Introduction
The experiment involved the use of a car, a ramp, and photogates to investigate
position, time, speed and acceleration. The purposes of the experiments were to explore
instantaneous speed, average speed, and acceleration. The initial hypotheses of the
experiment were that Group B would have the fastest acceleration because Group B had a
steeper ramp and that the speed would be constant which would make the acceleration 0
m/s². Another hypothesis was that if the distance between A and B increased, the
acceleration would decrease.
Since the focus of the experiment is on speed and acceleration, the following the
following information will discern useful background information about these topics.
Speed requires the knowledge of distance and change in time. Distance is how much
space an object has covered. However distance does not give direction. Since distance is
how far an object travels and does not give direction, it is not a vector measurement.
Distance is a scalar measurement. It only has magnitude. Also, distance is measured in
base units, which are fundamental units. The symbol for distance is D.
Speed is how fast an object is moving. Everything has a speed. Objects at rest
have a speed of zero. Fast moving objects cover more ground and slow moving objects
cover less ground. Knowing speed requires the knowledge of distance traveled and
change in time. Distance traveled can be represented by D, which is the symbol for
distance, and change in time is the time between two points in time. Change in time is
represented by the equation: ∆t = t1 – t0. The t1 represents the time at the end point and t0
represents the time at the start point. ∆t stands for change in time. The equation for speed
is:
Distance traveled
D
Speed= ———————— = ——
change in time
∆t
D
= ——
t1 – t0
Speed is a scalar measurement because it does not have direction. Also, speed is
measured in derived units because it is measured in a unit that involves both a unit of
distance and a unit of time. Derived units are combinations of base units. There are two
types of speeds. One is called instantaneous speed. Instantaneous speed is the speed of an
object at any one point or time. Average speed is when all the instantaneous speeds are
added up and divided by the change in time from the starting time to the end time.
Acceleration, another major component of the experiment, involves the
knowledge of velocity and time. Velocity is the rate at which an object changes its overall
position. The symbol for velocity is v. Knowing velocity requires the knowledge of
displacement and change in time. Displacement is overall change in the position of an
object. Change in time is the time between the start and end point. Displacement is
represented by S and change in time is represented by ∆t or t1 – t0 where t1 represents the
time at the end point and t0 represents the time at the start point. ∆t stands for change in
time. The equation for velocity is:
Displacement
S
v = —————— = ——
change in time
∆t
S
= ——
t1 – t0
Velocity is a vector measurement because it has magnitude and direction. Velocity is
measured in derived units because it is measured in a unit that includes both a unit of
displacement and a unit of time. Instantaneous velocity is the velocity of an object at any
one point or time. Average velocity is when all the instantaneous velocities are added up
and divided by the change in time.
Acceleration is a vector measurement and is usually measured in m/s². It is the
rate at which an object changes its overall velocity. The equation for acceleration is:
change in velocity
Δv
a = ———————— = ——
change in time
∆t
v1 – v0
= ———
t1 – t0
At constant acceleration the velocity of an object must always be increasing. At constant
velocity the acceleration of an object is 0 m/s². When value for a in the equation for
acceleration is negative, the rate at which an object changes its overall velocity is called
deceleration. When the value for a in the equation for acceleration is positive, the rate at
which an object changes its overall velocity is still called acceleration. When the value
for a in the equation for acceleration is 0 m/s², the object is said to be at rest.
Materials and Methods
There were various pieces of equipment used in the experiment. The materials
used in the experiment were a physics stand, a pole, a car (one that would fit on the
supplied ramp), a ramp, a timer, two photogates, a red chord, a blue chord, and a
calculator. The physics stand, the pole, and the ramp were used to set up a ramp; the
photogates, the red chord, the blue chord the electric timer were used to measure the time
it took for the car to travel down the ramp at specific points. The calculator was used to
compute the speed and acceleration of the car, and the average speed and the average
acceleration of the car.
The experiment first began with the assemblage of the ramp. First the physics
stand was inspected to see if it was on a flat surface before beginning. To check if the
surface is flat, there is a circle with concentric circles and a bubble inside the circle. If the
bubble is in the smallest circle in the middle then the surface is flat. If the bubble is not in
the smallest circle then the height of the physics stand’s legs need to be adjusted. Once
the physics stand was leveled, the screw on the bottom of the pole was removed and the
bottom of the pole was inserted in the physics stand. The screw was then put back on the
bottom of the pole by flipping the physics stand so that screwing the screw back on was
possible. The screw was screwed on tight so that the pole would not move. Then the car
was put on the ramp so that it fit perfectly on the track. Next the black wheel on the side
of the ramp was removed so that the ramp could be inserted into the pole. After the black
wheel was removed, a metal tube was revealed. The metal tube was then inserted into the
designated hole in the pole. Then the wheel was put back on metal tube. The pole was
enclosed by one side of the ramp and by the black wheel. The black wheel was used to
hold the ramp in place. Once the ramp was constructed, the photogates and the timer also
needed to be assembled. Since this particular electric timer ran on batteries, it did not
require a power chord. The blue chord was inserted in input A in the timer and connected
to one of the photogates. The red chord was put in input B in the timer and connected to
the other photogates. Both A and the B buttons were pressed so that the A and B
photogates could be used. The interval mode was selected for this experiment. The A
photogate was then clamped onto the 5 cm mark and was left there during the duration of
the experiment. The B photogate was clamped onto the appropriate points so that the
specified distance between the photogates was in accordance with the supplied tables.
Once the photogates were clamped, the car was brought up to the top of the ramp
and released down the ramp. The time for A and B was recorded. Then only the A light
was left lit so that the A time could be recorded. The B light was then left on to record the
B time could be recorded. The ramp was inserted in the tenth and sixth hole in the pole.
Once the times were recorded, speed and acceleration was calculated with the use of a
calculator and formulas. The first formula used was the speed formula. To find the speed
of the car at photogate A the following formula was used:
5 cm
speed at A= —————
time at A
The speed at A was the speed of the car when it went through photogate A. 5 cm was the
width of the wing of car and the time at A was the time it took for the wing of the car to
go through the photogate. The width of the wing was divided by this time to find the
speed of the car when it passed through photogate A. To find the speed of the car at
photogate B the following formula was used:
5 cm
speed at B = —————
time at B
The speed at B was the speed of the car when it went through photogate B. The width of
the car remained 5 cm and the time at B was the time it took for the wing of the car to go
through photogate B. The width of the wing was divided by this time to find the speed of
the car when it passed through photogate B.
After the speeds were calculated, then the accelerations of the car were computed
through the use of a calculator and another formula. This formula is:
(Speed B – Speed A)
Acceleration = —————————
Time from A to B
Although acceleration usually uses velocity instead of speed, the displacement was the
same as the distance. Therefore, using speed was acceptable in this situation although in
most normal cases speed cannot not be used when calculating acceleration. Finding
acceleration requires the difference of speed B and speed A which means subtracting the
speed at A from the speed of B. This difference is then divided by the time it took for the
car to go from photogate A to photogate B. The result is the acceleration of the car. The
average speed and the average acceleration were calculated. For Table 1, all the speeds at
A were added up and the sum was divided by 8. The same procedure was the same when
calculating the average speed at B except all the speeds at B were added up and the sum
was divided by 8. The accelerations were added up and this total was also divided by 8.
The same process was followed for computing the average speed at A, the average speed
at B, and the average acceleration.
Results
Table 1 (ramp in tenth hole)
Position
Distance
Time
Time at
Time at
Speed at A
Speed at B
Acceleration
on
from A
from A
A
B
(rounded
(rounded
(rounded to
ramp
to B
to B
to nearest
to nearest
nearest
hundredth)
hundredth)
hundredth)
64.51
111.61
355.20
seconds seconds seconds
cm/s
cm/s
cm/s²
.2183
64.60
144.51
366.06
seconds seconds seconds
cm/s
cm/s
cm/s²
.2868
63.29
170.07
372.32
cm/s
cm/s
cm/s²
1
2
3
10 cm
20 cm
30 cm
.1326
.0775
.0774
.0790
.0448
.0346
.0294
seconds seconds seconds
4
5
6
40 cm
50 cm
60 cm
.3474
.0789
63.37
193.05
373.29
seconds seconds seconds
cm/s
cm/s
cm/s²
.3949
63.45
211.86
375.82
seconds seconds seconds
cm/s
cm/s
cm/s²
.4433
62.8 cm/s
229.36
375.73
cm/s
cm/s²
247.52
377.67
cm/s
cm/s²
66.67
263.16
378.45
cm/s
cm/s
cm/s²
.0788
.0796
.0259
.0236
.0218
seconds seconds seconds
7
70 cm
.4891
.0796
.0202
62.8 cm/s
seconds seconds seconds
8
80 cm
.5192
.0750
.0190
seconds seconds seconds
When this portion of the experiment was performed, the ramp was inserted into the tenth
hole in the pole. When the distance between photogate A and photogate B was 10 cm, the
time it took for the car to travel from A to B was .1326 seconds while the time at A was
.0775 seconds and the time at B was .0448 seconds; the speed at A was 64.51 cm/s while
the speed at B was 111.61 cm/s and the acceleration was 355.20 cm/s². When the distance
between photogate A and photogate B was 20 cm, the time it took for the car to travel
from A to B was .2183 seconds while the time at A was .0774 seconds and the time at B
was .0346 seconds; the speed at A was 64.60 cm/s while the speed at B was 144.51 cm/s
and the acceleration was 366.06 cm/s². When the distance between photogate A and
photogate B was 30 cm, the time it took for the car to travel from A to B was .2868
seconds while the time at A was .0790 seconds and the time at B was .0294 seconds; the
speed at A was 63.29 cm/s while the speed at B was 170.07 cm/s and the acceleration
was 372.32 cm/s².When the distance between photogate A and photogate B was 40 cm,
the time it took for the car to travel from A to B was .3474 seconds while the time at A
was .0789 seconds and the time at B was .0259 seconds; the speed at A was 63.37 cm/s
while the speed at B was 193.05 cm/s and the acceleration was 373.29 cm/s². When the
distance between photogate A and photogate B was 50 cm, the time it took for the car to
travel from A to B was .3949 seconds while the time at A was .0788 seconds and the time
at B was .0236 seconds; the speed at A was 63.45 cm/s while the speed at B was 211.86
cm/s and the acceleration was 375.82 cm/s². When the distance between photogate A and
photogate B was 60 cm, the time it took for the car to travel from A to B was .4433
seconds while the time at A was .0796 seconds and the time at B was .0218 seconds; the
speed at A was 62.8 cm/s while the speed at B was 229.36 cm/s and the acceleration was
375.73 cm/s². When the distance between photogate A and photogate B was 70 cm, the
time it took for the car to travel from A to B was .4891 seconds while the time at A was
.0796 seconds and the time at B was .0202 seconds; the speed at A was 62.8 cm/s while
the speed at B was 247.52 cm/s and the acceleration was 377.67 cm/s². When the distance
between photogate A and photogate B was 80 cm, the time it took for the car to travel
from A to B was .5192 seconds while the time at A was .0750 seconds and the time at B
was .0190 seconds; the speed at A was 66.67 cm/s while the speed at B was 263.16 cm/s
and the acceleration was 378.45 cm/s². The car had the fastest acceleration when the
distance between A and B was 80 cm. The car had the slowest acceleration when the
distance between A and B was 10 cm.
Table 2 (ramp in sixth hole)
Position
Distance
Time
Time at
Time at
Speed at A
Speed at B
Acceleration
on
from A
from A
A
B
(rounded
(rounded to
(rounded to
ramp
to B
to B
to nearest
nearest
nearest
hundredth)
hundredth)
hundredth)
52.97
88.97 cm/s
224.72
1
10 cm
.1602
.0944
.0562
seconds seconds seconds cm/s
2
3
4
5
6
7
8
20 cm
30 cm
40 cm
50 cm
60 cm
70 cm
80 cm
.2567
.0916
114.16
232.06
seconds seconds seconds cm/s
cm/s
cm/s²
.3505
135.50
235.15
seconds seconds seconds cm/s
cm/s
cm/s²
.4238
152.91
236.22
seconds seconds seconds cm/s
cm/s
cm/s²
.4905
168.92
238.31
seconds seconds seconds cm/s
cm/s
cm/s²
.5496
183.15
238.28
seconds seconds seconds cm/s
cm/s
cm/s²
.6006
195.31
238.48
seconds seconds seconds cm/s
cm/s
cm/s²
.6535
207.41
237.77
cm/s
cm/s²
.0942
.0947
.0961
.0958
.0960
.0961
.0438
.0369
.0327
.0296
.0273
.0256
.0241
54.59
cm/s²
53.08
52.80
52.03
52.19
52.08
52.03
seconds seconds seconds cm/s
When this portion of the experiment was performed, the ramp was inserted into the sixth
hole in the pole. When the distance between photogate A and photogate B was 10 cm, the
time it took for the car to travel from A to B was .1602 seconds while the time at A was
.0944 seconds and the time at B was .0562 seconds; the speed at A was 52.97 cm/s while
the speed at B was 88.97 cm/s and the acceleration was 224.72 cm/s².When the distance
between photogate A and photogate B was 20 cm, the time it took for the car to travel
from A to B was .2567 seconds while the time at A was .0916 seconds and the time at B
was .0438 seconds; the speed at A was 54.59 cm/s while the speed at B was 114.16 cm/s
and the acceleration was 232.06 cm/s².When the distance between photogate A and
photogate B was 30 cm, the time it took for the car to travel from A to B was .3505
seconds while the time at A was .0942 seconds and the time at B was .0369 seconds; the
speed at A was 53.08 cm/s while the speed at B was 135.50 cm/s and the acceleration
was 235.15 cm/s².When the distance between photogate A and photogate B was 40 cm,
the time it took for the car to travel from A to B was .4238 seconds while the time at A
was .0947 seconds and the time at B was .0327 seconds; the speed at A was 52.80 cm/s
while the speed at B was 152.91 cm/s and the acceleration was 236.22 cm/s². When the
distance between photogate A and photogate B was 50 cm, the time it took for the car to
travel from A to B was .4905 seconds while the time at A was .0961 seconds and the time
at B was .0296 seconds; the speed at A was 52.03 cm/s while the speed at B was 168.92
cm/s and the acceleration was 238.31 cm/s². When the distance between photogate A and
photogate B was 60 cm, the time it took for the car to travel from A to B was .5496
seconds while the time at A was .0958 seconds and the time at B was .0273 seconds; the
speed at A was 52.19 cm/s while the speed at B was 183.15 cm/s and the acceleration
was 238.28 cm/s². When the distance between photogate A and photogate B was 70 cm,
the time it took for the car to travel from A to B was .6006 seconds while the time at A
was .0960 seconds and the time at B was .0256 seconds; the speed at A was 52.08 cm/s
while the speed at B was 195.31 cm/s and the acceleration was 238.48 cm/s². When the
distance between photogate A and photogate B was 10 cm, the time it took for the car to
travel from A to B was .6535 seconds while the time at A was .0961 seconds and the time
at B was .0241 seconds; the speed at A was 52.03 cm/s while the speed at B was 207.41
cm/s and the acceleration was 237.77 cm/s².
Table 3
Average Speed at A
Average Speed at B
Average Acceleration
(rounded to nearest
(rounded to nearest
(rounded to nearest
hundredth)
hundredth)
hundredth)
ramp in 10th hole
63.94 cm/s
196.39 cm/s
371.82 cm/s²
ramp in 6th hole
52.72 cm/s
155.79 cm/s
235.12 cm/s²
When the ramp was in the 10th hole the average speed at A was 63.94 cm/s while the
average speed at B was 196.39 cm/s and the average acceleration was 371.82 cm/s².
When the ramp was in the 6th hole the average speed at A was 52.72 cm/s while the
average speed at B was 155.79 cm/s and the average acceleration was 235.12 cm/s².
Discussion
Many conclusions can be drawn from the data collected from this experiment.
One of the many conclusions drawn from the results was that the Speeds at A for Table 1
were around the same number. For Table 1, the Speeds at A should be around the same
number because point A was a fixed point all throughout the experiment and the starting
point was also a fixed point. Only photogate B was moved, so the speeds at A should be
precise or close to being precise. This concept should be the same for the Speeds at A for
Table 2; however the Speeds at A for both Tables 1 and 2 do not have to be around the
same number because they are at different ramp angles. The degree of the ramp causes
the Speeds at A for Tables 1 and 2 to be different.
In the first portion of the experiment when Group B had the ramp in the tenth
hole, it was hypothesized that the cars of Group B would have the fastest acceleration
because the ramp was steeper than the ramp of Group A when the ramp was in the sixth
hole. This was proven correct when Group B switched to using the sixth hole and Group
A used the tenth hole. When comparing the data, the average acceleration when the ramp
was in the tenth hole (371.82 cm/s²) was greater than the average acceleration when the
ramp was in the sixth hole (155.79 cm/s²) verifying that when Group B had the ramp in
the tenth hole, the car would have a faster acceleration than Group A which had the ramp
in the sixth hole. However when Group A and B switched the hole in which the ramp was
inserted into, the cars of Group A had a faster acceleration than the cars of Group B. The
hypothesis was supported.
The other hypothesis was that the speed would be constant so the acceleration
would be 0 m/s² was incorrect. The speed was not constant and the acceleration was not 0
m/s². The speed and the acceleration of the car varied. Since the hypothesis was
disproved by the results, it was rejected.
It was also hypothesized that if the distance between A and B was increased, the
acceleration would decrease. However when looking at both Tables 1 and 2, it can be
seen that the exact opposite happened. In most trials, when the distance between A and B
increased, the acceleration also increased. For Table 1, the car had the fastest acceleration
of 378.45 cm/s² when the distance between A and B was 80 cm and the car had the
slowest acceleration of 355.20 cm/s² when the distance between A and B was 10 cm. For
Table 2, the car had the fastest acceleration of 238.48 cm/s² when the distance between A
and B was 70 cm and the car had the slowest acceleration of 224.72 cm/s² when the
distance between A and B was 10 cm
This hypothesis was also rejected. Although not all of the data agree with this,
however this is the general trend of the accelerations and distances. Also, sometimes
numbers, such as the acceleration when photogate B is in position 6 in Table 1 and when
photogate B is the positions of 6 and 8 in Table 2, may be due to variables like human
error and errors caused by the equipment.
Despite the slight inaccuracy of the data, a general trend could be concluded so
that the hypotheses could be supported or rejected. To clarify areas of doubt in the
results, this experiment could be performed again except without the variables in the
experiment and in a more controlled environment and with more consistent performers to
release the car from the top of the ramp.
Literature Cited
Dolphin, Warren D. 1997. Writing Lab Reports and Scientific Papers.
<http://www.mhhe.com/biosci/genbio/maderinquiry/writing.html> McGraw-Hill
College Division
Hsu, Tom. 2002. Foundations of Physical Science. Massachusetts: Cambridge
Physics Outlet