T.C. MARMARA UNIVERSITY

FACULTY OF ARTS AND SCIENCES PHYSICS DEPARTMENT

PHYSICS LABORATORY - I

DEPARTMENT: NAME: SURNAME: NUMBER:

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T.C.MARMARA UNIVERSITY PHYSICS DEPARTMENT

PHYSICS LABORATORY –I MANUAL

EXPERIMENT NO:

EXPERIMENT NAME:

THE DATE:

GROUP NO:

NAME:

NUMBER:

DELIVERY TIME:

REPORT NOTE:

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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

B dis

B dis

F W

F m 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

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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.

2

3 2

( ). ( )

[ ] [ ]. [ ]

V area r height h

V cm area cm height cm

6.)Use the volume and mass of the cylinder and calculate the density of it.

3

3

[ ][ / ]

[ ]

m grd gr cm

v cm

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:

6

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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7

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.

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:

0 A 1

Magnitude

Starting point

Ending

point

0 A

west east

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.

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.

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.

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.

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.

Figure I. Figure II.

Figure III. Figure IV.

EXPERIMENT:

Build an experimental set-up as shown in figure:

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 E (N) Q (N) P (N) Angle

(Degrees)

Rn (N)

Experimental

Rn (N)

Theoretical

%

difference

1

2

3

P

E

Q

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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1

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.

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,

Metal Bar

10g 20g

L(1) L(2) L(0)

2

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

TRIAL 1 2 3 4 5 6 7 8

Mass (g) m(1)

Position of Mass (m) 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%

3

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

REFERENCES

1. Experiments for Physics Labs Herbert H.Gottlies

TRIAL 1 2 3 4 5 6 7 8

Kn

ow

n T

orq

ue

Position of Mass (m)

L(1)

Distance from point of suspension

(m) X(1)

Force (N)

f(1)

Torque (Nm)

T(1)

Un

kno

wn

To

rqu

e

Mass (g)

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%

REPORT

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1

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 Notice that the

first law of motion is contained in the second law as a special case, for if , 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 and are shown Figure2. ,the tension in the string ,pulls on the body

to right ; is the downward pull of the ground on the body and is the vertical force exerted

on the body by the smooth table. The body of mass will accelerate in the – direction only, so

that

Figure 2. A free body diagram showing all forces acting on m1 and m2

2

Hence, we can write

From these equations we conclude that . We do not know so we cannot solve for .

To determine we must consider the motion of the body of mass . Because the string and body

are accelerating, we cannot conclude that equals . In fact, if were to equal , the

resultant force on 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.

.

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.

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

3

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/t2 (cm/sec2)

1

2

3

4

5

6

7

8

4

ii. Variation of Acceleration with Mass (Constant Force)

Distance moved x = ............................. cm

Accelerating force F=.............................N

REFERENCES

1. Experiment for Physics Labs, Herbert H.Gottlies

2. Fundemental of Physics, Halliday and Resnick

TRIAL Mass of

Disk,container,

weigth and added

mass (g)

TIME (t)

(sec)

Acceleration, a = 2x/t2 (cm/sec

2)

1

2

3

4

5

6

7

8

REPORT

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EXPERIMENT 5

DETERMINATION OF FRICTION COEFFICIENT

Purpose: Determine μk, the kinetic coefficient of friction and μs, 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 called the coefficient of kinetic friction. The kinetic friction

force fk is given by

(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 fk=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,

M2= μs M1 (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,

M2= μk M1 (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 for the static friction for the four trials at each value of

M1. Calculate the value of as and then calculate .

2. Calculate the mean value of for the kinetic friction fort he four trials of X at each

value of M1. For each of the values of calculate the value of as .

Calculate .

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 M2 masses.

GRAPHS

1. For horizontal plane case, graph the static friction data with as vertical axis and M1

as horizontal axis. Show the straight line obtained from the fit.

2. Repeat Step 1 for the kinetic friction coefficient.

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 X0 m (kg) F=mg (N) xi (m) Δx (m) k

1

2

3

4

5

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 T1, T2, T3, and T4 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 T2

(s2).

6. From eq3. and the slope of the graph, find the spring constant k.

N m (kg) 10 T(s) T(s) T2(s

2)

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

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:

3

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 :

2. /F N m kg g m s (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.

4

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

Hertz (Hz) and the relation between frequency and period :1

Tf

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.

5

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 cosmg while the tangential component is

sinmg .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.

sinF mg

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:

' 2 32 3( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ...1! 2! 3!

f a f a f af x f a x a x a x a

Taylor expantion of sin ;

3 5 7

sin ...3! 5! 7!

write sinθ≈θ,then the force;

sin ( / ) ( / )F mg 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 :

2 2 2

( )

m m LT

mgk g

L

2L

Tg

.

6

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) g (m/s2) 1 2 3 4 5 6 7 8 9 10 g ort (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.

7

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.

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.