Motion

ELATE: E-Learning and Teacher Education

TEACHER’S GUIDE

PHYSICS

TOPIC: MOTION

PREREQUISITE KNOWLEDGE:

Students have ability to:

• Define velocity, acceleration, uniform velocity, and uniform acceleration.
• Describe formula relating acceleration to final velocity, initial velocity and time.

The teacher should be:

• Conversant with the set up and how a ticker timer works.

UNIT: TICKER-TIMER EXPERIMENTS

This unit deals with setting up a ticker timer and using it to measure velocity and acceleration in relation to frictional and gravitational forces.

This unit is designed for senior 2.

6. NUMBER OF LESSONS (OR HOURS):

Minimum:160 minutes(2 double lessons)

Maximum: 240 minutes (3 double lessons).

UNIT OBJECTIVES:

By the end of the unit students should be able to:

• Describe how friction compensation is done on a runway.
• Describe the experimental procedures taken to measure velocity of a trolley using the ticker timer.
• Identify ticker tapes that show uniform velocity and those that show accelerated motion.
• Calculate velocity from a ticker tape.
• Calculate acceleration from a ticker tape.
• Describe the experimental procedures taken to measure acceleration of a trolley using the ticker timer.
• Describe the experimental procedures taken to measure acceleration due to gravity using the ticker timer.

BRIEF DISCRIPTION OF UNIT:

This unit will involve the:

• Description of how friction compensation is done on a runway.
• Description of the experimental procedures taken to measure velocity of a trolley using the ticker timer.
• Identification of ticker tapes that show uniform velocity and those that show accelerated motion.
• Calculation of velocity from a ticker tape.
• Calculation of acceleration from a ticker tape.
• Description of the experimental procedures taken to measure acceleration of a trolley using the ticker timer.
• Description of the experimental procedures taken to measure acceleration due to gravity using the ticker timer.

APPARATUS

In this unit, the following equipments are needed: trolleys, ticker-timers, tapes, runaways, and rulers.

The ticker timer (after Tom Duncan “Physics”)

A tape chart for uniform velocity

A tape chart for accelerated motion

Useful Tips

• Discuss with the class working of the ticker timer (no need for technical & electrical details)
• The teacher sets up the ticker timer and trolley on a runaway.
• Discuss with the class how to make the trolley move down the runaway at a constant speed.
• Assist students to produce various tapes for constant velocity and accelerated motion.
• Instruct students to examine the various ticker tapes obtained.
• Ask students to describe the ticker tapes that show uniform velocity and those that show accelerated motion.

	Tape (take initial part of the tape to be on the left)	Describe in each case how spacing between dots varies	Describe the type of motion represented
A
B
C
D
E

DETERMINING VELOCITY FROM THE TICKER TAPE

Discuss the following with the students:

• If frequency of the ticker timer is f, what is the time interval between two successive dots? ……
• If frequency of the ticker timer is 50Hz, what is the time interval for the following cases?
• From the 1^st to the 2^nd dot. ………………..
• From the 1^st to the 5^th dot……………………
• From the 1^st to the 100^th dot…………………

The following examples show various tapes each of length obtained using a ticker timer of frequency 50 Hz. In each case find the time interval of the tape and the velocity in ms^-1.

	Tape	Time interval	Velocity
A
B
C

DETERMINING ACCELERATION FROM A TICKER TAPE

• Set up the experiment and produce a number of ticker tapes using a trolley running on an inclined runway.

• Sample ticker tape:

• Discuss how to choose the interval for the initial and final velocities on the accelerated tape.
• Discuss why the initial dots could be ignored (cut off).
• The students calculate initial and final velocities on the accelerated tapes.
• Discuss how to obtain the time taken to change from initial to final velocity.
• The students calculate acceleration on the accelerated tapes.

Students calculate acceleration for the tapes below, in the steps given. Take frequency f = 50Hz

A	The distance x = 18cm The distance y = 30cm	Time for initial interval x or final interval y, t/s
		Initial velocity, u/ms-1
		Final velocity, v/ms-1
		Time to change from average velocity u to average velocity v, T/s
		Acceleration, a
B	The distance x = 14cm The distance y = 24cm	Time, t
		Initial velocity, u
		Final velocity, v
		Time, T
		Acceleration, a

Determining acceleration due to gravity using the ticker timer.

• Discuss set up of the experiment.

• Set up the experiment and produce a number of ticker tapes.
• Use the method of finding acceleration to determine the acceleration due to gravity.

	Time for initial interval x or final interval y, t/s
	Initial velocity, u
	Final velocity, v
	Time to change from average velocity u to average velocity v, T/s
	Acceleration, a

TEACHER’S NOTES:

• Velocity is the rate of change of displacement (velocity = displacement/time)
• Acceleration is the rate of change of velocity [acceleration is change in velocity/time;

a = (v – u)/t]

• Uniform velocity is the constant rate of change of displacement.
• Uniform acceleration is the constant rate of change of velocity.
• Acceleration due to gravity is the constant rate of change of velocity of a body falling freely under gravitational force only.
• Friction on the runway makes the trolley slows down motion of the trolley on the runway. To compensate for friction on the runway the runway is inclined until the component of the weight of the trolley along the runway is just enough to overcome the frictional force so that the trolley moves down the runway at constant speed.
• The ticker timer works by making dots at regular time intervals (constant frequency) on a paper tape running through it.
• The rate at which the ticker timer makes the dots is the frequency, f, which is frequency of the a.c. voltage connected to it.
• Time between any two dots is equal to the reciprocal of frequency (T = 1/f).
• Time on a ticker tape = number of spaces on the tape divided by frequency of the ticker timer.
• (t = n/f)
• From the ticker tape: Velocity = distance occupied by the spaces divided by the time t.
• When the runway is horizontal an a trolley is made to run on it the trolley decelerates due to friction.
• In order to make a trolley run at a constant velocity on the runway, friction is compensated for by inclining the runway to make the component of the trolley's weight overcome friction.

	Tape	Describe in each case how spacing between dots varies	Describe the type of motion represented
A		Uniform spacing	Constant / uniform velocity
B		Uniform spacing	Constant / uniform velocity
C		Uniform spacing	Constant / uniform velocity
D		Increasing spacing	Increasing velocity / acceleration
E		Decreasing spacing	Decreasing velocity / deceleration.

If the frequency of the ticker timer is f, what is the time interval between any two dots? ……1/f

Find the time interval for the following cases, given that frequency of the ticker timer was 50Hz:

From the 1^st to the 2^nd dot. …………t = 1/f = 1/50 = 0.02seconds……..

From the 1^st to the 5^th dot……………t = n/f = 4/50 = 0.08seconds ………

From the 1^st to the 100^th dot…………… t = n/f = 99/50  100/50 = 2seconds ……

DETERMINING VELOCITY FROM THE TICKER TAPE

The following examples show various tapes each 8 cm obtained using a ticker timer of frequency 50 Hz. In each find the time interval of the tape and the velocity in ms^-1.

	Tape	Time interval	Velocity
A		t = n/f = 4/50 = 0.08s	Displacement s = 8cm = 0.08m. V = s/t = 0.08/0.08 = 1ms-1.
B		t = n/f = 6/50 = 0.12s	s = 8cm = 0.08m. V = s/t = 0.08/0.12 = 0.67ms-1.
C		t = n/f = 12/50 = 0.24s	s = 8cm = 0.08m. V = s/t = 0.08/0.24 = 0.33ms-1

DETERMING ACCELERATION FROM THE TAPE.

The first dots on the tape are ignored because they cannot be properly distinguished.

Initial velocity can be obtained by choosing an interval of measured length x having a number of spaces n, at the beginning of the tape. Final velocity is got from an interval of measured length y having a number of spaces n, at the end of the tape.

Initial velocity u = xf/n. Final velocity v = yf/n

Time taken to change from the initial velocity u to the final velocity v, T = N/f.

This time interval is taken from halfway the initial interval t halfway the final interval.

This is because the calculated initial and final velocities are in reality just average velocities since the body is constantly accelerating.

Acceleration, a = (v – u)/T

Students calculate acceleration for the tapes below, in the steps given.

A	The distance x = 18cm The distance y = 30cm	Time, t for initial and final intervals	t = n/f t = 4/50 = 0.08s
		Initial velocity, u	x = 0.18m u = x/t = 0.18/0.08 = 2.25ms-1.
		Final velocity, v	y = 0.30m v = y/t = 0.30/0.08 = 3.75ms-1.
		Time, T	T = N/f T= 5/50 = 0.1s
		Acceleration, a	a = (v – u)/T = (3.75 – 2.25)/0.25 a = 1.5/0.1 = 15ms-2.
B	The distance x = 14cm The distance y = 24cm	Time, t for initial and final intervals	t = n/f t = 2/50 = 0.04s
		Initial velocity, u	x = 0.14m u = x/t = 0.14/0.04 = 3.5ms-1.
		Final velocity, v	y = 0.24m v = y/t = 0.24/0.04 = 6ms-1.
		Time, T	T = N/f T = 2/50 = 0.04s
		Acceleration, a	a = (v – u)/T = (6 – 3.5)/0.04 a = 2.5/0.04 = 62.5ms-2.