Instruction Manual and

Experiment Guide for the

PASCO scientific

Model ME-8930

SMART TIMER

012-06734A

09/98

Plane4

© 1998 PASCO scientific $7.50

Smart Timer 012–06734A

012–06734A Smart Timer

Section

Table of Contents

Page

Table of Contents..........................................................................................................................i

Copyright, Warranty, and Equipment Return ................................................................................ ii

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

Equipment................................................................................................................................... 3

Operating the Smart Timer .......................................................................................................... 4

Smart Timer Modes of Operation ................................................................................................ 4

Quick Cross-Reference for Suggested Activities and Smart Timer Modes.............................. 5

Time Modes....................................................................................................................... 6

Speed Measurement Modes ................................................................................................. 7

Table 1: Summary of Timing Modes................................................................................ 8–9

Acceleration Measurement Modes ..................................................................................... 10

Count Modes .................................................................................................................... 10

Test Mode ........................................................................................................................ 11

Timing Diagrams ................................................................................................................ 11

LOCK Switch: ................................................................................................................... 11

Caring for the Smart Timer ........................................................................................................ 12

Specifications ............................................................................................................................. 12

Accessory Options...................................................................................................................... 12

Troubleshooting ........................................................................................................................ 14

Experiment One: Acceleration of Gravity ................................................................................... 15

Experiment Two: Newton’s Second Law ................................................................................... 17

Experiment Three: Conservation of Momentum In Collisions .................................................... 19

Experiment Four: Conservation of Angular Momentum ............................................................. 25

Other Suggested Experiments ..................................................................................................... 31

Technical Support ......................................................................................................... back cover i

Copyright, Warranty, and Equipment Return

Please— Feel free to duplicate this manual subject to the copyright restrictions below.

Copyright Notice

The PASCO scientific 012-06734A Smart Timer manual is copyrighted and all rights reserved. However, permission is granted to non-profit educational institutions for reproduction of any part of the manual providing the reproductions are used only for their laboratories and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific, is prohibited.

Limited Warranty

PASCO scientific warrants the product to be free from defects in materials and workmanship for a period of one year from the date of shipment to the customer.

PASCO will repair or replace at its option any part of the product which is deemed to be defective in material or workmanship. The warranty does not cover damage to the product caused by abuse or improper use. Determination of whether a product failure is the result of a manufacturing defect or improper use by the customer shall be made solely by

PASCO scientific. Responsibility for the return of equipment for warranty repair belongs to the customer. Equipment must be properly packed to prevent damage and shipped postage or freight prepaid. (Damage caused by improper packing of the equipment for return shipment will not be covered by the warranty.) Shipping costs for returning the equipment after repair will be paid by PASCO scientific.

Equipment Return

Should the product have to be returned to PASCO scientific for any reason, notify PASCO scientific by letter, phone, or fax BEFORE returning the product.

Upon notification, the return authorization and shipping instructions will be promptly issued.

ä NOTE: NO EQUIPMENT WILL BE

ACCEPTED FOR RETURN WITHOUT AN

AUTHORIZATION FROM PASCO.

When returning equipment for repair, the units must be packed properly. Carriers will not accept responsibility for damage caused by improper packing. To be certain the unit will not be damaged in shipment, observe the following rules:

➀ The packing carton must be strong enough for the item shipped.

➁ Make certain there are at least two inches of packing material between any point on the apparatus and the inside walls of the carton.

➂ Make certain that the packing material cannot shift in the box or become compressed, allowing the instrument come in contact with the packing carton.

Address: PASCO scientific

10101 Foothills Blvd.

Roseville, CA 95747-7100

Phone:

FAX: email: web:

(916) 786-3800

(916) 786-3292 [email protected]

www.pasco.com

ii

012–06734A

Introduction

The PASCO ME-8930 Smart Timer is an accurate, versatile digital timer and measurement system for the student laboratory. The Smart Timer offers 0.1 ms timing resolution and an easy-to-use memory function. The Smart Timer measures several types of events detected with PASCO’s digital sensors, including speed and acceleration using standard photogates. The PASCO ME-9387 Smart Pulley, the ME-9207B Free Fall

Adapter, the ME-6810 Time-of-Flight Accessory, or the ME-9259A Laser Switch also work with the Smart Timer. The Smart Timer counts radiation emission events detected with the SN-7927 G-M Tube/Power Supply or the SE-7997 G-M Tube. The Smart Timer features two input channels and a 2-line, 16-character alphanumeric liquid crystal display that indicates the operating mode and experimental results.

Features:

The Smart Timer’s memory function makes it easy to time events that happen in rapid succession, such as a Dynamics Cart passing twice through the photogate, once before and then again after a collision. The 0.1 ms resolution is especially useful in some experiments, such as measuring velocity or acceleration during free fall. The Smart

Timer can calculate velocity before and after a collision between two carts using a single timer. With the new fence design and sensing logic, parallax errors are eliminated and timing accuracy is improved considerably over existing timing options. The Smart

Timer’s internal microcontroller also eliminates the problem of incorrect readings due to multiple passes through the same photogate by “understanding” the type of measurement selected and ignoring multiple passes.

The Smart Timer has many different options for timing and calculating values based on inputs from a variety of sensors. The graphics on the keypad aid in the selection of the appropriate timing mode. Options include One or Two Gates, Fence, and Pendulum modes. These modes allow you to measure the speed of an object as it passes through the photogate or between two photogates, or to measure the period of a pendulum. The stopwatch mode lets you use the timer as an electronic stopwatch.

The Smart Timer can measure speed and acceleration for both linear and rotational motion experiments. Alternatively, the time can be measured directly, and the speed and acceleration can then be calculated by the student. The speed and acceleration measurement features can be enabled or disabled using a switch inside the Smart Timer.

Use With Photogates:

The Smart Timer is optimized for use with PASCO’s ME-9204B Accessory Photogate

(available separately). These narrow-beam infrared photogates plug directly into the

Smart Timer and are used 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.

Smart Timer

1

Smart Timer

In One Gate Mode, a single photogate lets you measure the time, velocity, or acceleration of a fence as it passes through the photogate. Two photogates are used for collision experiments using one or two carts or for experiments where the velocity of a cart must be measured at two different points. In Two Gate Mode, two photogates are used and the time to travel between the two can be measured. This mode can also be used to measure time of flight using the ME-6810 Time-of-Flight Accessory.

Use with the Smart Pulley:

For rotary motion studies, the ME-9387 Smart Pulley (available separately) is ideal. It combines a photogate with a pulley, and when used with the Smart Timer, allows direct measurement of angular speed and acceleration. When used with a string connected to a glide or Dynamics Cart, the Smart Timer and Smart Pulley can be used to determine linear acceleration (cm/s

2

) as well.

➤ Note: The use of pulleys with different diameters and/or different number of spokes than the Smart Pulley or the ME-9450 Super Pulley will give incorrect results in the speed and acceleration calculations.

Power Options:

The Photogate Timer can be powered using the included 9VDC adapter. It will also run on 4-AA size, 1.5 volt alkaline batteries which will provide over 100 hours of operation in typical use.

Experiments:

Four copy-ready experiments and 9 additional suggested experiments are included in this manual, showing a variety of ways to use the Smart Timer. The equipment requirements vary for different experiments. For many of the experiments, you will need a Dynamics

Track and Dynamics Carts. Some experiments also require two ME-9204B Accessory

Photogates or the ME-9387 Smart Pulley. Check the equipment requirements listed at the beginning of each experiment.

012–06734A

2

Smart Timer 012–06734A

Equipment

Included:

Smart Timer

Smart Timer Picket Fences (2)

9 VDC adapter mode illustrations connector for 9VDC adapter

(side panel)) on/off switch

(side panel) touchpad keys liquid crystal display

Plane4 battery compartment

(bottom panel) input channel 2 input channel 1

9 VDC adapter

1 cm fence

5 cm fence

1 cm flag

Figure 1

Included equipment

Smart Timer Picket Fences

3

Smart Timer 012–06734A

Operating the Smart Timer

1. Plug the ¼-inch phone plug from the photogate into the

Smart Timer’s input channel 1 or 2 (see Figure 2). For all experiments using a single photogate or pulley, either of the two available jacks may be used interchangeably. For all other modes see the individual descriptions below.

2. Plug the 9 VDC power adapter into the small receptacle on the side of the timer and into a standard 110 VAC, 60 Hz wall outlet.

3. 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.

4. Slide the power switch to the ON position. The Smart

Timer will “beep” and show PASCO scientific on the display. From this point, the three-step setup of the Smart

Timer is easy:

1. Press the Select Measurement key until the desired measurement type is displayed on the top line of the display. Note that the menu rolls over to the beginning after the last type is selected.

2. Press the Select Mode key until the measurement mode is displayed after the measurement type.

You cannot begin a measurement until both the type and mode have been selected.

3. Once a complete measurement has been selected, press Start/Stop to begin. You will hear a “beep”, and a asterisk (*) will appear on the second line of the display. In most modes, the (*) indicates that the Smart Timer is now waiting for an event to occur, like a fence passing through a photogate.

5. If an event occurs, the Smart Timer beeps again, displays a result, and the (*) disappears. Pressing Start/Stop before an event occurs will remove the (*) and allow you to change the measurement type.

Smart Timer Modes of Operation

The Smart Timer has 18 modes of operation organized into five groups: Time, Speed, Acceleration, Counts, and Test. A

4

Pla ne4 input channel 2 input channel 1

Figure 2

Connecting the photogate to the Smart

Timer

➤ Note: Smart Timers shipped to certain locations are supplied with a transformer for 220/240 VAC, 50 Hz power.

ä Important Setup Note:

The Smart Timer incorporates a feature to increase the battery lifetime. The photogate turns on only when Start/Stop is pressed to start an experiment. Photogate power is turned off when the measurement is complete or the operator presses Start/

Stop. The exception is the Test mode in which photogate power is turned on as soon as the display reads Test:Gates and is not turned off until Select Measurement is pressed again. Setup for the experiment is often best accomplished in Test:Gates mode.

012–06734A Smart Timer

5

Smart Timer 012–06734A summary of the mode suggested for a given experimental activity can be found on page 5

(Quick Cross-Reference for Suggested Activities and Smart Timer Modes). Refer to the timing diagrams in Table 1 (pages 8 and 9) for a detailed look at how the Smart Timers times events on its input(s) and an explanation of how speed and acceleration calculations are performed internally.

The following are detailed descriptions of the Smart Timer’s modes of operation.

Time Modes

One Gate: In One Gate mode, timing begins when the beam is first blocked and continues until the beam is blocked again. This mode can be used to measure the speed 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.

Fence: In Fence 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. The Smart Timer can remember ten such interruptions and will allow the user to scroll through the times using either the Select

Measurement or the Select Mode keys. Pressing the Start/Stop once will allow another measurement type to be selected. Pressing it twice begins a new Fence Mode measurement. Note that once a measurement has begun with an initial block of the photogate, the Smart Timer will continue to time until ten interruptions are counted before stopping the measurement and displaying the result. Pressing Start/Stop will stop the measurement, and any recorded times will be displayed.

Two Gates: In this mode, the Smart Timer measures the time between blocking two photogates. This mode is useful for not only air tracks and Dynamics Tracks but also with the ME-6810 Time-of-Flight Accessory. In this mode, you must plug the photogate you expect to encounter first into input channel 1, and the second photogate into input channel 2.

Pendulum: 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. Press the Start/Stop key again to begin a new timing cycle.

Stopwatch: The Manual mode is actually a dual-use function. It provides a means of manually timing events (like a using a Stopwatch) by pressing the Start/Stop key. It also allows timing of events using the ME-9207B Free-Fall Adapter and the ME-9259A Laser

Switch, which function via a block/unblock sequence.

Using the Stopwatch: Enter Stopwatch mode and press the Start/Stop key. The

Smart Timer will beep and a “*” will appear on the second line of the LCD. Press the Start/Stop key again to start the timer. Press the Start/Stop key to stop timing and display the elapsed time. Press the Start/Stop key again. The old result is

6

➤ Note: The picket fence supplied with the

Smart Timer is designed to increase timing accuracy when used with photogates. The fence has three sections: the 1 cm flag, the 5 cm fence, and the 1 cm fence; one of these must be aligned with the photogate light path before the experiment can proceed.

012–06734A Smart Timer cleared and the “*” reappears. This RESET-START-STOP sequence is repeated for each new elapsed time. Whenever the “*” is not showing, the mode may be changed.

Using the Alternate Timing Function: Connect an appropriate accessory to input channel #1 or #2. Enter Stopwatch mode and press the Start/Stop key. The Smart

Timer will beep and a “*” will appear on the second line of the LCD. At this time the accessory will be powered. By blocking and unblocking the beam in the case of the Laser Switch, or by dropping the steel ball in the case of the Free Fall Adapter, the elapsed time will be measured. The Smart Timer will resolve 100 microseconds in the alternate timing mode.

➤ Notes about the Stopwatch Mode:

1. Although it is possible to use older style fences in the alternate timing function to obtain photogate beam block times, the Smart Timer will provide much higher accuracy when used with the included fences and the standard timing modes.

2. Two photogates cannot be plugged into the Smart Timer when you are using a photogate to start and stop the timer. A single photogate can be plugged into channel

#1 or #2 to start and stop the timer. But if two photogates are plugged in, when one gate is blocked, the other gate immediately is counted as an unblock, and the timer will display 0.0001 seconds, regardless of the length of time the first photogate is blocked.

3. You cannot start the timing with the Start/Stop key and end it with a photogate block or vice versa.

4. If a photogate is plugged in and blocked when you try to use the Start/Stop key as a stopwatch, the Smart Timer will be timing the photogate and waiting for the photogate to become unblocked. So when you push the Start/Stop key, the asterisk disappears and when you push the Start/Stop key again, the asterisk reappears. No time is displayed until the photogate is unblocked.

Speed Modes

One Gate: In this mode a 1 cm flag passes through the photogate. The Smart Timer measures the time and calculates the average speed in cm/s.

Collision: In this mode either one or two carts and one or two photogates can be used for a collision experiment. Once Start/Stop is pressed, the Smart Timer waits for the first collision and begins timing. The Smart Timer stops timing when two carts have passed through their respective photogates twice. Timing can always be stopped manually by pressing Start/Stop and the Smart Timer will display speed(s) based on the information it has (you will need to press Start/Stop for single cart collisions). The display will present the results in the following format:

1: xx.x,yy.y

2: xx.x,yy.y

The first number represents the input jack and the following two numbers indicate the initial speed (xx.x) and final speed (yy.y), respectively.

➤ Note:

The stopwatch function is not a precision timing mode and is therefore most useful for events that are longer than one second.

The accuracy of the stopwatch is

+/-10 milliseconds.

➤ Hint:

For easier alignment of the laser with the

Laser Switch, use the Test:Gates mode.

7

Table 1. Summary of Smart Timer Modes

Type Modes

One Gate

Key Sequence* Timing Diagram**

Fence

Two Gates

Pendulum

Stop Watch

One Gate (cm/s)

Collision (cm/s)

Pulley (rad/s)

Pulley (rev/s)

Calculation Algorithm

One Gate

Linear Pulley

Angular Pulley

Two Gates

30 seconds

60 seconds

5 minutes

Manual

One Gate

* The key sequences show n are valid in the initial or power-on  situation only.

Smart Timer

Pulley (rad/s): The Smart Timer will measure the speed of a pulley passing through a photogate in units of radians/second. One measurement will be taken each time the Start/

Stop switch is pressed. The Smart Timer cannot differentiate between clockwise and counterclockwise directions. Note that, as in many other modes, if a “*” shows in the first character position of the second line, the Smart Timer is actively waiting for an external timing event to occur. If the “*” is not showing, the Timer measurement mode may be changed. This mode has a minimum speed requirement. The photogate must be blocked twice within two seconds to obtain a valid reading, translating to a minimum speed of

0.31 rad/s.

Pulley (rev/s): Besides displaying in different units, this mode uses the display differently than in the radians/second measurement. The display provides a real-time measurement of the speed of the pulley by updating once per second. Once a speed is displayed, press the

Start/Stop key to freeze the display. The Smart Timer indicates that the measurement is frozen by displaying a “!” in the first column. Press Start/Stop to erase the “!” and start collecting new measurements. Any time the first column is blank or has a “!” displayed, the type of measurement being done can be changed by pressing the Select

Measurement or Select Mode keys. To move to a different measurement, press Start/

Stop again. Like the radians/second measurement, there is a two-second maximum time for two photogate blocks, translating to a minimum speed of 0.05 rev/s. Also note that accuracy decreases rapidly as pulley speeds increase above 600 rpm. At 600 rpm, accuracy is 1%.

Acceleration Modes

One Gate: The Smart Timer uses the time measurement between two equally spaced (5 cm) block/unblock/block sequences to calculate average acceleration. In activities using the Smart Timer Picket Fence, the Picket Fence must be positioned so that the photogate blocks only the 3-bar segment (5cm fence) of the Picket Fence. Note that the Smart Timer is able to discern between acceleration (positive number) and deceleration (negative number).

Linear Pulley: In this mode, the Smart Timer converts rotary motion of a PASCO pulley to an equivalent linear acceleration in cm/s

2

.

Angular Pulley: In this mode, the Smart Timer converts rotary motion of a PASCO pulley to an equivalent angular acceleration in rad/s

2

.

Two Gates: When two photogates are placed an arbitrary distance apart, the average acceleration between the two can be calculated. In this mode, the inputs used are not arbitrary. The first photogate to be encountered must be connected to input #1 and the second to input #2.

Count Modes:

30 Seconds: The timed 30-second count mode will count high-to-low voltage transitions on either input and display them on the second line of the liquid crystal display. After the counting period is over, the Smart Timer will beep once, remove the power to the external device, and freeze the display. Pressing Start/Stop erases the old count and begins a new

10

012–06734A

012–06734A Smart Timer timing interval. If you wish to stop the count during a timing interval, press Start/

Stop. The display will freeze the current count and the “*” will disappear from the first column. At this time you may select a new measurement or start a new timing interval. The maximum counting rate for any of the counting modes is 5,000 counts per second and the maximum count is 9,999,999.

60 Seconds: Other than timing the count interval for 60 seconds, the 60-second count mode is the same as the 30-second mode.

5 Minutes: Other than timing the count interval for 5 minutes, the 5-minute count mode is the same as the 30-second mode

Manual: Manual mode will count high-to-low voltage transitions on either input and display them on the second line of the liquid crystal display. There is no time limit for counting, however the upper limit on the number of total counts is still 9,999,999. Each count will be accompanied by a short beep. Used with a PASCO SN-7927 G-M Tube/

Power Supply, this mode is useful for group demonstrations to show the random nature of atomic disintegration and the inverse-square relationship between number of disintegration’s detected and distance from the radioactive source.

Test Mode

Gates: In the Test:Gates measurement, the external measuring accessory is powered as long as the top line of the display reads Test:Gates. This mode is useful for experiment setup or for testing accessory photogates, G-M tubes, or other Smart Timer accessories.

Pressing the Select Measurement key will exit the test mode and remove power to the external device. The display graphics depict a blocked photogate as a vertical line and an unblocked photogate as an arrow.

Timing Diagrams

The timing diagrams on pages 8 and 9 show the interval, t, that is measured in each timing mode. In each diagram, an elevated line corresponds to the photogate being blocked, and a depressed line corresponds to the photogate being unblocked. The calculation modes assume the use of a fence of fixed width (1 cm or 5 cm) or a pulley having a diameter (groove to groove) of 4.8 cm and 10 spokes, such as the Super Pulley or Smart Pulley.

LOCK Switch

The internal LOCK switch provides a way to temporarily lock out speed and acceleration modes. To access the LOCK switch, turn the power off, and remove the bottom half of the

Smart Timer case as if you were going to replace the batteries.

Look along the lower edge of the printed circuit board, and note the LOCK switch button at the edge (Figure 3). The circuit board also has the words “LOCK” and “UNLOCK” printed along the same edge. Moving the switch to the LOCK position will cause the display to read MODE UNAVAILABLE whenever speed or acceleration modes are selected.

circuit board

LOCK switch

Figure 3

Location of the LOCK switch on the circuit board.

11

Smart Timer

Caring for the Smart Timer

• Do not use a pointed object (such as a pen) to press the keypad buttons. Wrap the

Smart Timer separately when transporting it with other items. The transparent covering over the keypad can be creased by a fingernail or other sharp object.

• Clean the keypad with a soft cloth and mild detergent, avoiding hard rubbing of the transparent window.

• Do not leave the Smart Timer exposed to direct sunlight except for brief periods.

Strong ultraviolet light can damage the Smart Timer display.

• Remove the batteries prior to storage for more than one month. Batteries can leak and damage the internal circuitry, especially if the batteries are old.

• For best results, use alkaline batteries. Rechargeable NiCad batteries may be used, but the operating time between charges is much shorter than the lifetime of alkaline batteries.

012–06734A

Specifications

Resolution: The basic timing resolution of the Smart Timer is 100 microseconds in all modes except Stopwatch, which is 10 ms.

Calculated Values: Calculated values are displayed to one or two decimal places with typical accuracy being +/- 1 in the least significant digit. For extremely high speeds (such as might be generated by hand spinning a Super Pulley), accuracy is degraded for calculated parameters because of the very short timing intervals involved.

Maximum Output Power: The Smart Timer allows many different accessories to be used as inputs. The total 5-volt load (both inputs added together) that can be accommodated is 180 mA, maximum.

Accessory Options

The following PASCO accessories are available to help extend the utility of the Smart

Timer. See the current PASCO catalog for more information.

Accessory Photogate (ME-9204B): The stereo phone plug of the Accessory Photogate plugs into either of the phone jacks on the side of the Smart Timer, giving you the option of two identical photogates operating from a single timer. (Some of the experiments in this manual require the use of a Smart Timer with two Accessory Photogates.)

12

012–06734A

Time-of-Flight Accessory (ME-6810): The Timer-of-Flight Accessory facilitates the accurate measurement of the flight time of a ball launched by a PASCO projectile launcher. See page 33 (Time of Flight and Initial Velocity and Figure 9.1) for details of the setup.

Free Fall Adapter (ME-9207B): The Free Fall Adapter facilitates easy and accurate measurements of the acceleration of gravity. 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 Smart Timer, so you get more accurate measurements of the free fall time of the steel ball. See page 34

(Determining the acceleration due to gravity (g) with the Free Fall Adapter and Figure

10.1) for details of the setup.

Laser Switch (ME-9259A): This highly collimated photodetector is identical to a photogate, except that a laser (available separately) is used as the light source. With the

Laser Switch, the motion of objects that are too big to fit through a standard photogate can be measured. Thus, you can measure the period of a bowling ball pendulum or the velocity of a car, for example.

G-M Tube/Power Supply (SN-7927): The G-M Tube Power Supply is a Geiger-Muller

Probe that senses beta, gamma, and alpha radiation. See page 34 (Counting radiation

with the G-M Tube/Power Supply and Figure 11.1) for details of the setup.

Smart Timer

13

Smart Timer 012–06734A

14

012–06734A Smart Timer

Experiment One: Acceleration Due to Gravity

EQUIPMENT AND MATERIALS REQUIRED

• Smart Timer (ME-8930)

• Photogate (ME-9498A)

• Smart Timer Picket Fence

Purpose

The purpose is to determine the acceleration due to the Earth’s gravity.

Theory

The accepted value for the acceleration due to gravity on the Earth’s surface is 9.8 m/s 2 .

With the Smart Timer, the acceleration due to Earth’s gravity can be quickly determined experimentally. The acceleration may be calculated from measurements of distance and time, or it can be measured directly.

To calculate the acceleration from time measurements, the following formula must be used:

g =

∆ v t

= v

2

– v

1 t

2 where v

1

= 5cm t

1 and v

2

= 5cm t

2

– t

1

Note that

D t is not t

2

, but is 1/2 t

2

(see Figure 1.1).

The 5 cm fence should block the photogate beam.

Picket Fence must be dropped at a

90º angle.

∆

t = 1 2 t

1

+ 1 2 (t

2

– t

1

)

= 1 2

∆

t = 1 2 t

1 t

2

+ 1 2 t

2

– 1 2 t

1 t

1 t

2

V

1

V

2

Photogate

Smart Timer

Picket Fence

∆ t

Figure 1.1

Explanation of why ½t

2 lating g

is used in the formula for calcu-

Procedure

PART A—Determining the acceleration from time and distance measurements

1. Mount the photogate on a stand, or hold the Photogate steady so it is parallel to the floor, as shown in

Figure 1.2.

Figure 1.2

Experiment setup

To Smart Timer channel 1 or 2

15

Smart Timer

2. Insert the plug of the photogate into channel 1 or 2 of the Smart Timer, and set up the

Smart Timer to measure Time, Fence.

3. Hold the Smart Timer Picket Fence in a position so it will drop vertically through the photogate and so the 5 cm fence will block the photogate beam as the fence drops through the photogate.

Note: Three conditions must be met for greatest accuracy:

1. The Picket Fence must be dropped at a 90º angle to the photogate beam in such a way that it does not rotate on the way down. One method to improve the drop is to hold the edge of the Picket Fence with a clothspin or binder clip, and drop the fence by squeezing the clothespin or clip.

2. The Picket Fence must be dropped so the 5 cm marks cut the photogate beam.

3. The Picket Fence must pass close to the LED that emits the photogate beam.

4. Press and drop the fence.

5. Record t

1

and t

2

, and calculate the acceleration in meters/second 2 .

PART B—Determining the acceleration directly.

1. Repeat steps 1 – 4 in Part A with the following modification: Set the Smart Timer to measure Acceleration: One Gate. Repeat several times and calculate the average acceleration (g).

012–06734A

Questions

1. How do the two methods for determining the acceleration on a body due to Earth’s gravity compare?

2. How do the experimental measurements compare to accepted values?

16

012–06734A Smart Timer

Experiment Two: Newton’s Second Law

EQUIPMENT AND MATERIALS REQUIRED

• Smart Timer (ME-8930) • Photogate (ME-9498A)

• Dynamics Cart (ME-9430 or ME-9454) • Photogate Bracket (part no. 003-04662)

• Dynamics Cart Track (ME-9429A)

• 500 gram bar mass

• Super Pulley (ME-9450)

• Mass Hanger and Mass Set (ME-9348)

• Ohaus Triple-Beam Balance (SE-8707) or similar

• Physics String (SE-8050)

Purpose

The purpose is to verify Newton’s Second Law, F = ma.

Theory

Newton’s Second Law, F = ma, is a description of the relationship between F, the net force acting on the object of mass m, and a, the resulting acceleration of the object. For a cart of mass m

1

on a horizontal track with a string attached over a pulley to a mass m

2

(see Figure

2.1), the net force F on the entire system (cart and hanging mass) is the weight of hanging mass, F = m

2

g, assuming that friction is negligible.

According to Newton’s Second Law, this net force should be equal to ma, where m is the total mass that is being accelerated, which in this case is m

1

+ m

2

. This experiment will check to see if m

2

g is equal to (m

1

+ m

2

)a.

Procedure

1. Level the track by setting the cart on the track to see which way it rolls. Adjust the leveling screw at the end of the track to raise or lower that end until the cart placed at rest on the track will not move toward either end.

2. Use the balance to find the mass of the Dynamics Cart and record the mass in Table 2.1.

3. Attach the Super Pulley to the end of the track as shown in Figure 2.1.

4. Connect the Photogate to the Smart Timer, and adjust the Photogate so that when the pulley turns, the spokes of the pulley will block the photogate beam.

Dynamics Cart Photogate

Photogate

Bracket to Smart Timer m

1 m

2

Super

Pulley

Mass Hanger and Mass

Adjustable

End Stop

IDS Track

Figure 2.1

Experiment setup to determine the acceleration of the masses

17

Smart Timer 012–06734A

5. Place the Dynamics Cart on the track, attach a string to the hole in the end of the cart, and tie a mass hanger on the other end of the string. The string must be just long enough so the cart hits the end stop before the mass hanger reaches the floor.

6. Pull the cart back until the mass hanger reaches the pulley. Make a test run to determine how much mass is required on the mass hanger so that the cart takes about 2 seconds to complete the run. Record the hanging mass in Table 2.1.

7. Set up the Smart Timer to record Acceleration: Linear Pulley.

Note: Use masses of between 50 and 100 g, and be sure that the runs are not longer than 2 seconds.

8. Pull the cart back until the mass hanger reaches the pulley. Release the cart from rest, and activate the Smart Timer once the car has started moving. (The timing will begin when the photogate beam is first blocked.) Repeat this measurement 3 times with the same masses. Record all the values in Table 2.1. Calculate the average accelerations and record in Table 2.1.

9. Increase the mass of the cart using the bar mass and repeat the procedure.

Table 2.1 Data cart mass ( m

1 hanging

) mass ( m

2 ave. measured theoretical

) accel. 1 accel. 2 accel. 3 accel.

force a (m

1

+ m

2

)a force m

2 g

% difference*

* % difference = theoretical – measured theoretical x 100%

Analysis

1. Calculate the measured force F = (m

1

+ m

2

)a and record in Table 2.1.

2. Calculate the theoretical force F = m

2

g and record on Table 2.1.

3. Calculate the percent difference of the theoretical force vs. the measured force and record in Table 2.1.

Questions

1. Did the results of this experiment verify that F = ma? Explain.

2. Why is the mass in F = ma not just equal to the mass of the cart?

3. When calculating the force on the cart using mass times gravity, why isn’t the mass of cart included?

4. Discuss the impact on the results of assuming the frictional force to be zero.

18

012–06734A Smart Timer

Experiment Three: Conservation of Momentum In Collisions

EQUIPMENT AND MATERIALS REQUIRED

• Smart Timer (ME-8930)

• Collision Cart with mass (2) (ME-9454)

• Dynamics Cart Track (ME-9429A)

• (2) Photogate (ME-9498A)

• (2) Photogate Bracket (Part No. 003-04662)

• (2) Smart Timer Picket Fence

• balance

Purpose

The purpose of this experiment is to show that momentum is conserved in collisions.

Theory

When two carts collide with each other, the total momentum ( p = mv ) of both carts is conserved regardless of the type of collision. An elastic collision is one in which the two carts bounce off of each other with no loss of kinetic energy — accomplished in this experiment, through the use of the carts’ magnetic bumpers. A completely inelastic collision is one in which the two carts hit and stick to each other—accomplished in this experiment using the Velcro patches on one end of each cart.

Procedure

PART A: Inelastic Collisions

1. Level the track by setting a cart on the track to see which way it rolls. Adjust the leveling screw at the end of the track to raise or lower that end until a cart placed at rest on the track will not move.

2. Put a Picket Fence into the slots in the top of each cart and place the Collision Carts so the Velcro patches face each other. Position the two photogates just far enough apart so the collision can take place between the photogates. Adjust the height of the photogate so the 1 cm fence will block the photogate beams. Connect the photogates to the Smart

Timer (see Figure 3.1).

Adjustable

End Stop

1 cm flag to channel 1 of the Smart

Timer to channel 2 of the Smart

Timer

Photogate 2

1 cm flag leveling foot

Smart Timer Picket Fence Photogate 1 Smart Timer Picket Fence photogate brackets

Figure 3.1

Experiment setup for Conservation of Momentum experiments

19

Smart Timer 012–06734A

20

3. Set up the Smart Timer to measure Speed: collision (cm/s). Press to activate the

Smart Timer.

➤ Note: If the flags of both carts do not go through the photogate beams twice, the Smart Timer will not complete the timing cycle and display velocities automatically. You will need to push to stop timing. The completed timing measurements will be displayed, and the uncompleted measurements will be registered as 0. Press or to view the velocities from photogate 2. You can scroll back and forth between the displayed velocities from photogates 1 and 2 by pressing either of these keys. Press to reactivate the Speed: collision

(cm/s) mode or to change modes.

4. Perform each of the following completely inelastic collisions:

Equal Masses

a. Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest.

b. Start both carts at one end of the track. Give the first cart a slow velocity and the second cart a faster velocity so that the second cart catches the first cart.

Unequal Masses

Put two mass bars in one of the carts so that the mass of one cart (3M) is approximately three times the mass of the other cart (1M). (Weigh the carts and record the masses in

Table 3.1.)

a. Place the 1M cart at rest in the middle of the track. Give the 3M cart an initial velocity toward the cart at rest.

b. Start the carts at opposite ends of the track at approximately the same speed toward each other.

c. Place both carts at one end with the 1M in front of 3M. Give 3M a slightly greater velocity than 1M so the carts collide between the photogates.

Table 3.1 Data

M

1

M

2 v c a tr 1 b e f o r e v c a tr 2 b e f o r e

T ir a l 1

T ir a l 2

T ir a l 3

T ir a l 4

T ir a l 5 v if n a l

Note: Do each experiment at least 3 times.

012–06734A

Analysis

1. For each of the cases, calculate the momentum of each cart before the collision. Record the results in Table 3.2.

2. For each of the cases, calculate the total momentum of both carts before the collision.

Record the results in Table 3.2.

3. For each of the cases, calculate the total momentum of both carts after the collision.

Record the results in Table 3.2.

4. For each of the cases, calculate the percent difference between the total momentum of the carts before and after the collision and record in the table.

Questions

Table 3.2 Results p

1

B e f o r e p

2

B e f o r e

T ir a l 1

T ir a l 2

T ir a l 3

T ir a l 4

T ir a l 5

P

B e

T O T A L f o r e

P

A

T O T A L tf e r D i

% ff e r o f e n c e

Smart Timer

1. When two carts moving toward each other have the same mass and the same speed, they stop when they collide and stick together. What happens to each cart’s momentum? Is momentum conserved? Explain.

2. Kinetic energy is not conserved in inelastic collisions. For one of the collisions, calculate the percentage of the kinetic energy that is lost in the collision. Where does this energy go?

21

Smart Timer

Part B—Elastic Collisions

Set up the carts so the magnetic ends face each other, so the carts will repel each other when they collide. Record the data in Tables 3.3 and 3.4.

Equal Masses

a. Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest.

b. Start both carts at opposite ends of the track at approximately the same speed.

Unequal Masses

Put two mass bars in one of the carts so that the mass of one cart (3M) is approximately three times the mass of the other cart (1M). (Weigh the carts and record the masses in

Table 3.3.)

a. Place the 3M cart at rest in the middle of the track. Give the 1M cart an initial velocity toward the cart at rest.

b. Start the carts at opposite ends of the track at approximately the same speed toward each other.

c. Start cars at the same end, with the 3M car ahead of and moving slower than the

1M car.

Note: Do each experiment at least 3 times.

012–06734A

Table 3.3 Data

M

1

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Trial 6

Trial 7

M

2 v

1 v

2

FINAL v

1

FINAL v

2

22

012–06734A

Table 3.4 Results p

1

Before

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Trial 6

Trial 7 p

2

Before p

1

After p2 After

P

TOTAL

Before

Smart Timer

P

TOTAL

After

% of

Difference

Questions

1. Kinetic energy is not conserved in inelastic collisions but it is conserved in ideal elastic collisions. For one of the collisions, calculate the percentage of the kinetic energy that is lost in the collision. Was kinetic energy conserved? Explain your results.

23

Smart Timer 012–06734A

24

012–06734A

Experiment Four: Rotational Inertia of a Disk and Ring

Smart Timer

EQUIPMENT REQUIRED

• Rotating Platform (ME-8951)

• Rotational Inertia Accessory (ME-8953)

• Smart Pulley (ME-9387)

• Smart Timer (ME-8930)

• Ohaus Triple-Beam Balance (DE-8707) or similar

• paper clips (for masses < 1 g)

• calipers

Purpose

The purpose of this experiment is to find the rotational inertia of a ring and a disk experimentally and to verify that these values correspond to the calculated theoretical values.

Theory

Theoretically, the rotational inertia, I, of a ring about its center of mass is given by:

I = 1

2

M(R

1

2

+ R

2

2

) where M is the mass of the ring, R

1

is the inner radius of the ring, and R

2 is the outer radius of the ring. See Figure 4.1a.

The rotational inertia of a disk about its center of mass (Figure 4.1b) is given by:

MR

2 where M is the mass of the disk and R is the radius of the disk. The rotational inertia of a disk about its diameter (Figure 4.1c) is given by:

M R

2

R

1

R

2

Figure 4.1a

Definition of R

1

and R

2

of a ring

Figure 4.1b

Disk rotating about its center of mass

Figure 4.1c

Disk rotating about its diameter

25

Smart Timer 012–06734A

To find the rotational inertia experimentally, a known torque is applied to the object and the resulting angular acceleration is measured. Since t

= I a

,

I = where a is the angular acceleration, which is equal to a/r, and t

is the torque caused by the weight hanging from the thread that is wrapped around the base of the apparatus.

τ

= rT where r is the radius of the 3-Step Pulley about which the thread is wound and T is the tension in the thread when the apparatus is rotating.

Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 4.2)

Σ

F = mg – T = ma

Smart Pulley

T rotational disk

"A" base hanging mass mg a

Figure 4.2

Rotational Apparatus and Free-Body Diagram

Solving for the tension in the thread gives:

T = m g – a

Once the linear acceleration of the mass (m) is determined, the torque and the angular acceleration can be obtained for the calculation of the rotational inertia.

26

012–06734A

Setup

1. Place the disk directly on the center shaft as shown in Figure 4.3. The side of the disk that has the indentation for the ring should be up.

2. Place the ring on the disk, seating it in this indentation.

3. Mount the Smart Pulley to the base and connect it to channel 1 or 2 of the Smart Timer.

Procedure

Measurements for the Theoretical Rotational Inertia

1. Weigh the ring and disk to find their masses and record these masses in Table 4.1.

2. Measure the inside and outside diameters of the ring and calculate the radii R

1

and R

2

.

Record in Table 4.1.

3. Measure the diameter of the disk and calculate the radius R and record it in Table 4.1.

Table 4.1. Theoretical Rotational Inertia Data

Mass of Ring

Mass of Disk

Inner Radius of Ring

Outer Radius of Ring

Radius of Disk

Smart Timer

Accounting for Friction

1. Set up the Smart Timer to measure Speed, Pulley (rev/s).

2. Tie several paper clips onto the string that hangs over the Smart Pulley.

3. Start the disk spinning slowly.

4. Adjust the hanging mass (number of paper clips) until the speed remains constant.

5. Record this “friction mass” in Table 4.2.

6. Repeat for each setup below: ring and disk combined, disk alone, and disk vertical.

Measurements for Determining the Rotational Inertia Experimentally

1. Set up the Smart Timer to measure Acceleration, Linear Pulley (cm/s 2 ).

2. Find the acceleration of the ring and disk using a hanging mass of about 50 g. Wind the thread up and let the mass fall. Record the acceleration (press ) when the mass has fallen about 1/3 of the total fall distance (to minimize the effect of friction). Repeat at

27

Smart Timer least three times and record the average values for weight of the hanging mass and acceleration in Table 4.2.

3. Using calipers, measure the diameter of the pulley about which the thread is wrapped and calculate the radius.

4. Since in step 2, the disk is rotating as well as the ring, it is necessary to determine the acceleration and the rotational inertia of the disk by itself. This rotational inertia can be subtracted from the total, leaving only the rotational inertia of the ring. To do this, take the ring off the rotational apparatus and repeat step 2 using a hanging mass of approximately 30 g.

5. Remove the disk from the shaft and rotate it up on its side. Mount the disk vertically by inserting the shaft in one of the two “D”-shaped holes on the edge of the disk. See

Figure 4.4.

6. Repeat steps and 2 and record the data in Table 4.2.

012–06734A rotational disk

“D” hole of rotational disk rotating shaft

“A” base

Figure 4.4

Disk mounted vertically

28

Table 4.2. Experimental Rotational Inertia Data

Ring and Disk

Combined

Disk Alone

Friction Mass

Hanging Mass

Hanging Mass–

Friction Mass

Acceleration (a)

Disk Vertical

012–06734A

Calculations

Record the results of the following calculations in Table 4.3.

1. Subtract the “friction mass” from the hanging mass used to accelerate the apparatus to determine the mass, m, to be used in the equations.

2. Calculate the experimental value of the rotational inertia of the ring and disk together.

3. Calculate the experimental value of the rotational inertia of the disk alone.

4. Subtract the rotational inertia of the disk from the total rotational inertia of the ring and disk.

Note: This calculation will be the rotational inertia of the ring alone.

5. Calculate the experimental value of the rotational inertia of the disk about its diameter.

6. Calculate the theoretical value of the rotational inertia of the ring.

7. Calculate the theoretical value of the rotational inertia of the disk about its center of mass and about its diameter.

8. Use a percent difference to compare the experimental values to the theoretical values.

Smart Timer

Rotational Inertia for the

Ring and Disk Combined

Rotational Inertia for the

Disk Alone

Rotational Inertia for the

Ring

Rotational Inertia for the

Vertical Disk

Theoretical Experimental % Difference

29

Smart Timer 012–06734A

30

012–06734A

Other Suggested Experiments

Note: The following experiments are in copy-ready form in the manual for the

Dynamics Cart Accessory Track Set (manual number 012-05035)

• Acceleration Down an Incline (Experiment 8):

Use a Photogate and the Smart Timer instead of a stop watch (Figure 5.1). Adjust the height of the Photogate so the light path is intersected with the 5 cm fence of the Smart

Timer fences. Set up the Smart Timer to measure Acceleration, One Gate. Press to activate the Smart Timer, and release the cart.

Smart Timer

Smart Timer

Picket Fence

Photogate

Head

Dynamics

Cart

To Smart Timer

Photogate mounting bracket

Figure 5.1

Setup for the Acceleration Down an Incline Experiment

Smart T imer Picket Fence

• Simple Harmonic Oscillator

(Experiment 3):

Use a Photogate and the Smart

Timer instead of a stop watch, and use the ME-9471 Picket Fence

(part number 648-04704) , not the

Smart Timer Picket Fence (Figure

6.1). Set up the Smart Timer to measure Time, Pendulum. Press

to activate the Smart Timer to measure the period of oscillation.

spring

To Smart Timer

Photogate

Head

ME-9471

Picket Fence

Super Pulley

Mass and Hanger

Figure 6.1

Setup for the Simple Harmonic Oscillator Experiment

31

Smart Timer

• Oscillations on an Incline

(Experiment 4):

Use a photogate and the Smart

Timer instead of a stop watch, and use the ME-9471 Picket Fence

(part number 648-04704), not the

Smart Timer Picket Fence (Figure

7.1). Set up the Smart Timer to measure Time, Pendulum. Start the cart oscillations, and Press activate the Smart Timer to measure the period of oscillation.

Photogate

Head to Smart Timer

ME-9471

Picket Fence

Photogate

Mounting

Bracket

Figure 7.1

Setup for the Oscillations on an Incline Experiment

• Springs in Series and Parallel (Experiment 5):

Use the setup illustrated in Figure 7.1. Set up the Smart Timer to measure Time,

Pendulum. Start the cart oscillations, and activate the Smart Timer to measure the period of oscillation.

Note: The following experiment is in copy-ready form in the manual for the

Introductory Dynamics System with Computer Timing Kit (manual number

012-04894)

• Conservation of Energy (Experiment 8):

Use a Photogate and the Smart Timer instead of a computer and IDS Timer software, and set the experiment up as directed in the experiment. Set up the Smart Timer to measure

Speed, One Gate. To measure the velocity of the cart, activate the Smart Timer and before releasing the plunger of the Dynamics Cart.

012–06734A spring

32

012–06734A Smart Timer

Note: The following experiment is in copy-ready form in the manuals for the

Mini Launcher (manual number 012-05479) and the Ballistic Pendulum/

Projectile Launcher (manual number 012-05375)

• Projectile Motion Using

Photogates ( Experiment 2):

Use the Smart Timer instead of a computer and IDS Timer software, and set the experiment up as directed in the experiment.

Plug the photogates into the

Smart Timer as shown in Figure

8.1, and set up the Smart Timer to measure Time, Two Gates.

Press to activate the Smart

Timer and fire the launcher.

Calculate the initial velocity using the time required for the ball to pass through the photogates.

To Smart Timer channel 1

ME-6825 Mini Launcher

(or ME-6800 Projectile

Launcher)

To Smart Timer channel 2

Photogates

Photogate

Mounting

Bracket

Figure 8.1

Setup for the Projectile Motion Using Photogates Experiment

Note: The following experiment is in copy-ready form in the manual for the

Time of Flight Accessory (manual number 012-05088)

• Time of Flight and Initial

Velocity ( Experiment 1):

Use the Smart Timer instead of a

Photogate Timer, and set the

Smart Timer to measure Time,

Two Gates. Be sure the plug from the Photogate is connected to channel 1 of the Smart Timer and the plug from the Time of

Flight Accessory is connected to channel 2 (see Figure 9.1). Press

to activate the Smart Timer and fire the launcher.

WEAR

SAFETY

GLASSES –

WHEN IN USE.

CAUTION!

DO NOT LOOK

DOWN BARREL!

ME-6800

SHORT RANGE

PROJECTILE LAUNCHER

Projectile

Launcher

Photogate

Mounting Bracket

To Smart Timer channel 1

To Smart Timer channel 2

Time of Flight

Accessory

Figure 9.1

Setup for the Timer of Flight and Initial Velocity Experiment

33

Smart Timer

• Determining the acceleration due to gravity (g) with the

Free Fall Adapter (ME-9207B)

Insert the plug of the Free Fall

Adapter into channel 1 or 2 of the

Smart Timer (Figure 10.1) Set up the Stopwatch mode of the Smart

Timer. Press once. The Smart

Timer is now activated and will record the time the interval between the release of the ball and the contact of the ball with the receptor pad of the Free Fall

Adapter.

to Smart Timer channel 1 or 2 controller box of the

Free Fall Adapter steel ball ball release mechanism

012–06734A support rod and base receptor pad

Figure 10.1

Setup for determining the acceleration due to gravity with the

ME-9207B Free Fall Adapter.

34

• Counting radiation with the

G-M Tube/Power Supply

(SN-7927)

Insert the plug of the G-M Tube/

Power Supply into channel 1 or 2 of the Smart Timer (Figure 11.1)

Set up the Smart Timer to measure Counts, 30 seconds, 60

seconds, 5 minutes, or Manual.

Press to activate the Smart

Timer.

To Smart Timer channel 1 or 2

G-M Tube/

Power Supply

Figure 11.1

Setup for counting radiation with the SN-7927 G-M Tube/Power Supply

012–06734A Smart Timer

Technical Support

Feedback

If you have any comments about the product or manual, please let us know. If you have any suggestions on alternate experiments or find a problem in the manual, please tell us. PASCO appreciates any customer feedback. Your input helps us evaluate and improve our product.

To Reach PASCO

For technical support, call us at 1-800-772-8700

(toll-free within the U.S.) or (916) 786-3800.

fax: e-mail: web:

(916) 786-3292 [email protected]

www.pasco.com

Contacting Technical Support

Before you call the PASCO Technical Support staff, it would be helpful to prepare the following information:

➤ If your problem is with the PASCO apparatus, note:

Title and model number (usually listed on the label);

Approximate age of apparatus;

A detailed description of the problem/sequence of events (in case you can’t call PASCO right away, you won’t lose valuable data);

If possible, have the apparatus within reach when calling to facilitate description of individual parts.

➤ If your problem relates to the instruction manual, note:

Part number and revision (listed by month and year on the front cover);

Have the manual at hand to discuss your questions.

35