Trolley

1
The motion of a trolley moving along a straight
runway is studied.
A paper tape is attached to the tail of the
trolley
The paper tape passes through a ticker tape timer
Ticker Tape Timer
The timer prints dots on the tape at regular time
intervals
Trolley
Paper tape attached to the trolley
2
As the trolley moves, the paper passes under
through the timer and dots are printed at regular
time intervals on the tape.
Ticker Tape Timer
Dot printed by the ticker tape timer on the paper
tape
3
Dots are printed on the tape with fixed time
intervals Dt.
If the trolley is moving with uniform velocity,
the dots are evenly spaced.
4
Dots are printed on the tape with fixed time
intervals Dt.
If the trolley is moving with increasing speed,
the spacing of the dots increases.
first dot
last dot
5
Dots are printed on the tape with fixed time
intervals Dt.
If the trolley is moving with decreasing speed,
the spacing of the dots decreases.
first dot
last dot
6
The frequency of the ticker tape timer fs
fs is the number of dots that the timer prints
in one second.
fs is measured in Hz (Hertz).
If fs 50 Hz , 50 dots are printed in 1 s.
If fs 100 Hz , 100 dots are printed in 1 s.
7
The time interval Dt between printing two
adjacent dots is given by
If fs is in Hz, Dt is in s.
If fs 50 Hz , Dt 0.02 s. One dot is
printed every 0.02 s.
If fs 100 Hz , Dt 0.01 s. One dot is
printed every 0.01 s.
8
The time interval between printing two adjacent
dots is also known as a tick.
For a ticker tape timer of 50 Hz,
a one-tick interval is 0.02 s ,
a two-tick interval is 0.04 s ,
a three-tick interval is 0.06 s ,
a five-tick interval is 0.1 s .
9
The time interval between printing two adjacent
dots is also known as a tick.
For a ticker tape timer of 100 Hz,
a one-tick interval is 0.01 s ,
a two-tick interval is 0.02 s ,
a three-tick interval is 0.03 s ,
a five-tick interval is 0.05 s .
10
A tape can be analyzed in one-tick intervals.
A section of the tape is selected for analysis.
first dot
last dot
11
A tape can be analyzed in one-tick intervals.
A section of the tape is selected for analysis.
The distance travelled by the object is l1 from
t 0 to t Dt
The average velocity in this time interval is
V1 can be assumed to be the instantaneous
velocity of the object at the instant t 0.5 Dt
12
A tape can be analyzed in one-tick intervals.
A section of the tape is selected for analysis.
The distance travelled by the object is l2 from
t Dt to t 2Dt
The average velocity in this time interval is
V2 can be assumed to be the instantaneous
velocity of the object at the instant t 1.5 Dt
13
A tape can be analyzed in one-tick intervals.
A section of the tape is selected for analysis.
The distance travelled by the object is l3 from
t 2Dt to t 3Dt
The average velocity in this time interval is
V3 can be assumed to be the instantaneous
velocity of the object at the instant t 2.5 Dt
14
A velocity-time graph is now available.
Note that V1 V2 V3 l1 l2 l3
15
The average acceleration of the object in the
interval t1 lt t lt t2 is given by
16
The average acceleration of the object in the
interval t2 lt t lt t3 is given by
17
If the object is moving with uniform
acceleration, the velocity-time graph is a
straight line.
V3 - V2 V2 V1
l3 - l2 l2 l1
V1 ,V2 , V3 form an arithmetic progression and
so do l1 ,l2 , l3
18
If the object is moving with uniform
acceleration, the velocity-time graph is a
straight line.
a12 a23
19
If the object is moving with uniform
acceleration, the velocity-time graph is a
straight line.
The uniform acceleration is also given by
20
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 50
Hz. The time interval for one tick is 0.02 s
first dot
last dot
21
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 50
Hz. The time interval for one tick is 0.02 s
first dot
last dot
22
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 50
Hz. The time interval for one tick is 0.02 s
first dot
last dot
23
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 50
Hz. The time interval for one tick is 0.02 s
first dot
last dot
24
Very often, a ticker tape is analyzed in
intervals longer than one tick. This is because

• the length is very short for one tick. There is
  large percentage error in measuring the length
  corresponding to one tick.
• the spacing between the dots may vary in an
  irregular pattern. The reason may be that the
  timer does not print the dots in exactly the same
  time interval. Analyzing the paper tape at
  intervals of more than one tick may help to
  averaging the errors.

25
A tape can be analyzed in five-tick intervals.
The time interval for one-tick is Dt
last dot
first dot
The instant when the first dot is printed is
assigned t 0.
The instant when the sixth dot is printed is
assigned t 5Dt.
The instant when the eleventh dot is printed is
assigned t 10Dt.
The instant when the sixteenth dot is printed is
assigned t 15Dt.
26
A tape can be analyzed in five-tick intervals.
The time interval for one-tick is Dt
last dot
first dot
The distance travelled by the object is l1 from
t 0 to t 5Dt
The average velocity in this time interval is
V1 can be assumed to be the instantaneous
velocity of the object at the instant t 2.5 Dt
27
A tape can be analyzed in five-tick intervals.
The time interval for one-tick is Dt
last dot
first dot
The distance travelled by the object is l2 from
t 5Dt to t 10Dt
The average velocity in this time interval is
V2 can be assumed to be the instantaneous
velocity of the object at the instant t 7.5 Dt
28
A tape can be analyzed in five-tick intervals.
The time interval for one-tick is Dt
last dot
first dot
The distance travelled by the object is l3 from
t 10Dt to t 15Dt
The average velocity in this time interval is
V3 can be assumed to be the instantaneous
velocity of the object at the instant t 12.5 Dt
29
last dot
first dot
A velocity-time graph is now available.
Note that V1 V2 V3 l1 l2 l3
30
last dot
first dot
The average acceleration of the object in the
interval t1 lt t lt t2 is given by
31
last dot
first dot
The average acceleration of the object in the
interval t2 lt t lt t3 is given by
32
last dot
first dot
If the object is moving with uniform
acceleration, the velocity-time graph is a
straight line.
V3 - V2 V2 V1
l3 - l2 l2 l1
V1 ,V2 , V3 form an arithmetic progression and
so do l1 ,l2 , l3
33
last dot
first dot
If the object is moving with uniform
acceleration, the velocity-time graph is a
straight line.
a12 a23
34
last dot
first dot
The uniform acceleration is also given by
35
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 100
Hz. The time interval for one tick is 0.01 s
first dot
last dot
36
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 100
Hz. The time interval for one tick is 0.01 s
first dot
last dot
37
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 100
Hz. The time interval for one tick is 0.01 s
first dot
last dot
38
Consider the section of the paper tape below,
printed by a ticker tape timer of frequency 100
Hz. The time interval for one tick is 0.01 s
first dot
last dot
39
The disadvantages of using a ticker tape timer are

• The timer prints dots by hammering on the tape.
  As a result the object experiences a frictional
  force which opposes its motion. The motion of the
  object is affected. For good results, the timer
  has to be adjusted so that the hammering force on
  the tape has to be minimized but a weak hammering
  force will print dots which are not clear enough.
• The timer can only study the motion of an object
  moving along a straight line in one direction
  only. The method fails if the object reverses its
  direction of motion.