Download PHYSICS LABORATORY

T.C.
MARMARA UNIVERSITY
FACULTY OF ARTS AND SCIENCES
PHYSICS DEPARTMENT
PHYSICS LABORATORY - I
DEPARTMENT:
NAME:
SURNAME:
NUMBER:
2
T.C.MARMARA UNIVERSITY PHYSICS DEPARTMENT
PHYSICS LABORATORY –I MANUAL
EXPERIMENT NO:
EXPERIMENT NAME:
THE DATE:
GROUP NO:
NAME:
NUMBER:
DELIVERY TIME:
REPORT NOTE:
2
3
EXPERIMENT 1
ANALYSIS OF
VOLUME
AND DENSITY OF A SOLID
MATERIAL
AND
ARCHIMEDES PRINCIPLE
Purpose : 1.)The goal of this laboratory is to measure the mass and the dimensions of solids and to
determine their volume and density.
2.)Using Archimedes Principle and determine the volume and density of irregular shaped
solid materials.
Theory:
While doing a basic physics experiment, the researcher mainly focuses on a chosen problem and
tries to figure out the basic physical background and offers realistic methods to solve the general
concept. The experiment will help researcher to visualize the problem and researcher will determine
first of all the most suitable way to do the experiment and then will make a schedule to
himself/herself that he/she will follow as doing the research. In this way researcher will be able to
check the results in every step and be able to figure out if the chosen method is realible and
practical or not.
Physics experiments start with the basic concepts and one of the main topic in fresman physics
laboratory
is
“the
matter”.
Matter is
generally
considered
to
be
anything
that
has mass and volume. The volume is determined by the space in three dimensions that it occupies.
The mass is determined by its rest mass (or invariant mass), which is measured by the acceleration a
body has when a force is applied. The greater the mass, the slower the acceleration for the same
force. Matter is thus a general term for the substance of which all observable physical objects
consist.
Typically, matter includes atoms and other particles that have mass, but this definition confuses
mass and matter, which are not the same. Different fields use the term in different and sometimes
incompatible ways; there is no single agreed scientific meaning of the word "matter," even though
the term "mass" is better-defined.
The mass density or density of a material is its mass per unit volume. The symbol most often used
for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided

by volume:
m
v where ρ is the density, m is the mass, and V is the volume. The volume of any
solid which has a simple geometric form may be determined from its dimensions; which, if the
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body is small, are most conveniently measured by a vernier caliper and a micrometer screw gauge.
The mass; however is found by the use of the laboratory triple balance.
When you place an object in a fluid it will do one of those two things; it will float or sink. Perhaps
when you were in high school you learned that the typical way in which you can tell what the
object will do is by knowing its density and how it compares to the fluid it is in. If the density of
the object is less than the density of the fluid it is in, then it will float. If the density of the object is
more than the density of the fluid it is in, then it will sink. This is all well and good but it doesn’t
really get to the heart of the matter. This lab will hopefully give you a better feel for why objects
float or sink.
Archimedes Principle :Any object that is either partially or completely submerged in a fluid will
always feel a buoyant force acting on it. A buoyant force always acts in a direction opposite to that
of gravity. It can be calculated by using Archimedes Principle which states that an object will be
buoyed upwards by a force that is equal to the weight of the fluid that the object displaces. We also
know that W = mg so we can alter the equation as below
FB  Wdis
FB  mdis g
FB :Buoyant force(in Newtons, N)
Wdis :the weight of the displaced fluid (in Newtons, N)
mdis :the mass of the displaced fluid (in kilograms, kg)
g : the gravitational acceleration (9.8 m/s2)
Apparatus:
1.)Metal cylinders in different radius
2.)Vernier
3.)Ruler
4.)Calculator
5.)Newtonmeter or dynamometer
6.)irregular shaped solids
7.) graduated cylinder
8.)Water
9.)Glass Beaker
4
5
EXPERIMENTAL SETUP:
A.)Analysis of volume and density of regular shaped solids:
1.)First of all take three or four cylinder shaped bulk metals. We need to figure out these unknown
metal’s densities .
2.)Use your vernier and ruler for analysis and measure these cylinders height and diameter one by
one; firstly by vernier and then ruler. Write your measurement results in below table.
3.)Calculate the radius of all cylinders.
4.)Then use a Newtonmeter and measure the bulk metal’s weight one by one.
5.)Calculate the cylinders volume seperately and note the table.
V  area( r 2 ).height (h)
V [cm3 ]  area[cm2 ].height[cm]
6.)Use the volume and mass of the cylinder and calculate the density of it.
d [ gr / cm3 ] 
m[ gr ]
v[cm3 ]
n R:diameter(cm) r:Radius(cm)
H:height(cm) V:volume(cm3) M:mass(gr) Density
(g/cm3)
vernier
1
2
3
4
Average Density:
5
6
ruler
1
2
3
4
Average Density:
B.)Analysis of volume and density of irregular shaped solids:
Now we need to figure out the volume of irregular shaped solids for instance a piece of rock .
1.)Take two piece of rock and then lift the heaviest of the two types of blocks and try to guess the
mass in kilograms of each and their density ratio. Note your estimates in your table below.
2.)Measure the mass of the two types of blocks using the mass balance (note your measurements.)
3.) Use a ruler to measure the length, height, and width of the block. To what accuracy can you
measure the dimensions? Now use the calipers to measure the dimensions. Measure at three
locations and note down the readings and the average. Why is this a good idea to get the average?
Calculate the corresponding volumes and the average.
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4.) Find the slope of the line. If you plotted mass on the vertical axis and volume on the horizontal
axis, then the slope is equal to the density. Compare the density you found for the
metallic block set with the densities of common substances. Can you identify the substance?
How does the density ratio compare to your initial estimate?
5.) Completely fill the glass beaker with water. Tie a string around the rock and gently immerse into
the water in the jar. The excess water will spill over. Now remove the rock from the jar taking care
that no excess water is spilled, and all the water that drips from the rock falls back into the glass jar.
Using the graduated cylinder fill back the water that was lost in the glass jar. The volume of water
you poured using the measuring cylinder is the volume of the rock. (Note: 1 ml = 1 cm)
Weight of the rock in air
ma
Weight of the rock in water
mw
Weight loss
∆m= ma- mw
Volume of overfloating water
Vwater
Weight of overfloating water
mwater=1. Vwater
6.)Calculate the density of the rock and compare it with the density values table.
Error Calculation:
1.) Compare your experimental value of metal’s density to the accepted value and record the
percent error.
2.) Plot a graph of M vs. V for the rock. Record the value of the slope and then calculate the density
of the rock by using the slope.
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REPORT
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EXPERIMENT 2
SUMMING VECTOR QUANTITIES USING PARALELLOGRAM METHOD
Purpose : Summing the vector quantities using the parallelogram method
Apparatus:
Different masses between 1-1000 grams
A flat wood,
Two pulleys,
A few millimetric sheets.
Prior information:
Some quantities can be expressed in numbers, but there are some quantities that numbers are
not sufficient to express them. In some cases, addition to numbers, the directions of the
quantities should be given. Therefore, physical quantities are divided in two: scalar and vector
quantities.
Scalar Quantities:
There is no direction in the question for physical quantities such as mass, energy, temperature,
work, electric charge, time, volume…. We would have enough information when their
numerical values and units are given. These quantities are called scalar quantities.
Vector Quantities:
Some quantities such as velocity, force, acceleration, displacement are directional quantities.
The quantities of this type cannot be expressed by just their numerical values and units. The
quantities that are expressed by their magnitudes, starting points and directions are called
vector quantities.
When we say “a train goes with a speed of 30 km/hour”, it is said that the event is not
expressed clearly. A question then arises: to which direction? For example, if we say “a train
goes with a speed of 30 km/hour to north” the event would be expressed clearly.
Vector representation:
Ending
point
Starting
point
0
1
Magnitude
A
As can be seen from the figure above, vector quantities are represented by a directional
line segment. This vector has three elements:
Application (starting) point: This is the point where the vector is applied or this point is the
starting point. The application point of the above vector is at 0.
Magnitude: The magnitude of a vector is the numerical
value of it. As the figure on the right shows the magnitude of
the K vector is four units.
0
west
Direction: The direction of the arrow on the edge of a vector is defined as vector’s direction.
In the figure, the direction of the K vector is from 0 to A or to east.
Equivalence of Two Vectors: Two vectors with the same
directions and magnitudes are said to be equal to each other.
In the figure, K and L vectors are equal, since their
directions (east) and magnitudes (three units) are equal
(K=L).
Negative of a vector: A vector which has the same
magnitude, but in the opposite direction of the K vector, is
said to be a negative of the vector.
Vector Shift: It is possible to shift a vector quantity without
changing its magnitude and direction. If a vector is shifted
by changing its direction, then it is a different vector.
A
east
Vector Sum: There are several methods used to sum vectors: endwise addition (polygon)
method and parallelogram method.
Polygon Method: According to this method, the when two vectors are summed without
changing their magnitude and direction, the ending point of one vector is joined by the
starting point of the other vector. After that, a new vector whose starting and ending points
are drown from the starting point of the first vector to the ending point of the second vector.
This new vector is just the sum of two vectors.
Figure I.
Figure II.
Parallelogram method: In this method (follow Fig. III and Fig. IV), the starting points of
two-vectors are joined first. A line starting from the ending point of K vector is drawn as to be
parallel to vector L and another line starting from the ending point of L vector is drawn as to
be parallel to vector K. A new line starting from the joined starting points of K and L vectors
to the joined edges of two parallel lines is drawn. This new vector is again the sum of K and L
vectors.
Figure III.
Figure IV.
Note: When two or more vectors are summed, all the vectors involved must have the same
unit. For example, two sum a velocity vector and a displacement vector is meaningless.
EXPERIMENT:
Build an experimental set-up as shown in figure:
Q
P
E
An experimental set-up composed of two pulleys and three masses.
Attach the millimetric sheet on the flat wood as to be behind the set-up.
Connect a rope properly and pass it through the pulleys.
Then, attach three masses (P, E and Q) to the free edges of the rope and release the system.
Mark the rope path on sheet and measure the direction and angles in between.
For the stationary case, find the composite force and put it on the table below. The force
should be in N (Newton) units and compare this force with that E mass.
Find the composite force of the stationary system using the cosines theorem and put it on
table.
Using different masses and sheets repeat this experiment twice.
Exp. No
1
2
3
E (N)
Q (N)
P (N)
Angle
(Degrees)
Rn (N)
Rn (N)
Experimental Theoretical
%
difference
ERROR ANALYSIS:
Perform an error analysis using the exact values and the results found from experiment. Using
the cosines theorem, evaluate the relative error formula for the composite force of the
stationary system and calculate the relative error for one measurement. Write down the
sources of errors.
RESULTS and COMMENTS:
Write down the results and comments about this experiment.
REFERENCES:
Fundamentals of Physics, D. Halliday and R. Resnick, Page: 247-249.
REPORT
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EXPERIMENT : 3
TORQUES EXPERIMENT
Purpose : Torque measures the tendency of a force to rotate an object about an axis. The principles
of applying ana balancing torques are explored in this investigation.
Materials:
Metal bar, clamp, a ruler , different standart mass ( 10,50,100,150, gr ) ,1 suspend apparatus.
Metal Bar
L(1)
L(0)
10g
L(2)
20g
Introduction : A single particle off mass m whose location with respect to the origin O of an inertial
reference frame is described by a position vector . Let force
act on particle ana let its linear
momentum be . Here are two definitions and a relation between them:
i.
The torque  about O acting on a particle due to the force
ii.
The angular momentum of of the particle about O,
iii.
Newton’s second law of motion for a single particle, in rotational form,
,
1
PROCEDURES
i.)
Balancing torques on a metal bar.
Suspend a (metal bar) from an overhead support as shown in diagram. Slide the metal bar
along the clamp until you find a position for the clamp where the metal bar balances horizontally.
Record the position of this point of suspension L(0) in the data chart.
Exactly 15.0 cm to the right of the point of suspension, hang a 10 g standart mass. The
weight of the standart mass exerts a force on the metal bar that causes it to rotate around the point
of suspension. Observe whether the torque produced by this force is clockwise or counterclockwise.
Record the position L(1) via a ruler and weight f(1) of the Standard mass in data chart, using the
approximation that a mass of 10 g weighs 0,1 N.
Hang a 20 g standart mass on the left side of the metal bar and adjust its position until the
metal bar is balanced horizontally. Record this position L(2) and the weigth f(2) of the standart mass
(0,2N). Also note whether the weight of the mass creates a clockwise or counterclocwise torque
around the point of suspension.
Repeat the above procedure, using a variety of positions for the different standart masses
ana finding the corresponding
position of the
30 g mass that will balance
the metal bar
horizontally. Substitute different known masses on each side of the point of suspension. Repeat the
above precedures.
DATA and ANALYSIS
Location of point of suspension L(0) = ……………………………….. meter.
TABLE I
1
TRIAL
Mass (g)
Position of Mass (m)
2
3
4
5
6
7
8
m (1)
L (1)
Distance from point of suspension (m) X(1)
Force (N)
f(1)
Torque (Nm)
T(1)
Mass (g)
m (2)
Position of Mass (m)
L (2)
Distance from point of suspension (m) L (2)
Force (N)
f(2)
Torque (Nm)
T (2)
Percent Error
E%
2
ii.) Weighing an Unknown.
After making sure the metal bar is balanced horizontally when nothing is hung from it, hang a
known mass on one side of the metal bar and an object of unknown mass on the other side.
Adjust
the position of the unknown until the metal bar is again balanced horizontally.
Determine and record the positions of the two objects.
Move the known mass to different new positions. At each new position, move the unknown
until the bar is rebalanced ana recor the positions of the known and unknown.
DATA and ANALYSIS
Location of point of suspension L(0) = ……………………………….. cm.
Known mass m =………………………g
TABLE II
1
TRIAL
2
3
4
5
6
7
8
Position of Mass (m)
Known Torque
L(1)
Distance from point of suspension
(m) X(1)
Force (N)
f(1)
Torque (Nm)
T(1)
Mass (g)
Unknown Torque
m(2)
Position of unknown mass (m)
L(2)
Distance from point of suspension
(m) X(2)
Torque (Nm)
T(2)
Calculated weight (N)
%E
Measured weight (N)
Percent Error
E%
REFERENCES
1. Experiments for Physics Labs Herbert H.Gottlies
3
REPORT
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EXPERIMENT 4
MOTION WITH CONSTANT ACCELERATION
Purpose : To investigate Newton’s second law.
Materials: Air table, discs with different weight, spark timer, carbon paper, clamps, pulley,
string,container, standart masses.
Introduction :
Newton second law is summed up by the relation
, where
is the vector sum of all
forces that act on the body. In scalar form this law becomes
first law of motion is contained in the second law as a special case, for if
Notice that the
, then
. In other
words, if the resultant force on a body is zero, the acceleration of the body is zero. Therefore, in the
absence of a net applied force, a body will move with constant velocity or be at rest.
Figure 1 shows a body of mass m1 on a frictionless horizontal surface pulled by a massless
string attached to a second body of mass m2 hanging over a pulley. We assume that the pulley has
no mass and is frictionless and that it only serves to change the direction of the tension in the string
at that point. The magnitude of the tension is the same throughout a massless string.
Figure 1. a body of mass m1 on a frictionless horizontal surface pulled by a massless string attached to a second body of
mass m2
The forces acting on
to right ;
and
are shown Figure2.
,the tension in the string ,pulls on the body
is the downward pull of the ground on the body and
on the body by the smooth table. The body of mass
is the vertical force exerted
will accelerate in the
– direction only, so
that
Figure 2. A free body diagram showing all forces acting on m1 and m2
1
Hence, we can write
From these equations we conclude that
To determine
. We do not know
we must consider the motion of the body of mass
are accelerating, we cannot conclude that
resultant force on
equals
so we cannot solve for
.
. Because the string and body
. In fact, if
were to equal
, the
would be zero, a condition holding only if the system is not accelerated. The
equation of motion for the suspended body is
If
is the common magnitude of the two accelerations we have, taking the directions of the two
acceleration vectors properly into account
We then obtain from Eq..
These yield
PROCEDURES
In this experiment, the second law will be performed by comparing theoritycally and
experimentally determined values of acceleration.
The spark generator is designed to supply high voltage. This is not usually a problem,
but a shock hazard does exist when the generator is operating. All adjustment should be
made with the spark generator Turned off
.
i.
Put the carbon paper on the air table. Secure one disc at the top corner of air table as
shown Figure 3
ii.
Set the spark timer to 30 ms and turn it on.
2
iii.
Turn on the compressor and spark timer, press the pedal of the spark timer to start
generating sparks.
iv.
Draw two lines on the carbon paper for the inital and final positions. Apply an accelerating
force of ……N by adding ….. grams of metal mass to the container and record the time it
takes the disk to travel between two positions.
v.
Calculate the acceleration of the disk, using the equation a = 2x / t2
vi.
Repeat the above procedure several more times, increasing the accelerating force by ……N
or ….N each time by adding the mass to the container.
vii.
Plot a graph of acceleration versus force, using your data
viii.
With a constant accelerating force provided by the weight on the container, vary mass of
the accelerating system ( disk,container and different weigth) by adding known masses,
about 500 g at a time , strapped to the top of the disk. For each trial record the mass of
the system and resulting acceleration. Make a graph showing how the acceleration varies
with increased mass.
DATA
i.
Variation of Acceleration with Force (Constant Mass)
Distance moved x = ............................. cm
Mass of Disk and container with weigth M =.................................g
TRIAL
FORCE (N)
TIME (t)
Acceleration, a = 2x/t 2 (cm/sec2)
1
2
3
4
5
6
7
8
3
ii.
Variation of Acceleration with Mass (Constant Force)
Distance moved x = ............................. cm
Accelerating force F=.............................N
TRIAL
Mass of
TIME (t)
Disk,container,
(sec)
2
2
Acceleration, a = 2x/t (cm/sec )
weigth and added
mass (g)
1
2
3
4
5
6
7
8
REFERENCES
1. Experiment for Physics Labs, Herbert H.Gottlies
2. Fundemental of Physics, Halliday and Resnick
4
REPORT
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EXPERIMENT 5
DETERMINATION OF FRICTION COEFFICIENT
Purpose: Determine μk, the kinetic coefficient of friction and μ s, the static friction coefficient
by sliding block down that acts as an inclined plane. μs and μk will be determined by the board
with a pulley mounted on it in a horizontal position and applying known forces to the block.
Apparatus: Smooth wooden block with pulley attached to one end, string, mass holder,
slotted massed, an inclined plane and hook.
Theory: We encounter friction at almost all times during the day. Friction between our foot
and the floor helps us walk. In spite of its importance, friction is still not well understood.
However, empirical laws describe the friction between two surfaces. Friction is a resisting
force that acts along the tanget to two surfaces in contact when one body slides or attempts to
slide across another.
Normal force is the force that each body exerts on the other body, and it acts
perpendicular to each surface. The friction forces is directly proportional to the normal force.
Static friction occurs when two surfaces are still at rest with respect to each other, but an
attempt is being made to cause on of them to slide over the other one. The static friction force
fs is given by
fs≤μs N
(Eq.1)
Where N is the normal forces between the two surfaces and μs is a constant called the
coefficient of static friction. Eq.1 tells us that the static friction forces varies in response to
applied forces from zero up to a maximum value. If the applied force is less than the
maximum, then there is no motion. The object will begin to move and no longer friction force
is avaliabe.
When two surfaces are moving with respect to each other then, kinetic friction occours, thus
the friction is characterized by
force fk is given by
called the coefficient of kinetic friction. The kinetic friction
(Eq.2)
Where N again stands for the normal force. Kinetic friction does not vary with speed and both
friction coefficients are independent of the apparent are of contact between two surfaces.
If the block is placed on an inclined plane, after at some angle
, the block will slip
down. The block is in equilibrium for motion perperndicular to the plane, and these forces are
equal and given by,
(Eq.3)
Where θs is the angle where the block just begins to slip on the inclined plane. The free body
diagram is given by Fig.1 and shows the forces acts on a block on the inclined plane.
Generally,
therefore a push is needed to get started to slip the block.
Fig. 1 shows the forces acting on a block on an inclined plane.
(Eq.4)
From Equations 3 and 4 we get,
(Eq.5)
When the block is slipping down the plane at a constant velocity, it is in equilibrium with the
vector sum of forces on the block equal to zero.
N=mgcosθk
and f k=mgsinθk
(Eq.6)
Combining these two equations,
(Eq.7)
Equation 7. is used to determine the kinetic friction coefficient at which the block moves
down the inclined plane at constant velocity.
At horizontal position of the board a force needs to be applied to the block for sliding
down by means of a string running over a pulley and down to mass shown in Fig.2. For a
given block mass M1 it is possible to slowly add mass to M2 until M1 begin to move. When
the system is in equilibrium, static friction is acting, thus the following conditions are met:
T=fs
T=M2g
N=M1g
fs=μs N
(Eq.8)
Where T is the tension of the string. Combining these four equations,
fs=M2g= μs N= μs M1g
(Eq.9)
from Eq.9, we get,
M 2= μ s M 1
(Eq.10)
The same procedure can be applied to generate the coefficient of kinetic friction. Namely,
when the system is moving at a constant velocity, we say the system is in equilibrium, and
thus the following expressions can be obtain:
T=fk
T=M2g
N=M1g
fk= μk N
(Eq.11)
Fig.2 Shows force applied to a block on horizontal plane.
Combining these equations we get,
M 2= μ k M 1
(Eq.12)
Eq.12 is usefull to measure μk by finding the value of M2 .
EXPERIMENT
The Inclined Plane
1. On the block, there are three different A, B, and C surfaces. A and B surfaces were
made of wood but their surface area is different. A and C surfaces were made of
different material but their surface area is the same one another.
2. Place the block with the hook attached with its large surface down so that the block
begins to slide on board. Record the value of height of the block as Y. Measure the
angle with a goniometer and record the value of the angle.
3. Static friction can no longer hold the block when it begins to slide down. Record the
data of X, the distance from the pivot line of the board to the block as shown in Fig.3.
4. Repeat step 3 three more times for a total of four trials with only the block itself on top
of the board. Record the values of X associated with each of these trails (0 mass will
be added).
5. Repeat step 4 using a light type, attach 0.2 kg mass to the top of the block and record
X values.
6. Repeat step 5 using different masses (0.4 and 0.6 kg) on the block and record X
values. Determine the static friction coefficient
.
Fig.3 Shows X and Y positions, we need to measure.
Horizontal Plane with Pulley
1. Place the board in horizontal position on the table with the pulley beyond the edge.
2. Attach a piece of a string to the hook in the block. Place it over the pulley and attach the
mass holder to the other end of the string. Add mass to the mass holder to find the
minimum mass needed to just cause the block to move. Record the value as M2 . Include
0.05 kg mass of the holder in the total for M2.
3. Repeat Step 2 by adding 0.02 kg to the top of the block. Determine the minimum mass
needed to just begin to move. Try it for 3 times and record each as M2.
4. Repeat Step 3 for 0.04 and 0.06 kg.
CALCULATIONS
For inclined plane
1. Calculate the mean value of
M1. Calculate the value of
2. Calculate the mean value of
for the static friction for the four trials at each value of
as
and then calculate
for the kinetic friction fort he four trials of X at each
value of M1. For each of the values of
Calculate
.
calculate the value of
as
.
.
For horizontal plane
1. Calculate the mean
for the three trials of M2 for each of the values M1 for both
static and kinetic cases and record them.
2. Calculate standard deviation for the force act on M2 mass for three trial M 2 masses.
GRAPHS
1. For horizontal plane case, graph the static friction data with
as horizontal axis. Show the straight line obtained from the fit.
2. Repeat Step 1 for the kinetic friction coefficient.
as vertical axis and M1
REPORT
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EXPERIMENT 6
THE SPRING CONSTANT DETERMINATION
Purpose: One of the goals of science is the development of physical and mathematical
models to describe physical systems by using observational and experimental data. We
then use these models to either explain previously observed data or to predict results that
have not actually been observed where the quality of the model determines its predictive
value . The objective of the experiment is to determine the spring constant of a spiral spring
by Hooke’s law and by its period of oscillatory motion in response to a weight.
Apparatus: A spiral spring, a set of weights, a weight hanger, a balance, a stop watch, and a
lab scale.
Theory: The restoring force, F, of a stretched spring is proportional to its elongation, x, if the
deformation is not too great. This relationship for elastic behavior is known as Hooke's law
and is described by
F = -kx
(eq. 1)
where k is the constant of proportionality called the spring constant. The spring’s restoring
force acts in the opposite direction to its elongation, denoted by the negative sign. For a
system such as
shown in figure 1, the spring's elongation, x – x0 , is dependent upon the
spring constant,
k, and the weight of a 0 mass, mg, that hangs on the spring. If the system
of forces is in equilibrium (i.e., it has no relative acceleration), then the sum of the forces
down (the weight) is equal and opposite to the sum of the forces acting upward (the restoring
force of the spring), or
m g = k (x – x0)
(eq. 2)
Fig. 1. Illustration of Hooke’s Law. As additional weights are added, there is a linear
increase in the length of the spring.
Equation 2 is in the form of the equation of a straight line (y = mx + b) so, we can see that if
we plot the force produced by different masses (mg) as a function of the displacement from
equilibrium the data should be linear. Hence, the slope of the line will be equal to the spring
constant k. The unit of k in standard metric units is N/m. If the mass is vertically pulled so
that the spring is stretched beyond its rest position, the restoring force of the spring causes an
acceleration back toward the equilibrium position, thus the mass oscillates in simple harmonic
motion.
One complete oscillation is the amount of time describing as the period of vibration called T,
and for the system described above is:
(eq.3)
and
me = m + me-spring
(eq.4)
where m is the mass which hangs from the spring and me -spring is the spring's equivalent
mass. Substituting equation 4 into equation 3 and squaring both sides of the equation yields:
or,
(eq.5)
Comparing equation 5 to the equation for a straight line (y = mx + b), we see that the slope
and y-intercept, respectively, of the linear fit is:
and
(eq.6)
Suggesstion : Extension of a spring is proportional to the applied force and a spring will
return to its rest length when the force is removed so long as the elastic limit has not been
exceeded. Beyond the elastic limit, springs exhibit plastic behavior where additional force
causes deformation of the spring such that the original or rest length is altered.
EXPERIMENT
Part I.
1. Using a scale, read the position of the last coil of the freely hanging spiral spring and record
it on your data sheet as x0 .
2. Hang an approximate 0.100 kg mass to the spring. Remember to include the mass of the
hanger and weigh the masses on a balance. Record this mass on your data sheet.
3. Calculate and record the weight of the mass using F = mg, where m is in kg and g is 9.8
m/s2 .
4. Read xi, the position of the same last coil of the spring as in step 1.
5. Calculate and record the total displacement of the last coil of the spring, Δx, by Δx = xi –
x0.
6. Repeat steps 2-5 for masses approximately equal to 0.200 kg, 0.300 kg, and 0.400 kg.
7. Make a graph of the force, F, versus displacement (Δx). You will have five data points for
this graph: the four data points for each of the four masses, and an additional data point at
(0,0). This data point is valid because when 0 kg hung on the spring, it was displaced 0 m
from its equilibrium position.
8. Fit the data with a linear function in the form of y = mx + b. Determine the value of the
spring constant from the slope of the best-fit line.
N
1
2
3
4
5
X0
m (kg)
F=mg (N)
xi (m)
Δx (m)
k
Part II.
We will determine the spring constant by means of period formula (eq.3)
1.
Setup the apparatus shown in Fig.1
2.
Using 4 different masses, used in the experiment, find the period of oscillation for 10 s
and record them as T 1, T2, T3, and T 4 to the table.
3.
Divide the period values by 10 to find the periods for 1 s.
4.
Using eq3. find the spring constant k.
5.
Plot the graph of m (kg) versus T 2 (s2).
6.
From eq3. and the slope of the graph, find the spring constant k.
N
m (kg)
10 T(s)
T(s)
T2(s2)
1
2
3
4
5
QUESTIONS
1. Calculate % error for k value between the calculated k value from the experiment and
k real value.
2. Using k values, calculate the mean standard deviation.
3. Write up the detailed error reasons you faced while conducting the experiment.
REFERENCES
1.Physics for Scientists and Engineers with Modern Physics (Serway Jewett)
2. Principles of Physics (Allyn and Bacon)
REPORT
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T.C.
MARMARA UNIVERSITY
FACULTY OF ARTS AND SCIENCES
PHYSICS DEPARTMENT
PHYSICS LABORATORY - I
DEPARTMENT:
NAME:
SURNAME:
NUMBER:
2
T.C.MARMARA UNIVERSITY PHYSICS DEPARTMENT
PHYSICS LABORATORY –I MANUAL
EXPERIMENT NO:
EXPERIMENT NAME:
THE DATE:
GROUP NO:
NAME:
NUMBER:
DELIVERY TIME:
REPORT NOTE:
2
3
EXPERIMENT 2.ACCELERATION OF GRAVITY
Goals :Find the acceleration of gravity by basic harmonic motion.
Theory:
Mass on the Earth will be affected by the gravitational force whatever its phase is solid ,liquid
or gas. Acceleration of gravity is given by “g” and in SI unit sistem acceleration is given by
“meters per second per second” (m/s2) or “Newton per kilogram” (N/kg) .It is value will
change due to the gravitational force in different locations in Earth (between 9.78 ve
9.82 m/s2) and the standart value is 9.80665 m/s2 .
Newton’s Second Law will explain the relation between the gravitational force and the
acceleration of gravitation :
F  N   m  kg .g m / s 2 
(in SI unit system)
the “weight” of an object is the force on the object due to gravity, in SI unit it is given in
Newton. Weight is related with the mass:
Wt=m.g
g: accerelation of gravity
Lets assume that an object is felling down from a height to the ground. This object will
accelerate and the force which is applied to the object will be;
F=m.a
a: acceleration of object
The weight and the force which is applied to the object will be equal so ;
F=m.a=m.g
At the same height from the ground all objects will have same acceleration .If there is no air
resistance (Lets assume working in vacuum) all the object which are left from the same height
will reach to the ground at the same time. Object’s speed will increase as 9.8m/s in every
second.
V=g.t v: speed of the object (m/s)
t: time(s)
There are some basic experimental setups to measure the acceleration of gravity in freshman
physics laboratories and the basic pendulum is one of these techniques which is very practical
and fast.
Basic pendulum is constructed by hanging an object to a point height from ground by an
inelastic rope. Pendulum rope’s lenght is L and the stable position of the pendulum is the
point where it stands stil.
Object is just moves a little bit up from the stable position and is released from this position.
Object will oscillate between these two positions until its potential energy is zero. Then it will
stop its motion at the point where it is stable.
3
4
If the energy of this harmonic motion is worked in detail, at the first point there object is
released it will have only potential energy (P.E.=mgh) then this energy will completely
transfer to the kinetic energy at the point A (K.E.=mv2/2).Then object will rise to the point B
and here its potential energy will be maximum again. Object will continue to its harmonic
motion until its potential energy is zero.
Figure 1-Basic Pendulum
The period is the duration of one cycle in a repeating event (T),in Sı unit system its unit is
second(s). The number of the oscillations in one second is called as frequency(f).Its unit is
1
Hertz (Hz) and the relation between frequency and period : T 
f
Some important points about Basic Pendulum:
1.)As the pendulum lenght is fixed, period of the pendulum is independent of its mass, shape
or the content of the material.
2.)Period of the pendulum is independent of the amplitute of the oscillation.
3.) Period of the pendulum is directly proportional to the square root of the rope lenght.
4.) Period of the pendulum is inversely proportional to the square root of the acceleration of
gravity.
Before calculate the basic pendulum period first of all label the forces on the system and draw
the forces diagram of the object. The movement trajectory is the tangential direction of the
circle and radial direction is the direction where the object is hanged to the suspension point.
4
5
Check the figure. The gravitational force which is applied to the object “mg” is to the down.
The perpendicular and the vertical components of the force are drawn and the force
component of the radial direction is mg cos  while the tangential component is
mg sin  .Forces radial component will satisfy the required centripetal acceleration so as
to keep the object motion on the circle. As the tangential component forces object to
come back to the equilibrium position.
F  mg sin 
Here important point is that the force change with the sin  .If the θ value is so small then the
“small angle approximation” can be done and sin  can be expand in Taylor series around
θ=0.If θ is smaller than 150 tnis approximation can be done and the amount of the
displacement of the object on the circle x=L.θ. This small oscillations can be assummed to be
happen on a linear path.
Taylor Series:
f ' (a)
f 2 (a)
f 3 (a)
( x  a) 
( x  a) 2 
( x  a)3  ...
1!
2!
3!
f ( x)  f (a ) 
Taylor expantion of sin  ;
sin    
3 5 7
3!

5!

7!
 ...
write sinθ≈θ,then the force;
F  mg sin   mg ( x / L)  (mg / L) x
In small oscillations the force is directly proportional to the displacement and in the opposite
direction. This motion can be called as a basic harmonic motion and the force which creates
the motion is F  kx where k is constant. The period of the motion for small oscillations :
T  2
T  2
m
m
L
 2
 2
mg
k
g
( )
L
L
g
.
5
6
EXPERIMENTAL SETUP:
Apparatus:
1.)Inelastic rope
2.)Metal sphere (basic pendulum)
3.)stopwatch
4.)ruler
5.)note book and milimetric graph paper
6.)calculator
SETUP AND MEASUREMENTS:
1.) Tie the rope to a fixed and heigh point from the ground and
to the other end fix the metal sphere.
2.) Measure the lenght of the rope between two end points
3.) Measure your sphere diameter with vernier .
4.) R(çap)=..............................................................(cm)
r(yarıçap)=.......................................................(cm)
∆L=r+L=............................................................(cm)
5.)Move up the metal sphere and release it without first
acceleration , at this moment start the stopwatch and wait until
the sphere finish its first 5 harmonic oscillations. Then divide
this total time to 5 and find the time pass for one oscillation.
Repeat your measurement 3 times and fill the table for all
different L values.
6.)Repeat your measurement for least 7 different L values..
n Ip boyu L(m) T 1(s)
T 2(s)
T 3(s)
T ort.(s)
T2(s2)
1
2
3
4
5
6
7
8
9
10
g ort (m/s2)=
g (m/s2)
7.)Calculate the acceleration of gravity and write to the table.
8.)Plot the graph of Rope lenght (L) –period (T)
9.)Plot graph of Rope lenght (L) –period (T2) .
10.)Calculate the slope of the graphs and find the accelaration of gravity by using the graphs.
11.) Search the acceleration of gravity in our Latitude(in İstanbul) from the web and figure
out the (%) error between this value and the average value of your measurements.
12.)Use period formulation and derive the relative error formula.
13.)Calculate the Standart derivation of the acceleration of gravity.
14.)Interpret details of the work and make your comment for your measurements and
results.
6
7
Not:Teslim edilen ödev ve raporlarda sonuçlarını ve grafiklerini analiz ederek
yorumlamayan öğrencilerin raporları kabul edilmeyecektir. Yorum ve sonuç
değerlendirmesi için Fizik Lab I-föyü Hata Analizi Kısmını inceleyin.
7
REPORT
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APPENDIX A
THE INTERNATIONAL SYSTEM OF UNITS*
*University Physics, Young and Freedman, 12th ed.Addision-Wesley.
APPENDIX B
UNIT CONVERSION FACTORS*
*University Physics, Young and Freedman, 12th ed.Addision-Wesley.
APPENDIX C
FUNDAMENTAL PHYSICAL CONSTANTS and PREFIXES for POWERS of 10 *
*University Physics, Young and Freedman, 12th ed.Addision-Wesley.