of the flywheel g = gravitational acceleration = 9.81 ms-2 R = radius of the axle I = moment of inertia of the flywheel h = initial distance between load and floor t = time taken for the load to touch the floor = friction torque on the flywheel

Acceleration of load:

2t

ha = ............... (1)

Angular acceleration of wheel: Ra

= (2) For the load: mg T = ma... (3) T = m(g - a)... (4)

Using equation (1) to find the value of a. Using equation (2) and the calculated value of a to find the value of . Using equation (4) and the calculated value of a to find the value of T.

For the wheel: ITR = ... (5)

IT

IR

=

Graph of against T is a straight line, the gradient is s andIR

s = .

Moment of inertia of the flywheel is: .s

RI =

Procedure: 1. Measure the initial height of the load. This height is fixed. 2. Put mass onto the hanger. 3. Release the load, and start the stop-watch simultaneously. 4. Take the time for the load to touch the floor. 5. Vary the mass of the load, m. Repeat the above steps, and obtain a total of

eight (8) sets of values of m and t. 6. Tabulate: m, t, a, and T. 7. Plot a graph of against T. 8. From the graph, determine the moment of inertia of the flywheel.


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Practical 9 _____________________________________________________________________

To investigate the effect of buoyancy via PhET Buoyancy simulation

Objectives: To understand the meaning of buoyancy. To study the effect of buoyancy to a submerged object in liquid.

Apparatus and Materials: http://phet.colorado.edu/en/simulation/buoyancy

Buoyancy and Density Activity

Directions: Go to the following website to use an interactive simulation to work with buoyancy and density.

http://phet.colorado.edu/en/contributions/view/3350

Procedure: Getting Familiar

1. On the Intro screen, mess with the apparatus, changing the blocks, observing what happens when the mass, volume and densities are held constant.

2. Check and uncheck the boxes under Show Forces to see where they act.

Intro: Give a brief description of what the relationship is between mass, volume and density of each object and how it affects whether the object will sink or float.

Lab Setup 1. Click over to the Buoyancy Playground and begin the lab. 2. There are 5 different fluids to choose from in the lab and five different types of

materials. (Styrofoam, wood, ice, brick and aluminum) 3. Use the table supplied to organize your work.

Lab Procedure: Part 1 1. In each of the scenarios below, determine first, by predicting, whether the

object will sink or float. Use a mass of 2.5 kg. 2. Test each object once you have predicted and record the results.


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Part 1: Write an S for sink or an F for float. Predictions first!! Air Gasoline Olive Oil Water Honey Pred. Act. Pred. Act. Pred. Act. Pred. Act. Pred. Act.

Styrofoam Wood Ice Brick Aluminum

Lab Procedure: Part 2 1. Determine the volume of the fluid when an object is placed in that fluid. 2. Use a mass of 2.5 kg. 3. Record all values for different sets of combinations in the table below.

Air Gasoline Olive Oil Water Honey

Styrofoam

Wood

Ice

Brick

Aluminum

Lab Procedure: Part 3 1. In this part of the lab, determine the amount of buoyant force that is acting on

each block of mass 2.5 kg. 2. Determine how you will find the amount of buoyant force or buoyancy.

Perhaps try using the two scales given in the lab. 3. Record these values in the table below.

Air Gasoline Olive Oil Water Honey

Styrofoam

Wood

Ice

Brick

Aluminum


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Conclusions: 1. In the part 1 of the lab, what happened when the ice was placed in olive oil?

2. In part 2 of the lab, which of the objects had the greatest density?

3. From part 3, what is the relationship between the buoyant force and the weight of an object when the object:

a. Sinks

b. Floats

4. How is it possible to have two objects of the same mass where one object sinks and the other object floats? Use your observations from the Intro part of the lab to answer this question.

Additional Questions:

http://phet.colorado.edu/en/contributions/view/3408 Directions: Intro Tab:

1. How can you use a block and the other tools on the Intro tab to determine the

density of the Oil?

2. Determine what forces act on an object when the object is placed in a fluid. How are the forces similar and different when the object sinks, floats immersed in the fluid, and when it is only partially submerged.


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3. Give specific examples that you could use to explain what buoyancy is and how an objects weight can appear to change when in a fluid. Make sure to include situations where the object sinks, floats immersed in the fluid, and when it is only partially submerged.

Playground Tab:

4. Explain how you can use the information about the block and the fluid to determine if the block will sinks, floats immersed in the fluid, and when it is only partially submerged.

5. How can you determine the apparent mass of an object if you know the density of the object and the density of the fluid?

6. Challenge: Explain how an object that is more dense than water can be kept afloat by placing it on an object that is less dense than water

Mechanics Labmanual

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