PASCO ME-9215B User Manual

Instruction Manual and

Includes

Teacher’s Notes

and

Typical

Experiment Results

Experiment Guide for the PASCO scientific Model ME-9215B

PHOTOGATE TIMER

012-06379B

012-06379B Photogate Timer

Table of Contents

Page

Introduction ...................................................................................................... 1

Operation ......................................................................................................... 2

Accessories for the Photogate Timer ................................................................ 4

10 Copy-Ready Experiments: .......................................................................... 4

Experiment 1: Instantaneous vs Average Velocity .................................... 5

Experiment 2: Kinematics on an Inclined Plane ........................................ 7

Experiment 3: Speed of a Projectile .......................................................... 9

Experiment 4: Newton's Second Law ......................................................11

Experiment 5: The Force of Gravity ........................................................ 13

Experiment 6: Conservation of Momentum ............................................. 15

Experiment 7: Kinetic Energy .................................................................. 17

Experiment 8: Conservation of Mechanical Energy ................................. 19

Experiment 9: Elastic-Kinetic Energy ...................................................... 21

Experiment 10: Pendulum Motion ........................................................... 23

Teachers Guide ............................................................................................... 27

Maintenance .................................................................................................. 39

Photogate Timer 012-06379B

The PASCO scientific 012-06379B Instruction Manual is copyrighted with all rights reserved. Permission is granted to non-profit educational institutions for reproduction of any part of this manual, providing the reproductions are used only in their laboratories and classrooms, and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific, is prohibited.

Limited Warranty

For a description of the product warranty, see the PASCO catalog.

Technical Support

For assistance with any PASCO product, contact PASCO at:

Address: PASCO scientific

10101 Foothills Blvd.

Roseville, CA 95678-9011

Phone: 916-786-3800 (worldwide)

800-772-8700 (U.S)

FAX: (916) 786-3292

Web www.pasco.com

email: support@pasco.com

012-06379B Photogate Timer

Introduction

The PASCO ME-9215B Photogate Timer is an accurate and versatile digital timer for the student laboratory.

The ME-9215B memory function makes it easy to time events that happen in rapid succession, such as an air track glider passing twice through the photogate, once before and then again after a collision.

The Photogate Timer uses PASCO’s narrow-beam infrared photogate (see Figure 1) to provide the timing signals. An LED in one arm of the photogate emits a narrow infrared beam. As long as the beam strikes the detector in the opposite arm of the photogate, the signal to the timer indicates that the beam is unblocked. When an object blocks the beam so it doesn’t strike the detector, the signal to the timer changes. The timer has several options for timing the photogate signals. The options include Gate, Pulse, and Pendulum modes, allowing you to measure the velocity of an object as it passes through the photogate or between two photogates, or to measure the period of a pendulum. There is also a START/STOP button that lets you use the timer as an electronic stopwatch.

An important addition to your Photogate Timer is the ME-9204B Accessory Photogate, which must be ordered separately. It plugs directly into the Photogate Timer and triggers the timer in the same manner as the built-in photogate. In Pulse Mode, the Accessory Photogate lets you measure the time it takes for an object to travel between two photogates. In Gate mode, it lets you measure the velocity of the object as it passes through the first photogate, and then again when it passes through the second photogate.

LED: Lights when

beam is blocked

Detector

Figure 1: The PASCO Photogate Head

➤➤

➤ NOTES:

➤➤

Plug in RJ12 connector

from Photogate timer

Infrared beam

LED:

Source of infrared

beam

c The Photogate Timer can be powered using

the included 7.5 V adapter. It will also run on 4 C-size, 1.5 Volt batteries. Battery installation instructions are in the Appendix.

d Ten ready-to-use experiments are included

in this manual, showing a variety of ways in which you can use your Photogate Timer. The equipment requirements vary for different experiments. For many of the experiments, you will need an air track (dynamics carts will also work). Many also require a ME-9204B Accessory Photogate in addition to the Photogate Timer. Check the equipment requirements listed at the beginning of each experiment.

Photogate Timer 012-06379B

Operation

Photogate Head

Photogate beam

Plug in RJ12 connec-

tor from timer

Clamp screw: loosen to

adjust photogate angle or

height

7.5 volt

power adapter

to 120 VAC,

60 Hz

7.5 volt

power port

Photogate port

Rear panel

Figure 2: Setting Up the Photogate Timer

Accessory

photogate port

220/240 VAC,

50 Hz

To Operate the Photogate Timer:

c Plug the RJ12 phone connector from the timer into the

RJ12 phone jack on the Photogate Head.

d Plug the 7.5 volt power adapter into the small recep-

tacle on the rear of the timer and into a standard 110 VAC, 60 Hz (or 220/240 VAC, 50 Hz) wall outlet.

e Position the Photogate Head so the object to be timed

will pass through the arms of the photogate, blocking the photogate beam. Loosen the clamp screw if you want to change the angle or height of the photogate, then tighten it securely.

f If you are using a ME-9204B Accessory Photogate,

plug the stereo phone plug of the Accessory Photogate into the large receptacle (see Figure 2) on the rear of the timer.

g Slide the mode switch to the desired timing mode:

Gate, Pulse, or Pendulum. Each of these modes is described below. Switch the MEMORY switch to OFF.

h Press the RESET button to reset the timer to zero. i As a test, block the photogate beam with your hand to

be sure that the timer starts counting when the beam is interrupted and stops at the appropriate time.

j Press the RESET button again. You are ready to

begin timing.

Timing Modes

Gate Mode: In Gate mode, timing begins when the beam is first blocked and continues until the beam is unblocked. Use this mode to measure the velocity of an object as it passes through the photogate. If an object of length L blocks the photogate for a time t, the average velocity of the object as it passed through the photogate was L/t.

Pulse Mode: In Pulse mode, the timer measures the time between successive interruptions of the photogate. Timing begins when the beam is first blocked and continues until the beam is unblocked and then blocked again. With an Accessory Photogate plugged into the Photogate Timer, the timer will measure the time it takes for an object to move between the two photogates.

Pendulum Mode: In Pendulum mode, the timer measures the period of one complete oscillation. Timing begins as the pendulum first cuts through the beam. The timer ignores the next interruption, which corresponds to the pendulum swinging back in the opposite direction. Timing stops at the beginning of the third interruption, as the pendulum completes one full oscillation.

Manual Stopwatch: Use the START/STOP button in either Gate or Pulse mode. In Gate mode the timer starts when the START/STOP button is pressed. The timer stops when the button is released. In Pulse mode, the timer acts as a normal stopwatch. It starts timing when the START/STOP button is first pressed and continues until the button is pressed a second time.

TIMING DIAGRAMS

The following diagrams show the interval, t, that is measured in each timing mode. In each diagram, a low signal corresponds to the photogate being blocked (or the START/STOP button pressed). A high signal corresponds to the photogate being unblocked (and the START/STOP button unpressed).

MODE

GATE

PULSE

PENDULUM

DIAGRAM

t t t

012-06379B Photogate Timer

TIMING SUGGESTION

Since the source and detector of the photogate have a finite width, the true length of the object may not be the same as the effective length seen by the photogate. This parallax error may be minimized by having the object pass as close to the detector side of the photogate as possible, with the line of travel perpendicular to the beam. To completely eliminate the parallax error in experimental data, determine the effective length of the object as follows:

c With the Timer in Gate mode, push the object

through the photogate, along the path it will follow in the experiment.

d When the photogate is triggered (the LED on top

of the photogate comes ON), measure the position of the object relative to an external reference point.

e Continue pushing the object through the photo-

gate. When the LED goes OFF, measure the position of the object relative to the same external reference point.

f The difference between the first and second meas-

urement is the effective length of the object. When measuring the speed of the object, divide this effective length by the time during which the object blocked the photogate.

Memory Feature

When two measurements must be made in rapid succession, such as measuring the pre- and post-collision velocities of an air track glider, use the memory function. It can be used in either the Gate or the Pulse mode.

➤➤

➤ NOTE: If additional photogate interruptions

➤➤

occur after the second time is measured, and before the MEMORY switch is flipped to READ, they too will be measured by the timer and included in the cumulative time.

Figure 3: Timing an Air Track Glider

SPECIFICATIONS

Detector rise time: 200 ns max.

Fall Time: 200 ns max.

Parallax error: For an object passing through the photo-

gate, within 1 cm of the detector, with a velocity of less than 10 m/s, the difference between the true and effective length of the object will be less than 1 millimeter.

Infrared source: Peak output at 880 nm; 10,000 hour life.

To use the memory:

c Turn the MEMORY switch to ON. d Press RESET. e Run the experiment.

When the first time (t ately displayed. The second time (t cally measured by the timer, but it will not be shown on the display.

f Record t

, then push the MEMORY switch to READ.

The display will now show the TOTAL time, t Subtract t

from the displayed time to determine t2.

) is measured, it will be immedi-

) will be automati-

+ t2.

Figure 4: Photogate Timing a Pendulum

Photogate Timer 012-06379B

Accessories for the Photogate Timer

The following accessories are available to help extend the utility of your model ME-9215B Photogate Timer. All the accessories work equally well with either model. See the current PASCO catalog for more information.

ME-9204B Accessory Photogate

The stereo phone plug of the ME-9204B Accessory Photogate plugs into the phone jack on the rear of the Photogate Timer, giving you two identical photogates operating from a single timer. With the timer in Gate mode, you can measure the velocity of an object as it passes through one photogate, then again as it passes through the second photogate. With the timer in Pulse mode, you can measure the time it takes for an object to pass between the two photogates. (Many of the experiments in this manual are most easily performed using a Photogate Timer with an Accessory Photogate.)

ME-9207B Free Fall Adapter

For easy and accurate measurements of the acceleration of gravity, the ME-9207B Free Fall Adapter is hard to beat. The Free Fall Adapter plugs directly into the phone plug on the rear of the Photogate Timer. It comes with everything you need, including two steel balls (of different size and mass), a release mechanism, and a receptor pad. The release mechanism and the receptor pad automatically trigger the timer, so you get remarkably accurate measurements of the free fall time of the steel ball.

ME-9259A Laser Switch

This highly collimated photodetector is identical to a photogate, except that you use a laser (not included) as the light source. You can now time the motion of objects that are far too big to fit through a standard photogate. Measure the period of a bowling ball pendulum or the velocity of a car. The Laser Switch operates in all three timing modes (Gate, Pulse, and Pendulum).

10 Copy-Ready Experiments

The following 10 experiments are written in worksheet form. Feel free to photocopy them for use in your lab.

NOTE: In each experiment, the first paragraph is a list of equipment

needed. Be sure to read this paragraph first, as the equipment needs vary from experiment to experiment.

This manual emphasizes the use of an air track, but the air track experiments can also be performed with dynamics carts. Many also require a ME-9204B Accessory Photogate in addition to a Photogate Timer. Collision experiments, such as experiments 6 and 7, require four times to be measured in rapid succession and are therefore most easily performed using two Photogate Timers.

012-06379B Photogate Timer

Experiment 1: Instantaneous Versus Average Velocity

EQUIPMENT NEEDED:

- Photogate Timer with Accessory Photogate

- Air Track System with one glider.

Introduction

An average velocity can be a useful value. If you know you will average 50 miles per hour on a 200 mile trip, it’s easy to determine how long the trip will take. On the other hand, the highway patrolman following you doesn’t care about your average speed over 200 miles. He wants to know how fast you’re driving at the instant his radar strikes your car, so he can determine whether or not to give you a ticket. He wants to know your instantaneous velocity. In this experiment you’ll investigate the relationship between instantaneous and average velocities, and see how a series of average velocities can be used to deduce an instantaneous velocity.

Procedure

c Set up the air track as shown in

D/2

Figure 1.1, elevating one end of the track with a 1-2 cm support.

d Choose a point x

near the center

of the track. Measure the position of x1 on the air track metric scale,

1-2 cm support

and record this value in Table 1.1. If you are using an air track with-

Figure 1.1: Setting Up the Equipment

out a scale, use a meter stick to measure the distance of x1 from the edge of the upper end of the track.

e Choose a starting point x

for the glider, near the upper end of the track. With a pencil,

carefully mark this spot on the air track so you can always start the glider from the same point.

f Place the Photogate Timer and Accessory Photogate at points equidistant from x

shown in the figure. Record the distance between the photogates as D in Table 1.1.

g Set the slide switch on the Photogate Timer to PULSE.

h Press the RESET button.

i Hold the glider steady at x

displayed after the glider has passed through both photogates.

, then release it. Record time t1, the time

j Repeat steps 6 and 7 at least four more times, recording the times as t

through t5.

D/2

, as

Card-

board

k Now repeat steps 4 through 9, decreasing D by approximately 10 centi-

meters.

l Continue decreasing D in 10 centimeter increments. At each value of D,

repeat steps 4 through 8.

Figure 1.2: Measuring Veloc-

ity in Gate Mode

Photogate Timer 012-06379B

Optional

You can continue using smaller and smaller distances for D by changing your timing technique. Tape a piece of cardboard on top of the glider, as shown in Figure 1.2. Raise the photogate so it is the cardboard, not the body of the glider, that interrupts the photogate. Use just one photogate and place it at x1. Set the timer to GATE. Now D is the length of the cardboard. Measure D by passing the glider through the photogate and noting the difference in glider position between where the LED first comes on, and where it goes off again. Then start the glider from x

as before, and make several measurements of the time it takes for the

glider to pass through the photogate. As before, record your times as t1 through t5. Continue decreasing the value of D, by using successively smaller pieces of cardboard.

Data and Calculations

For each value of D, calculate the average of t1 through t5. Record this value as t

Calculate v

avg

= D/t

. This is the average velocity of the glider in going between the two

avg

photogates.

Plot a graph of v

x1 =

versus D with D on the x-axis.

avg

Table 1.1 Data and Calculations

avg

Questions

Which of the average velocities that you measured do you think gives the closest approximation to the instantaneous velocity of the glider as it passed through point x

Can you extrapolate your collected data to determine an even closer approximation to the instantaneous velocity of the glider through point x maximum error you expect in your estimated value.

D t1 t

? From your collected data, estimate the

avg

In trying to determine an instantaneous velocity, what factors (timer accuracy, object being timed, type of motion) influence the accuracy of the measurement? Discuss how each factor influences the result.

Can you think of one or more ways to measure instantaneous velocity directly, or is an instantaneous velocity always a value that must be inferred from average velocity measurements?

012-06379B Photogate Timer

Experiment 2: Kinematics on an Inclined Plane

EQUIPMENT NEEDED:

-Photogate Timer -Meter stick

-Ball and ramp, [A ball bearing (approximately 1.8 cm diameter) and a U-channel ramp (approximately 50 cm long with an inside width of approximately 1 cm) will work well, but the exact dimensions are not important].

Introduction

In this lab you will investigate how the velocity of an object varies as it undergoes a constant acceleration. The object is a ball rolling down an inclined ramp. Instead of the usual investigation of velocity as a function of time, you will measure its velocity as a function of the distance it has travelled from its starting point.

➤➤

(

➤ Note: This experiment is just as easily per-

➤➤

formed with a glider on an inclined airtrack.)

Ball

Ramp

Photogate

Timer

Procedure

c Set up the apparatus as shown in Figure 2.1.

Fig-

d Move the ball slowly through the photogate, using the

meter stick as shown in Figure 2.2. Determine the point at which the ball first triggers the Photogate Timer—this is the point at which the LED on top of the photogate first turns ON—and mark it with a pencil on the side of the channel. Then determine the point at which the ball last triggers the timer, and mark this point also. Measure the distance between these marks and record this distance as and mark it in pencil on the side of the channel.

Δ Δ

Δd. Determine the mid-point of this interval,

Δ Δ

LED comes ON

e Set the Photogate Timer to GATE mode and press the

RESET button.

Figure 2.2: Measuring

f Move the ball to a point 5 cm along the track above your mid-point. Hold it at this

position using a ruler or block of wood. Release the ball so that it moves along the ramp and through the photogate. Record the distance travelled (from the starting point to the midpoint) and the time (t

) in Table 2.1.

g Repeat the trial 3 times so you have a total of four measured times, then take the aver-

age of your measured times. Record your results in the table.

Mark with a pencil

on side of channel.

LED goes OFF

Meter Stick

Δ Δ

Δd

Δ Δ

h Move the ball to positions 10, 15, 20…40 cm from the midpoint, and repeat steps 3-5.

Data and Calculations

c For each distance from the midpoint of the photogate, calculate the final velocity of the

ball by dividing Δd by your average time.

d Construct a velocity versus distance graph, with distance on the horizontal axis.

Photogate Timer 012-06379B

e If the graph doesn't turn out to be a straight line (as it shouldn't), manipulate the data math-

ematically and replot it until you obtain a straight line graph. For example, try plotting dis-

tance as a function of

, v2, 1/v, etc. From your graph, what is the mathematical relation-

ship between the velocity of an object on an inclined plane and the distance from its starting point that it has travelled along the plane?

Questions

Table 2.1 Data and Calculations

Distance inside photogate =

ΔΔ

Δd:

ΔΔ

Distance

Travelled

Average

Time

Final

Velocity

The standard equations for motion with a constant acceleration (starting from rest) include: x = 1/2 at

and v = at. Eliminate t from these equations to determine the relationship between x and v. Using your result and your graph, can you determine the acceleration of the ball as it rolled down the plane?

d From your answer to question 1, write the equation of motion for the accelerating ball, giving

its position as a function time. Why do you think equations of motion are most often expressed as a function of time instead of simply relating position to velocity and acceleration?

012-06379B Photogate Timer

Experiment 3: Speed of a Projectile

EQUIPMENT NEEDED:

-Photogate Timer, with Accessory Photogate

-Ball and ramp -Meter stick

-Plumb bob -Carbon paper

Introduction

Projectile motion adds a new dimension, literally, to experiments in linear acceleration. Once a projectile is in motion, its acceleration is constant and in one direction only—down. But unless the projectile is fired straight up or down, it will have an initial velocity with a component perpendicular to the direction of acceleration. This component of its velocity, since it is perpendicular to the applied force of gravity, remains unchanged. Projectile motion is therefore a superposition of two relatively simple types of motion: constant acceleration in one direction, and constant velocity in an orthogonal direction.

In this experiment you will determine the initial velocity of a projectile directly, using the Photogate Timer, and compare that with a value calculated by examining the motion of the projectile.

Procedure

c Set up the apparatus as in figure 3.1, so the

ball rolls down the ramp onto the table, then passes through the photogate, interrupting the beam.

d Tape a piece of paper to the table, under the

Accessory Photogate. Use the ramp to push the ball slowly through the Accessory Photogate, as shown in Figure 3.2. Determine the point at which the ball first triggers the Photogate Timer—this is the first point at which the LED turns ON—and mark it on the paper. Then determine the point at which the ball last triggers the timer, and mark this point also. Measure the distance between these marks and record this distance as Replace the ramp as in Figure 3.1.

e Use a plumb bob to determine the point

directly below where the ball will leave the edge of the table after rolling down the ramp. Measure the distance from the floor to the top of the table at the point where the ball leaves the table and record this value as d

f To measure the position where the ball will

strike the floor after rolling down the ramp, tape a piece of plain paper onto the floor with a piece of carbon paper on top. The impact of the ball will leave a clear mark for measuring purposes.

Δ Δ

Δd.

Δ Δ

Accessory

Ball

Ramp

Figure 3.1: Equipment Setup

Mark with pencil

Photogate

Ramp

LED comes ON LED goes OFF

Figure 3.2: Measuring

Photogate

Δ Δ

Δd

Δ Δ

Ramp

Photogate Timer 012-06379B

g Set the Photogate Timer to GATE mode. Now move the ball to a starting point somewhere

on the ramp. Mark this starting position with a pencil so you will be able to repeat the run, starting the ball each time from the same point. Hold the ball at this position using a ruler or block of wood. Press the RESET button. Release the ball so that it moves along the ramp and through the photogate. Record the time in Table 3.1.

h Repeat the trial at least four more times with the same starting point, and record your times in

the table.

i Measure the distance from the point directly below the ramp to each of the landing spots of

your ball. Record these distances in the data table.

Data and Calculations

c Take the average of your measured times and of your measured distances. Record these aver-

ages in the data table. Also record the average distance as d of the table.

Table 3.1

Data from Photogate Timer

Trial Time Distance

Δ Δ

Δd =

Δ Δ

in the space provided to the right

Vertical height, dy =

Average horizontal distance, dx =

Averages

v0 (avg)

d Divide

Δ Δ

Δd by your average time to determine v0, the velocity of the ball just before it left the

Δ Δ

Horizontal velocity, v0 =

Percentage difference =

table.

e Now determine the horizontal velocity of the sphere using the equations for projectile motion

and your measured values for d

= v0t; dy = 1/2 at2;

where a equals the acceleration caused by gravity (9.8 m/s

f Compare your two values for v

and dy:

or 980 cm/s2).

. Report the two values and the percentage difference.

Optional

If you have time, choose a value for dx and a value for dy. For what value of v0 will the ball travel the distance dx as it falls the distance dy? Adjust the height and angle of the ramp and the starting point until you produce the predicted value of v0. Now run the experiment to see if your calculated values for dx and dy are correct.

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