Physics Laboratory 1
last update: 2007. 4. 2
Exp. 4. Small Velodrom
Purpose of Experiment
Velodrome
Cycling stadium of which track, paved with asphalt and special wood, is tilted. It is designed to
use the centrifugal force with maximum when rounding a corner. There are outdoor stadium and
indoor stadium.
The inertial force, making something lean toward outside, acts on bike and person that goes
around Velodrome. Like this force is centrifugal force. In the case of Velodrome, it is designed to
tilt toward the inner. So the normal force acts with maximum by inclined plane. The frictional force,
being proportional to this force, acts as the centripetal force. So it pushes the cycle to accomplish
equilibrium with the centrifugal force. Then It prevents that the cycle with rounding and going
slides toward outside..
The magnitude of centripetal force varies according to the mass of rotator, angular velocity, and
distance from rotation axis to rotation mass. In this experiment, find the equilibrium states
between the centrifugal force by rotation of weight and centripetal force by restoring force of
spring by rotating a hanging weight to equipment, affixed the spring in outer side. And check the
relation between the centripetal force and each value by measuring the rotation period, the
position of weight, and compressed length. We measure the period of a rotation using by the
Photogate detector and see the relation between the radius of an orbit and the centripetal force.
The figure shows the juwibulnoli. When we rotate the jwibul, we have to pull with the centripetal
force has same magnitude with the centrifugal force, acting on the can, in order to rotate the
juwibul with constant speed and radius. To rotate the jwibul which is suspended by long wire, is
the larger force needed or no needed than with the case of juwibul is suspended by short wire?
Or to rotate more fast, how much is force needed?
Experiment Outline
When the object is rotating, understand the concept of a velocity, an angular velocity, and a
period.
- When we define the displacement per a time the velocity, we will define the rotation angle per
a time the angular velocity. The period is defined as the time required for one complete
revolution. How do we express the relation between them?
Understand the fundamental concept for the centripetal and centrifugal force.
- Are the centripetal and centrifugal force real force? Is the relation of the centripetal force and
centrifugal force the relation of action-reaction? Or is it the equilibrium of the force?
-By changing the rotation velocity and the mass of a weight Measure the radius of Experiment by
changing the velocity of rotation and the mass of weight, and measure the radius of an orbit of
rotation and the period of rotation.
- When we change the condition of experiment, see what changes and doesn't change. Which
change is good?
- When we don't know the mass of a weight, by comparing the centripetal and the centrifugal
force can we calculate the mass?
What can we know? Conclude.
- What is the relation among mass of object, radius of orbit, and centripetal force?
- Is there the difference between the theory and the result of a real experiment?
Experimental Method
These items of equipment are provided in the laboratory. (The number of item is indicated in
parentheses.)
Measuring equipment of spring constant (1)
Weight for spring constant measurement (weight with attaching an indication needle 1, weight whose
mass is written 1)
Photogate detector - SG1122 model, 110V use (Photogate detector)(1)
Power supply - 220V use (1)
Equipment of centripetal force (1)
Weight for rotation experiment (2 pair weight whose mass is known, 1 pair mass-coded weight)
3½" Diskette (1, prepare individually)
If you need other items, check with your teaching assistant or the experiment preparation room
(19-114), or prepare them yourself.
It is no limited to specific experiment, but the following is a recommended experiment method.
Experimental Procedure
1) Before doing the rotation experiment, calculate the spring constant by seeing the displacement of a
spring in order to know the centripetal force by spring.
① Replace the experiment equipment as figure. Remove a spring which is used in the rotation experiment,
and place it perpendicular to measuring equipment of spring constant. Since the spring is the
compression spring, put a weight with attaching an indication needle on a spring.
② Before putting other weight on, read the indicating height of an indication needle of standing ruler in the
side.
③ Put the weight on the plate. Read the height where the indication needle indicates by seeing the ruler.
From this, we can see the displacement of spring.
④ By using assuming that the net force which is the sum of gravitational force F = mg (acting on a spring
by weight) and the restoring force of a spring F = - kx is 0. We can calculate the spring constant k as
equilibrium state.
2) Place the experiment equipment of centripetal force as figure.
① Use weight whose mass is known as rotator. After checking the mass of weight, open the cover and Insert
rotator in rotation rod. Then Insert spring. Fix volt in order not to fall. Hang weight which has a same mass
at the both sides wing. And fix volt enough in internal in order not to remain the space between weight and
spring where spring is not compressed.
② If the timer of Photogate detector doesn't connect, connect it to sensor. Check whether rotator, spring,
Photogate detector, and ruler, used to measure the position, are all setting in the rotation equipment.
③ After seeing weight with white line on the center by using ruler for position measurement, record how far
is the distance from center in initial position.(it’s about 2.8cm, but it can be vary according to each
equipment.)
And press weight until spring isn’t any more compressed, read the position of white line by using ruler for
position measurement and then record. (It’s about 8cm, but it can be different according to equipment.). If
you finish checking, close the cover with the slide.
④ Connect the power of the rotation equipment.
When Power supply is turned off, plug the red line and blue line correctly in order to connect the red
terminal of Voltage output to the red terminal of rotation equipment and the white terminal of output to the
blue terminal of rotation equipment. Check whether DC output switch is pressed, turn DC Voltage
control handle with the counterclockwise direction. Check if the plug is plugged in, and then turn on
the power supply.
⑤ If you insert the plug of Photogate detector into 220V power receptacle, it displays 0000 on the
light emitting diode(LED). By moving the left side switch of Photogate detector, place the
operation at the PEND mode, place the MEMORY switch at OFF. And if you place the significant figure
control switch to 0.1ms, you can check as tenths in milliseconds unit.
3) In order to check the relation between the radius of rotation and the centripetal force for the constant
mass, Experiment by changing the radius of circular orbit. Raise the voltage in order to move the white
line position of weight near about 4cm and then wait until the rotation velocity and the position
of weight become stable. If you think that they are stable, read the position of white line by using ruler for
position measurement and then record. And Press the RESET switch of Photogate detector. It measures the
taken time ( period of rotation) during one cycle. In that state, measure the period more than 5 times and
record that.( If you press RESET after reading the time every time, you can measure again). In this way,
calculate the average value and the standard deviation of measured period of a rotation. After finishing the
experiment check the position of weights again, and compare with the initial position.
② Raise the voltage in order to make weight move outside about 5mm, and then measure the period more
than 5 times. If this measurement finishes, obtain more than 5 kinds data for different radius. (If there are
many data for different radius, it can be convenient to analysis.). In here, Remember the limited position of
weight and you must measure in its length. Draw the graph about rotation radius by using calculated
average of rotation period.
4) For other weight whose mass is known, repeat the experiment as above.
5) After finishing the experiment, experiment by using weight whose mass is unknown as rotator. The code
number is written on weights. Experimental assistants can see the mass by using this code, but
don’t tell the information to students. Repeat the previous experiment for one weights whose
mass is unknown. And calculate the mass of weights by using theoretical expression, then submit
the report which written the mass and code number.
6) After finishing the experiment, put weights in a box as before the experiment. After checking amount of
weight, go out the laboratory.
Background Theory
- When the force isn't acting on an object, the shape of a motion is uniform motion which is no change of
the direction or the velocity. Since the circular motion is the motion that makes the direction of a motion of
an object change, for making the circular motion, that is the acting force, in order to change the direction of
a motion of an object continuously, is the centripetal force. And the direction is perpendicular to the
direction of a motion. And by the inertia, the inertial force acts on the opposite direction to central direction
of a circular motion. That is the centrifugal force.
If we reference the chapter 3-8 of fundamentals of physics written by Haliday & Resnick , the magnitude of a
centripetal acceleration is constant. And it is defined by
. The magnitude of a centripetal force is constant. By the Newton's second law
. If it is no acting, the object isn't in circular uniform motion. Because the centripetal acceleration and force
are the vector, their magnitude is constant. However they vary continuously so as to always point toward the
center of the circle.
For example, if we assume that an object which being in circular uniform motion is the Jwibulnoli cans which
rotating on the edge of a wire, the tension of wire wil be the centripetal force. The centripetal force which
acts on moon, almost being in circular uniform motion, can be the gravitational force. This centripetal force
is not a new kind of force. It can be a tension, a gravitational force, or any other force. In this experiment,
the restoring force of a spring acts as the centripetal force.
For the restoring force
The objects of solid states act the restoring force when we make them change by pulling or pressing.
Specially, when the degree of strain is small, this force is proportional to the magnitude of strain. This
property is called the elasticity, and that force is called the elastic force or the restoring force. We can easily
observe the strain by elasticity in spring. If the spring is either stretched or compressed a distance x from its
equilibrium configuration, the restoring force will occur. That force F is proportional to the length x, so it is
represented by
. In here, the minus sign means that the direction of restoring force is opposite to the displacement x. We
call this proportional relation the Hooke's law. And we call the proportional constant k the force constant or
the spring constant.
The relation of angular velocity, velocity, and period
when time △t goes to 0, if we define the displacement during this time as △θ, the angular velocity ω is
the ration of △θ/△t. That is, the magnitude of an angular velocity is
. If we assume that the length of cut arc by the angle θ is s,
(radian measure). Therefore,
. In here, the velocity of rotating object the circular orbit is
Therefore, by Eq(3), Eq(5), and Eq(6)
. When the period of a circular motion is T, the period is the taken time during one cycle. (The distance is
2πr, The angle is 2π)
.If we use the experiment result for the same radius and different mass,
.(In upper expression, we assume that F is equal because we think as the displacements of them are same.
Since it relates with the displacement of spring, it doesn’t relate with mass).
If we draw the graph for m*r and period T2, (F/4π2) will be the slope. It is possible when F is same. If we
calculate F from this slop, we can compare it with measured centripetal force from the displacement of
spring.
And Since we observe the period of one revolution of circular motion, we can calculate the magnitude of
force by substituting the velocity, obtained by substituting period and radius into Eq(9), to Eq(2) (In the case
of we use the weight whose mass is known). We can compare this result with calculated restoring force from
Eq(3). Are the magnitudes of two force same?
Check how the rotation velocity changes when we experiment for two weights whose radius is same and
mass is different. And think whether there is other condition with except above relation expression.
Or when we don’t know the mass of weight, if we know the radius and velocity of circular motion,
compression length of spring, and spring constant, we can infer the mass of weight under the assumption
that the above is right.
Things to Think About
Rounding a curve in a car
Someone is sitting in the center of the near seat of a car moving at a high speed along a flat road. When
the driver suddenly turns left to turn the curve, he slides across the seat toward the right then jams against
the car wall. What is going on? When rounding a curve, it is in uniform circular motion. The centripetal force
is a frictional force on the tires from the road. Its direction is toward the inner. And we can write the
magnitude of that as Eq(2). If the frictional force from seat is great enough, this people will be in uniform
circular motion with sitting in the center. However it slipped because it isn't. When we observe in ground
coordinate system, he maintains the linear motion. While the car wall moves toward him because the seat
moves. The push of the wall of a car on him provided the needed centripetal force on him, and he joined
the car's uniform circular motion.
Orbitting Earth
This time imagine someone is a passenger in the space shuttle without the effect of a gravitational force. In
this situation what is going on? The centripetal forces that make the passenger and the shuttle be in uniform
circular motion are gravitational pulls( the pull on the passenger and the pull on the shuttle). This force is
toward the center of the Earth and we can write the magnitude as Eq(2).
Both car and shuttle are in uniform circular motion, acted on by a centripetal force. But the sensations in the
two situations are quite different. In the car, jammed up against the wall, he is aware of being compressed
by the wall. In the orbiting shuttle, however, he is floating around with no sensation of any force acting on
him. Why this difference?
The difference is due to the nature of the two centripetal forces. In the car, the centripetal force is the push
on the part of someone body touching the car wall. In the shuttle, the centripetal force is Earth's
gravitational pull on every atom of the body. Thus, there is no sensation of a force on any one part of his
body.
Reference

Measurement way of velocity of an object - photogate detector

Treatment of measurement data

Analysis method based on the graph

The Amusement Park – Story for centripetal force and examples

centripetal force and centrifugal force - The Columbia
Encyclopedia
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