PASCO ME-6569 User Manual

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Experiment Results

Instruction Manual and Experiment Guide for the PASCO scientific Model ME-6569

RMS/IDS KIT

012-06408A

6/97

10101 Foothills Blvd. • P.O. Box 619011 • Roseville, CA 95678-9011 USA

Phone (916) 786-3800 • FAX (916) 786-8905 • web: www.pasco.com

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RMS/IDS Kit 012–06408A

012–06408A RMS/IDS Kit

Table of Contents

Section Page

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

Equipment .....................................................................................................................1

Assembly .................................................................................................................. 23

Suggested Experiments

Experiment 1: Correlation of velocity and acceleration vectors for a cart

undergoing an elastic collision ....................................................56

Experiment 2: Comparison of momentum and impulse of an inelastic collision .... 79

Experiment 3: Conservation of momentum vs. loss of kinetic energy in an

inelastic collision ................................................................... 1115

Experiment 4: Conservation of momentum kinetic energy in an elastic collision

. 1621

Teachers Notes............................................................ 2329

Technical Support ........................................................................................ Back Cover

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

The PASCO scientific 012-06408A manual is copyrighted and all rights reserved. However, permission is granted to non-profit educational institutions for reproduction of any part of the RMS/ IDS Kit 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.

Credits

Author: Sunny Bishop

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.

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. P.O. Box 619011 Roseville, CA 95678-9011

Phone: (916) 786-3800

FAX: (916) 786-3292

email: techsupp@pasco.com

web: www.pasco.com

012–06408A RMS/IDS Kit

Introduction

The PASCO CI-6569 RMS/IDS Kit allows the PASCO CI-6538 Rotary Motion Sensor (RMS) to function as a Smart Pulley for measuring the absolute location of a PASCO Dynamics Carts (ME-9430 or ME-9454) running on PASCO Introductory Dynamics System Tracks (ME-9429A or ME-9452).

The IDS track pulley bracket and the cartstring bracket included in the RMS/IDS Kit, together with the required IDS Mount Accessory (CI-6692), allow the connection of the Dynamics Cart to the large pulley of the RMS with a sturdy thread. The thread is anchored on the Dynamics Cart and passed over the large pulley on the RMS, allowing bidirectional linear motion of the Dynamics Cart to be logged into

Science Workshop

700). Science Workshop can then display the motion data in terms of absolute location, velocity, and acceleration.

through a PASCO computer interface (500 or

Two sets of Dynamics Carts, Rotary Motion Sensors, and connecting brackets can be installed on a single Dynamics Track to allow simultaneous measurement of linear motion of two carts (700 interface only).

Equipment

Included:

 IDS track pulley bracket  cartstring bracket  spool of sturdy thread

Additional Required:

 Rotary Motion Sensor (CI-6538)  IDS Mount Accessory (CI-6692)  Dynamics Cart (ME-9430 or ME-9454)  Dynamics Track (ME-9429A or ME-9452)  PASCO computer interface (500 or 700)  Science Workshop version 2.2 or higher  computer

IDS track pulley bracket

cart—string bracket

thread

RMS/IDS Kit 012–06408A

Setup

Equipment

1. Mount the Rotary Motion Sensor (RMS) on the IDS track with the

IDS Mount Accessory so the RMS can be used like a Smart Pulley (see IDS Mount Instruction Sheet and Figure 3).

2. Mount the IDS track pulley bracket on the same side of the track

at the other end (Figure 1).

3. Mount the cartstring bracket on the cart (Figure 2).

IDS track pulley bracket

Figure 1

Mounting the IDS track pulley bracket on the IDS track

IDS track

4.. Cut a length of thread about 2.5 m long (for the 1.2 m track).

cart—string bracket

IDS cart

IDS track

Figure 2

Attaching the cartstring bracket to the Dynamics Cart

Anchor one end of the thread under the screw of the cartstring bracket on the cart. Thread the string over and under the large pulley of the RMS (Figure 3).

5. Pull the thread under and over the top of the small pulley on the

bracket.

6. Pull the thread taunt and secure the end under the thumbscrew of

the cartstring bracket.

7. Adjust the height of the large and small pulleys so the top half of

the string is horizontal and so the bottom half moves without being obstructed by the track or brackets (Figure 3).

012–06408A RMS/IDS Kit

IDS track pulley bracket

Top thread is parallel to the table.

cart—string bracket

IDS Mount Accessory

RMS

to computer interface

Thread is free of obstruction.

large pulley of 3-step pulley

Figure 3

Completed assembly

8. If necessary, adjust the tension of the string by moving the IDS

track pulley bracket along the track.

Science Workshop

1. Insert the digital plugs of the the RMS into digital ports 1 & 2 or

3 & 4 of the computer interface box.

2. Open Science Workshop and set up the RMS in the setup window

(refer to the RMS manual (012-06053A for details).

3. Double-click on the RMS icon (

Pulley (Groove) OK

in the Linear Calibration dialog box. Click

) and choose

Large

RMS/IDS Kit 012–06408A

➤

Note: The manual has been written with the assumption that

the user has a basic familiarity with Science Workshop and has access to the Users Guide for Science Workshop. Users can gain basic skills with Science Workshop by viewing the training video and by doing the tutorial within Science Workshop. Another useful resource is the Quick Reference Card for Science Workshop.

012–06408A RMS/IDS Kit

Experiment 1: Correlation of velocity and acceleration vectors for a cart undergoing an elastic collision

Purpose

The purpose of the experiment is to develop a correlated, graphic display of the position, velocity, and acceleration of a cart during an elastic collision.

Materials and Equipment Required

• Rotary Motion Sensor (RMS) (CI-6538) • Dynamics Track (ME-9435A or ME-9458)

• RMS/IDS Kit • Adjustable End Stop (ME-9448A)

• IDS Mount Accessory (CI-6692) • PASCO computer interface (500 or 700)

• Dynamics Cart (ME-9430 or ME-9454) • Science Workshop version 2.2 or higher

• pages 2 and 3 of this manual • computer

Procedure

Set Up the Equipment

1. Mount on the IDS track the RMS, using the IDS Mount Accessory, and the IDS track

2. Attach the Adjustable End Stop to the end of the track (Figure 1.1). Move the IDS track

IDS Mount Accessory

RMS

to computer interface

pulley bracket, as directed in the Equipment Setup section (pages 2 & 3) of this manual.

pulley bracket, if necessary.

IDS track pulley bracket

thread

cart—string bracket

Adjustable End Stop

IDS track

IDS cart

large pulley of the 3-step pulley

Figure 1.1

Equipment setup for experiment 1

RMS/IDS Kit 012–06408A

3. Place the cart on the track with the magnets facing the Adjustable End Stop, and attach the

cartstring bracket to the cart.

4. Thread the string as directed in the Equipment Setup section of this manual. Check to be

sure the string moves freely without obstruction, is horizontal across the top of the pulleys and cartstring bracket, and is taunt enough so it does not slip on the pulleys.

Set Up Science Workshop

1. Set up the RMS in Science Workshop as directed in the setup section on page 3 of this

manual.

2. If you are not in the setup window for the RMS, double-click on the RMS icon (

3. Set the Division/Rotation to

4. Double-click on the Sampling Options button and set the sampling rate to 50 Hz. Click

5. Drag and drop a Graph display icon to the RMS icon and choose

Velocity (linVel)

pop-up menu.



Collect the data

1. Position the cart at the end of the track with the RMS.

2. Start recording data.

3. Give the cart a gentle push towards the end stop. (Use the amount of force needed for

smooth movement of the cart.)

4. After the cart rebounds from the end stop, stop recording.

, and

1440

. Click OK.

Acceleration (linAcc)

Position (linPos)

from the Choose Calculations to Display

Questions

Analyze the data

1. Sketch the three graphs and label the axis (or print out the graph).

2. Label the graphs for the following: 1) cart moving towards the end stop; 2) the elastic

collision of the cart; 3) cart moving away from the end stop.

1. Just before the collision, what is the velocity and acceleration of the cart?

2. Describe what happens to the carts velocity during the collision. What is happening to the

carts position when it has negative velocity?

3. Describe what happens to the carts acceleration during the collision. What is happening to

the carts position when the acceleration is changing from zero to negative? What is happening to the carts position when the acceleration is changing from negative to zero?

012–06408A RMS/IDS Kit

Experiment 2: Comparison of momentum and impulse of an inelastic collision

Purpose

The purpose of the experiment is to quantitatively compare magnitude of the momentum of a moving cart with the impulse of its inelastic collision with a stationary object.

Materials and Equipment Required

• Rotary Motion Sensor (RMS) (CI-6538) • ±50 Force Sensor (CI-6537)

• RMS/IDS Kit (CI-6569) • Force Sensor Bracket & Collision Bumpers (CI-6545)

• IDS Mount Accessory (CI-6692) • PASCO computer interface (500 or 700)

• Dynamics Cart (ME-9430 or ME-9454) • Science Workshop version 2.2 or higher

• Dynamics Track (ME-9435A or ME-9458) • computer

• pages 2 & 3 of this manual • block of wood (or similar) about 10 cm in height

Theory

The momentum of a system is determined by the relationship:

P = mv

where P = momentum, m = mass, and v = velocity.

The impulse, or change in momentum, of a collision is determined by the relationship:

P= Fd

∆

The area under the curve of a graph of the force versus time, as determined by integrating the curve, equals the total change in momentum.

In an inelastic collision, where the final velocity is zero, the following relationship exists:

mv = Fdt

Procedure

Set Up the Equipment

1. Mount the RMS on the IDS track using the IDS Mount Accessory, and mount the IDS track

pulley bracket on the IDS track (refer to the equipment setup section, pages 2 & 3, of this manual).

RMS/IDS Kit 012–06408A

IDS Mount Accessory

IDS track pulley bracket

RMS

cart—string bracket

IDS cart

Force Sensor

Force Sensor Bracket

block

IDS track

Figure 2.1

Equipment setup for experiment 2

2. Attach the Force Sensor to the end of the track using the Force Sensor Bracket (Figure 2.1).

Move the IDS track pulley bracket, if necessary.

3. Unscrew the hook from the Force Sensor and replace it with the collision cup that is stored

on the Force Sensor Bracket.

4. Make a cone of clay that is about 1 cm in base diameter and 3 cm in height, and press it onto

the collision cup.

5. Place the cart on the track so the magnets face the Force Sensor.

thread

collision cup

cone of clay

6. Attach the cartstring bracket and connect the string as shown in the equipment setup

section of this manual (page 2). Check to be sure the string moves freely without obstruction, is horizontal across the top of the pulleys and cartstring bracket, and is taunt enough so it does not slip on the pulleys.

Set Up Science Workshop

1. Set up the RMS in Science Workshop as directed in the setup section on page 3 of this

manual.

2. If you are not in the setup window for the RMS, double-click on the RMS icon (

3. Set the Division/Rotation to

4. Double-click on the Sampling Options button and set the sampling rate to 50 Hz. Click OK.

5. Drag and drop a Graph display icon to the RMS icon and select Velocity (LinVel) from the

Choose Calculations to Display pop-up menu.

6. Set up the Force Sensor in Science Workshop (refer to the manual for the Force Sensor for

details.

1440

. Click OK.

012–06408A RMS/IDS Kit

7. Drag and drop a Graph display icon to the Force Sensor icon.

Collect the data

1. Hold the cart in place close to the RMS and elevate the track using the wooden block.

2. Begin recording data.

3. Release the cart, allowing gravity to be the sole force of acceleration.

Note: If the impact is not completely inelastic (the cart bumps back

from the clay stopper), repeat using a smaller angle of elevation.

4. Stop recording.

Analyze the Data

1. Use the statistics function of Science Workshop to determine the maximum velocity of the

cart.

2. Determine the mass of the cart

3. Calculate the momentum of the cart.

4. Use the statistics function to integrate the area under the curve.

5. Select the portion of the curve that represents the impact and record the integrated value.

Note: Select by clicking and dragging a box around the desired area.

6. Compare the magnitudes of the momentum of the cart and the impulse of the collision.

Question

1. Does your experimental data show that the momentum of the cart equals the impulse of the

collision? (Does

mv = Fdt

RMS/IDS Kit 012–06408A

Notes:

012–06408A RMS/IDS Kit

Experiment 3: Conservation of momentum vs. loss of kinetic energy in an inelastic collision

Purpose

The purpose of the experiment is to quantitatively and graphically demonstrate the conservation of momentum and the simultaneous loss of kinetic energy as a result of the collision of a cart with a cart at rest.

Materials and Equipment Required

• (2) Rotary Motion Sensor (RMS) (CI-6538) • Dynamics Track (ME-9435A or ME-9458)

• (2) RMS/IDS Kit (CI-6569) • PASCO computer interface (700)

• (2) IDS Mount Accessory (CI-6692) • Science Workshop version 2.2 or higher

• (2) Plunger or Collision Cart (ME-9430 or ME-9454) • computer

• pages 2 & 3 of this manual

Theory

Before the collision of the two carts, the situation can be represented as follows:

→

where m second cart, and v

= the mass of the first cart, v1 = the velocity of the first cart, m2 = the mass of the

= the velocity of the second cart, which is 0.

After the collision, the carts stick together and move as one mass, as represented below:

The momentum of the system at any point in time is expressed as follows:

P=m1v

where m

are the mass and velocity of the first cart and m2v2 are the mass and velocity of the

1v1

second. Since the momentum is conserved after the collision, the following relationship exists:

m1v

m2v2=m

v2 (= 0)

after

→m

m2v

aftervafter

where m

= the mass of the two carts and v

after

= the velocity of the two carts stuck together.

after

The total kinetic energy (KE) of the system at any moment in time is represented by:

KE =

m1v1+

1 2

m2v

RMS/IDS Kit 012–06408A

In contrast to the case with momentum, KE is not conserved after the collision:

Procedure

RMS

1 2

m1v

m2v

≠

aftervafter

Part A  Inelastic collision of equal masses

Set Up the Equipment

1. Mount the two Rotary Motion Sensors on the IDS track using the IDS Mount Accessories,

and mount the two brackets with small pulley on the IDS track (refer to the page 2 of this manual and Figure 3.1).

magnetic ends (Collision Carts)

Velcro tabs (Plunger Carts)

thread

IDS Mount Accessory

IDS track

cart 1 cart 2

Figure 3.1

Equipment setup for experiment 3

2. Attach the cartstring brackets to the carts, measure the mass of the carts, and record in

Table 3.1.

3. Place the carts on the track with the Velcro tabs (Plunger Cart) or nonmagnetic ends (Collision

Cart) facing each other.

4. Thread the string as shown in Figure 3.1 and pages 2 & 3 of the manual. Make the necessary

adjustments to the setup to insure that the string is unobstructed and moves freely.

5. Adjust the brackets with small pulley as necessary to insure that the thread is taunt and not

slipping on the pulleys.

Set Up Science Workshop

1. Insert the digital plugs for the RMS connected to cart 1 into digital channels 1 & 2, and the

digital plugs of the RMS connected to cart 2 into digital channels 3 & 4 of the interface box.

cart—string brackets

IDS track pulley brackets

012–06408A RMS/IDS Kit

2. Set up the Rotary Motion Sensors in Science Workshop as directed in the setup section on

page 3 of this manual.

3. If you are not in the setup window for the RMS, double-click on the RMS icon (

Set the Divisions/Rotation to 1440. Check to be sure that Large Pulley (Groove) is selected in the Linear Calibration dialog box. Click OK.

4. Repeat the setup (steps 2 and 3) for the other RMS.

5. Double-click on the Sampling Options button and set the sampling rate to 50 Hz. Click OK.

6. Define the calculation for display for momentum:

 Click on the Experimental Calculator icon. Create a new calculation for momentum by

clicking the New button and entering the calculation in the Expression Field using the

, , and keyboard buttons. Type a descriptive calculation name, such as Total

Momenum1, a short abbreviation for the name, and the units of the calculation in the appropriate fields. Press Enter to accept the calculation entry.

Note: For additional information on entering calculations, refer to

Using Calculations in the Users Guide for Science Workshop and to the

section on the Experiment Calculator Window in the Annotated Windows section of the Users Guide.

7. Define the calculation for display for kinetic energy (refer to step 6 above).

8. Make a Graph display that shows the velocity of cart 1, the velocity of cart 2, the Total

Momentum of the system, and the Total Kinetic Energy of the system plotted vs. time.

 Drag and drop a Graph icon to an RMS icon and select four calculations to display,

from the Choose Calculations to Display pop-up menu (these selections will be modified, so it doesnt matter which calculations are selected). A Graph display with 4 sets of y-axis plots vs. an x-axis plot for time will open.

 To set up the y-axis plot of linear velocity for cart 1, click on the Plot Input Menu

button (

) in the top y-axis plot and select

Digital1

and

Velocity (linVel)

from the pop-up menu.

 To set up the y-axis plot of linear velocity for cart 2, click on the Plot Input Menu

button in the second y-axis plot and select

Digital3

and

Velocity (linVel)

from the

pop-up menu.

 To set up the y-axis plot for Total Momentum, click on the Plot Input Menu button in

the third y-axis plot and select

calculations

and the name for the momentum

calculation from the pop-up menu.

RMS/IDS Kit 012–06408A

 To set up the y-axis plot for Total Kinetic Energy, click on the Plot Input Menu button

in the fourth y-axis plot and select calculation from the pop-up menu.

calculations

and the name for the kinetic energy

Collect the Data

1. Place the carts as indicated in Figure 3.1.

2. Start recording data.

3. Gently push cart 1 and release it, allowing it to glide to cart 2.

➤

Note: The force of the push should be sufficient to propel both carts

after the collision, but not hard enough to make the carts vibrate or jump the track. A smooth motion will produce the best results.

4. Stop recording data.

➤

Note: The data can be smoothed, if desired, by using the smooth

function in the Experiment Calculator. To smooth data, modify your equation in the Experiment Calculator by selecting (n,x). Set n = 8 at first. If you do not get the desired smoothing result, experiment with different values of n.

>Special>smooth

Analyze the Data

1. Click the Autoscale Tool on the Graph display.

2. Print the graph or make a sketch of it, and indicate the point at which the carts collided.

3. Explain what is happening in each of the panels before and after the collision.

4. Use the Smart Cursor to measure:

1) the velocity of cart 1 just before the collision.

2) the velocity of the carts just after the collision

3) momentum before and after the collision

4) kinetic energy before and after the collision Record in Table 3.1.

5. Complete Tables 3.1 and 3.2.

012–06408A RMS/IDS Kit

Table 3.1

Part A

Part B

Table 3.2

Part A

aftervafter

m1v1 + m2v

(kg) (m/s) (kg) (m/s) (kg) (m/s) (kg ms/) (kg m/s)

calculated

½m1v

calculated

+½m2v

(N s) (N s) %

measured

½m

calculated

aftervafter

measured

loss of KE

measured

aftervafter

measured

Part B

measured

Part B  Inelastic collision of unequal masses

1. Add a mass to cart 2 and repeat the data collection and analysis sections.

➤ Note: You will need to redefine the calculations in the Experimental

Calculator for Total Momentum and Total KE in Graph display with the new mass values.

Questions

1. How did the inelastic collision effect the total momentum and total kinetic energy in the

system?

2. What effect did friction have on the momentum and kinetic energy of the system?

3. What are other possible contributors to the variation of the experimental data from the

expected (theoretical) values?

RMS/IDS Kit 012–06408A

012–06408A RMS/IDS Kit

Experiment 4: Conservation of momentum and kinetic energy in an elastic collision

Purpose

Materials and Equipment Required

• (2) Rotary Motion Sensor (RMS) (CI-6538) • Dynamics Track (ME-9435A or ME-9458)

• (2) Collision Cart (ME-9454) • PASCO computer interface (700)

• (2) RMS/IDS Kit (CI-6569) • Science Workshop version 2.2 or higher

• (2) IDS Mount Accessory (CI-6692) • computer

• pages 2 & 3 of this manual

Theory

Before the collision of the two carts, the situation can be represented as follows:

→

where m second cart, and v

= the mass of the first cart, v1 = the velocity of the first cart, m2 = the mass of the

= the velocity of the second cart, which is 0.

During an elastic collision, the kinetic energy is converted to potential energy and back into kinetic energy as the carts bounce off one another. After the collision, the carts accelerate away from each other, or all the kinetic energy of one cart is transferred to the other cart, which accelerates away from the first cart has a velocity of zero. When acceleration reaches 0, the situation can be as represented below:

The momentum of the system at any point in time is expressed as follows:

after

v2 (= 0)

after

where m

P=m1v

are the mass and velocity of the first cart and m2v2 are the mass and velocity of the

1v1

m2v

second. Since the momentum is conserved after the collision, the following relationship exists:

m1v

m2v2=m

aftervafter

RMS/IDS Kit 012–06408A

where m

= the mass of the two carts and v

after

= the velocity of the two carts stuck together.

after

The total kinetic energy (KE) of the system at any moment in time is represented by:

KE =

m1v1+

1 2

m2v

After the elastic collision, kinetic energy and momentum are preserved:

1 2

m1v

m2v

after

Procedure

Set Up the Equipment

1. Mount the two Rotary Motion Sensors on the IDS track using the IDS Mount Accessories,

and mount the two brackets with small pulley on the IDS track (refer to the page 2 of this manual and Figure 3.1).

magnetic ends (Collision Carts)



RMS

IDS Mount Accessory

Figure 3.1

Equipment setup for experiment 3

2. Attach the cartstring brackets to the carts, measure the mass of the carts, and record in

Table 3.1.

3. Place the carts on the track with the magnetic ends facing each other.

4. Thread the string as shown in Figure 3.1 and pages 2 & 3 of the manual. Make the necessary

adjustments to the setup to insure that the string is unobstructed and moves freely.

IDS track

cart 1

thread

cart 2

cart—string brackets

IDS track pulley brackets

5. Adjust the brackets with small pulley as necessary to insure that the thread is taunt and not

slipping on the pulleys.

012–06408A RMS/IDS Kit

Set Up Science Workshop

1. Insert the digital plugs for the RMS connected to cart 1 into digital channels 1 & 2, and the

digital plugs of the RMS connected to cart 2 into digital channels 3 & 4 of the interface box.

2. Set up the Rotary Motion Sensors in Science Workshop as directed in the setup section on

page 3 of this manual.

3. If you are not in the setup window for the RMS, double-click on the RMS icon (

Set the Divisions/Rotation to 1440. Check to be sure that selected in the Linear Calibration dialog box. Click OK.

4. Repeat the setup (steps 2 and 3) for the other RMS.

5. Double-click on the Sampling Options button (

rate to 50 Hz. Click OK.

6. Define the calculation for display for momentum:

 Click on the Experimental Calculator icon. Create a new calculation for momentum by

clicking the New button and entering the calculation in the Expression Field using the

, , and keyboard buttons. Type a descriptive calculation name, such as Total

Momenum1, a short abbreviation for the name, and the units of the calculation in the appropriate fields. Press Enter to accept the calculation entry.

➤

Note: For additional information on entering calculations, refer to

Using Calculations in the Users Guide for Science Workshop and to the

section on the Experiment Calculator Window in the Annotated Windows section of the Users Guide.

Large Pulley (Groove)

) and set the sampling

7. Define the calculation for display for kinetic energy (refer to step 6 above).

8. Make a Graph display that shows the velocity of cart 1, the velocity of cart 2, the Total

Momentum of the system, and the Total Kinetic Energy of the system plotted vs. time.

 Drag and drop a Graph icon to an RMS icon and select four calculations to display,

 To set up the y-axis plot of linear velocity for cart 1, click on the Plot Input Menu

button (

from the pop-up menu.

 To set up the y-axis plot of linear velocity for cart 2, click on the Plot Input Menu

button in the second y-axis plot and select

) in the top y-axis plot and select

Digital3

Digital1

and

Velocity (linVel)

from the

RMS/IDS Kit 012–06408A

 To set up the y-axis plot for Total Momenutm, click on the Plot Input Menu button in

the third y-axis plot and select calculation from the pop-up menu.

 To set up the y-axis plot for Total Kinetic Energy, click on the Plot Input Menu button

in the fourth y-axis plot and select calculation from the pop-up menu.

calculations

and the name for the momentum

and the name for the kinetic energy

Collect the Data

1. Place the carts as indicated in Figure 3.1.

2. Start recording data.

3. Gently push cart 1 and release it, allowing it to glide to cart 2.

➤

Note: The force of the push should be sufficient to propel both carts

after the collision, but not hard enough to make the carts vibrate or jump the track. A smooth motion will produce the best results.

4. Stop recording data.

➤

Note: The data can be smoothed, if desired, by using the smooth

>Special>smooth

Analyze the Data

1. Click the Autoscale Tool on the Graph display.

2. Print the graph or make a sketch of it, and indicate the point at which the carts collided.

3. Explain what is happening in each of the panels before and after the collision.

4. Use the Smart Cursor to measure:

1) the velocity of cart 1 just before the collision.

2) the velocity of the carts just after the collision

3) momentum before and after the collision

4) kinetic energy before and after the collision Record in Table 4.1.

5. Complete Tables 4.1 and 4.2.

012–06408A RMS/IDS Kit

Table 4.1

(kg) (m/s) (kg) (m/s) (kg) (m/s) (kg) (m/s) (kg m/s) (kg m/s)

after

m1v1 + m2v

calculated

measured

calculated

after

Table 4.2

calculated

½m1v

+½m2v

(N s) (N s)

measured

½m

calculated

after

+ ½m

after

measured

after+

after

measured

Questions

1. How did the elastic collision effect the total momentum and total kinetic energy in the

system?

2. What effect did friction have on the momentum and kinetic energy of the system?

3. What are other possible contributors to the variation of the experimental data from the

expected (theoretical) values?

RMS/IDS Kit 012–06408A

012–06408A RMS/IDS Kit

Teachers Notes

Experiment 1

Run #1

P o sition (cm)

-10 0 10 20 30 40 50 60

0 50

Ru n #1

Velo city (cm/ s)

Run #1

Accel eration (cm/s/ s )

-1500 -1000 -500 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Time (s)

Figure TN-1

Schematic representation of typical experimental results for Experiment 1.

Questions

1. Students can use the Smart Cursor to find the velocity and acceleration of the cart just

before the collision.

2. During the collision, the velocity moves from positive, through zero, to negative. When the

velocity is negative, the cart is moving in the opposite direction.

3. During the collision, the acceleration varies from zero to negative and then back to zero as

the cart rebounds in the opposite direction.

RMS/IDS Kit 012–06408A

Experiment 2

maximum: x = 2.5475, y = 53.1248

Run #1

sVel (cm/s)

0 10 20 30 40 50

selected area for integration value

Run #1

sF orce (N)

0 2.0 4.0 6.0

1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6

Time (s )

Figure TN-2

Schematic representation of typical experimental data for Experiment 2 (data smoothed).





Listed below are some typical results for Experiment 2.

Value for integration under the selected portion of the Force curve: 0.27 N s

Formula for smoothing data (set in the Experimental Calculator):

Integr a ti on area = 0.27073 N s

mass of cart = 0.5 kg V

= 0.54 m/s

max

Force = smooth(8,@A.Force) Velocity = smooth(8,@1.linVel)

momentum = mv = 0.27 kg m/s (N s)

Question

1. The students data should show that the momentum of the cart equals the impulse of the

inelastic collision:

mv = Fdt

012–06408A RMS/IDS Kit

Experiment 3

Part AInelastic collision of carts with equal mass

collision starts

R un # 3

sVel1 (cm/s)

0 10 20 30 40

Ru n #3

sVel3 (cm/ s)

0 10 20 30 40

R un #3

0 0.10 0.20

sM omentum1 (kg m/s

Run #3

0 0.020 0.040

sTotal Kinetic Energy1

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6

Tim e (s )

Figure TN-3

Typical experimental results from Part A of Experiment 3 (smoothed).

Equations entered into the Equation Field of the Experimental Calculator:

Formulae for Momentum and Total Kinetic Energy:

 Total Momentum, Part A: .51*@1.linVel*.01+.46*@3.linVel*.01  Total KE, Part A: .51*(.5*(@1.linVel*.01)^2)+.5*(.46*(@3.linVel*.01)^2)

Formulae for smoothing data:

 Total Momentum, Part A (smoothed): smooth(8,Momentum1)  Total KE, Part A smoothed: .5*(.51*(smooth(8,@1.linVel)*.01)^2)+.5*(.46*(smooth(8,@3.linVel)*.01)^2)

RMS/IDS Kit 012–06408A

Part BInelastic collision of carts with unequal mass (m1=½m2)

collision starts

R un #1

sVel1 (cm/s)

0 10 20 30 40

R un #1

sVel3 (cm/s)

0 10 20 30 40

Run #1

0 0.10 0.20

sM omentum2 (kg m/s

Run #1

0 0.020 0.040

sTotal Kinetic Energy2

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Time ( s)

Figure TN-3

Typical experimental results from Part B of Experiment 3 (smoothed).

Equations entered into the Equation Field of the Experimental Calculator:

Formulae for Momentum and Total Kinetic Energy:

 Total Momentum, Part B (Momentum2): .51*@1.linVel*.01+.96*@3.linVel*.01  Total KE, Part B: .5*(.51*(@1.linVel*.01)^2)+.5*(.96*(@3.linVel*.01)^2)

Formulae for smoothing data:

 Total Momentum, smoothed (Part B): smooth(8,Momentum2)  Total KE, smoothed (Part B): .5*(.51*(smooth(8,@1.linVel)*.01)^2)+.5*(.96*(smooth(8,@3.linVel)*.01)^2)

012–06408A RMS/IDS Kit

Table 3.1

Part A

Part B

Table 3.2

Part A

Part B

aftervafter

m1v1 + m2v

aftervafter

(kg) (m/s) (kg) (m/s) (kg) (m/s) (kg ms/) (kg m/s)

0.51 0.40 0.46 0 0.96 0.19

0.51 0.37 0.96 0 1.5 0.12

½m1v

calculated

0.041.

calculated

0.035

+½m2v

(N s) (N s) %

0.041

measured

0.035

measured

½m

calculated

aftervafter

0.017

0.018

measured

calculated

0.011

measured

calculated

0.20

calculated

0.19

loss of KE

0.20

measured

0.19

measured

calculated

0.18

calculated

0.18

0.19

measured

0.18

measured

Questions:

1. Total momentum is unchanged after the collision, but the total KE drops significantly after

the collision.

2. Friction gradually reduced both the total momentum and total KE until both reach zero.

Friction reduced the momentum and KE more rapidly in the system with more mass (Part B).

3. Other variables include vibration in the system and a small amount of elasticity in the

collision.

RMS/IDS Kit 012–06408A

Experiment 4

collision begins

R un #7

sVel1 (cm/s)

0 10 20 30

R un # 7

sVel3 (cm/s)

0 10 20 30

Ru n #7

0 0.05 0.10 0.15

sM omentum1 (kg m/s

Run #7

0 0.010 0.020

sTotal Kinetic Energy1

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Tim e (s)

Figure TN-4.1

Typical results for Experiment 4 (smoothed)

Equations entered into the Equation Field of the Experimental Calculator:

Formulae for Momentum and Total Kinetic Energy:

 Total Momentum, Part A: .51*@1.linVel*.01+.46*@3.linVel*.01  Total KE, Part A: .51*(.5*(@1.linVel*.01)^2)+.5*(.46*(@3.linVel*.01)^2)

Formulae for smoothing data:

 Total Momentum, Part A (smoothed): smooth(8,Momentum1)  Total KE, Part A smoothed: .5*(.51*(smooth(8,@1.linVel)*.01)^2)+.5*(.46*(smooth(8,@3.linVel)*.01)^2)

012–06408A RMS/IDS Kit

Table 4.1

(kg) (m/s) (kg) (m/s) (kg) (m/s) (kg) (m/s) (kg m/s) (kg m/s)

0.51 0.31 0.46 0 0.51 0 0.46 0.32 0.16

after

m1v1 + m2v

calculated

after

0.15

0.16

measured

Table 4.2

calculated

0.025

½m1v

+½m2v

(N s) (N s)

0.026

measured

½m

calculated

after

0.024

+ ½m

after

0.023

measured

after+

after

0.15

after

measured

Questions:

1. Both total momentum and total kinetic energy are conserved after the collision, but the

total KE temporarily drops (having been converted to potential energy during the first half of the elastic collision) and then rises (as potential energy is converted to kinetic energy in the second half of the elastic collision.

2. Friction gradually reduced both the total momentum and total KE until both reach zero.

Friction reduced the momentum and KE more rapidly in the system with more mass (Part B).

3. Other variables include vibration in the system and mechanical effects.

T echnical 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: (916) 786-3292

e-mail: techsupp@pasco.com

web: 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.

PASCO ME-6569 User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual