PASCO ME-9892 Manuale utente

Ballistic Pendulum Accessory

ME-9892

Instruction Manual with

Experiment Guide

012-09842C

Ballistic Pendulum Accessory

2012-09842C

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Equipment Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Assemble the Apparatus, 4

Load the Launcher, 5

Prepare the Sensor, 6

Test Fire, 6

Foam Insert Replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Experiment 1: Ballistic Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Theory, 7

Experiment Set-up, 7

Procedure, 7

Analysis, 9

Question, 9

Further Study, 9

Experiment 2: Conservation of Momentum and Energy . . . . . . . . . . . . . . . . . . . . . . . . 10

Background, 10

Part 1: Measure Launch Velocity, 10

Part 2: Record Ballistic Pendulum Data, 10

Part 3: Determine Rotational Inertia of Pendulum-ball System, 11

Analysis, 13

Questions, 13

Further Study I: Different Launch Speeds, 14

Further Study II: Different Projectile Mass, 14

Further Study III: Different Center of Mass, 14

Further Study IV: Elastic Collision, 14

Further Study V: Alternative Determination of Rotational Inertia, 15

Further Study VI: Horizontal Collision, 16

Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Ballistic Pendulum Accessory

ME-9892

Included Equipment Part Number

1. Catcher and pendulum

rod

ME-9892

2. Pendulum attachment

screw

613-076

3. Replaceable foam

insert

648-09757

4. Ballast mass 648-06511

5. Ballast lock nut 614-029

6. Ballast fastening screw 617-027

7. Steel ball ME-9864 (4-pack)

Required Equipment

Short Range Launcher ME-6800

PASPORT Rotary Motion

Sensor with three-step

pulley1

PS-2120

Table Clamp ME-9472 or similar

90 cm mounting rod ME-8738 or similar

C-clamp SE-7286 or similar

Optional Equipment Part Number

Photogates (qty. 2)2ME-9498A or similar

Digital Adapter1, 2 PS-2159

Photogate Mounting

Bracket2ME-6821

Super Pulley with Clamp2ME-9448B

Hanging mass2ME-8979 or similar

Mini Rotational Accessory3CI-6691

Spherical Mass Set4ME-8968

Additional three-step

pulley5CI-6693

45 cm mounting rod5ME-8736 or similar

Multi clamp5ME-9507 or similar

1Sensor requires a PASPORT interface.

2For measuring launch velocity and rotational inertial. See

Experiment 2.

3Required for Experiment 2

4For Experiment 2, Further Study II: Different Projectile Mass

Ballistic Pendulum Accessory Introduction

4012-09842C

Introduction

Use the Ballistic Pendulum Accessory in combination with a Short Range Launcher

and Rotary Motion Sensor (RMS) to measure the velocity of a steel ball and study

rotational collisions. The launcher shoots the ball into the Ballistic Pendulum Acces-

sory. The RMS measures the resulting angular displacement and velocity of the pen-

dulum. The pendulum can be configured to catch the ball or allow the ball to bounce

off. With the addition of the Mini Rotational Accessory, the apparatus can be config-

ured as a physical pendulum or rotational system with adjustable moment of inertia.

This manual includes set-up instructions and experiment instructions.

Equipment Set-up

Assemble the Apparatus

1. Set up the launcher, C-clamp, table clamp, mounting rod, and RMS as shown in

Figure 1. The exact position of the RMS is not important yet. Note that the side

of the RMS without the model number on the label is facing you. (If the RMS is

mounted the other way, it will measure negative displacement.)

Figure 1: Launcher and RMS mounted on rod

2. Slide the three-step pulley onto the RMS shaft with the largest pulley out as

shown in Figure 2.

ROTARY MOTION SENSOR

FOR

INTERFACES

Three-step

pulley

Figure 2: Three-step

pulley on RMS

Model No. ME-9892 Equipment Set-up

012-09842C

3. Select one of the holes on the pendulum rod: either the center hole or the end

hole. Also select a side of the pendulum: either the catcher or the bumper. Thread

the attachment screw into the hole as shown in Figure 3. Screw it all the way in

so it is loosely captured.

4. Thread the screw into the end of the RMS shaft. Align the pendulum rod with the

tabs on the pulley as shown in Figure 4. Tighten the screw.

Figure 4: Attaching pendulum to RMS

5. Adjust the position of the RMS so the pendulum is aligned with the launcher as

shown in Figure 5. Leave a 2.5 cm gap between the launcher and the pendulum.

Load the Launcher

1. Swing the pendulum out of the way as shown in Figure 6.

2. Place the steel ball in the end of the barrel.

Caution: Use extra caution when using the launcher with a steel ball. Do not look down

the barrel. Do not leave the launcher loaded and unattended.

3. Use the pushrod included with the launcher to push the ball down the barrel until

the trigger catches in the first, second, or third position (for a slow, medium, or

fast launch).

Figure 6: Loading the launcher

End

hole

Attachment

screw

Center hole

Figure 3: Attachment

screw loosely captured

in center hole

Align rod with tabs

Figure 5: Pendulum

aligned with launcher,

bumper side (top) and

catcher side (bottom)

PushrodBall

Swing pendulum

out of the way

Ballistic Pendulum Accessory Foam Insert Replacement

6012-09842C

4. Return pendulum to its normal hanging position.

Prepare the Sensor

1. Connect the RMS to a PASPORT interface. If you will be using a computer, con-

nect the interface to it and start your data collection software.

2. Set the sampling rate of the RMS to 40 Hz.

3. Prepare a graph to show angular position versus time.

For detailed instructions, refer to the documentation that came with your interface or

press F1 to launch the software’s on-line help.

Test Fire

1. Start data recording.

2. Pull the trigger of the launcher.

3. Stop data collection.

Figure 7 shows typical data for an inelastic collision. If your data shows negative

angular displacement, disassemble the RMS from the mounting rod and pendulum

and remount it with the pendulum attached to the other end of the RMS shaft.

Foam Insert Replacement

With age and repeated use, the foam catcher insert may lose elasticity. If the catcher

does not reliably hold the ball, remove the foam insert and replace it with a new one.

(Contact PASCO Teacher Support for a replacement foam insert, 648-09757).

Figure 8: Removable foam insert

Figure 7: Typical data

Model No. ME-9892 Experiment 1: Ballistic Pendulum

012-09842C

Experiment 1: Ballistic Pendulum

Theory

The ballistic pendulum has historically been used to measure the launch velocity of a

high speed projectile. In this experiment, a projectile launcher fires a steel ball (of

mass mball) at a launch velocity, V0. The ball is caught by a pendulum of mass mpend.

As the momentum of the ball is transferred to the catcher-ball system, the pendulum

swings freely upwards, raising the center of mass of the system by a distance h.

The pendulum rod is hollow to keep its mass low, and most of the mass is concen-

trated at the end so that the entire system approximates a simple pendulum. During

the collision of the ball with the catcher, the total momentum of the system is con-

served. Thus the momentum of the ball just before the collision is equal to the

momentum of the ball-catcher system immediately after the collision:

(eq. 1.1)

where Vis the speed of the catcher-ball system just after the collision, and

(eq. 1.2) M =mball +mpend

During the collision, some of the ball's initial kinetic energy is converted into thermal

energy. But after the collision, as the pendulum swings freely upwards, we can

assume that energy is conserved and that all of the kinetic energy of the catcher-ball

system is converted into the increase in gravitational potential energy.

(eq. 1.3)

where g=9.81 m/s2, and the distance his the vertical rise of the center of mass of the

pendulum-ball system.

Combining equations 1.1 through 1.3 (eliminating V) yields

(eq. 1.4)

Experiment Set-up

1. Attach the ballast mass to the bottom of the catcher.

2. Set up the equipment and software as described on pages 4–6

with the pendulum rod attached to the RMS at the end hole and

the catcher side of the pendulum facing the launcher.

Procedure

Record Data

1. Load the launcher and push the ball in to the third (fastest) posi-

tion.

2. Start data collection.

mballV0MV=

---MV2Mgh=

V01mpend

mball

-------------





2gh=

Figure 1.1: Set-up

Catcher

side

Ballast

mass

Ballistic Pendulum Accessory Experiment 1: Ballistic Pendulum

8012-09842C

3. Launch the ball so that it is caught in pendulum.

4. After the pendulum has swung out and back, stop data collection.

5. Note the maximum angular displacement measured by the RMS. Record it in

Table 1.1.

6. Repeat steps 1 through 5 several times.

7. Calculate the average maximum displacement, max.

Find the Mass and Center of Mass

1. Fire the ball one more time (without recording data). Catch the pendulum near

the top of its swing so it does not swing back and hit the launcher (this will pre-

vent the ball from falling out or shifting).

2. Remove the pendulum from the RMS.

3. Remove the screw from the pendulum shaft.

4. With the ball still in the catcher, place the pendulum at the edge of a table with

the pendulum shaft perpendicular to the edge and the counterweight hanging over

the edge. Push the pendulum out until it just barely balances on the edge of the

table. The balance point is the center of mass. (See Figure 1.2.)

5. Measure the distance, r, from the center of rotation (where the pendulum was

attached to the RMS) to the center of mass. r= _____________________.

6. Remove ball from the catcher.

7. Measure the mass of the pendulum (without the ball). mpend = _______________

8. Measure the mass of the ball. mball = _____________________

Table 1.1: Maximum

Angular Displacement

Trial Angle

Tr i a l 1

Tr i a l 2

Tr i a l 3

Tr i a l 4

Tr i a l 5

Tr i a l 6

Avg: max=

Balance point

Figure 1.2: Pendulum-ball system balanced on table edge

Model No. ME-9892 Experiment 1: Ballistic Pendulum

012-09842C

Analysis

1. Use your value of max, the distance r, and Equation 1.5 to calculate the maxi-

mum height (h) that the center of mass rises as the pendulum swings up (see Fig-

ure 1.3).

(eq. 1.5) h = r(1 - cos (max))

h= _____________________

2. Use your value of hand Equation 1.4 to calculate the launch velocity of the ball.

V0= _____________________

Question

The theory for this experiment ignores the rotational inertia of the pendulum. Because

the pendulum is not really a simple pendulum (a point mass on a massless rod), a sys-

tematic error is introduced. Does this simplistic analysis tend to give a launch velocity

that is too high or too low? (See Experiment 3 for a more exact treatment.)

Further Study

Use two photogates to measure the launch velocity of the ball. Compare this value to

the value you found using the ballistic pendulum.

qmax

x= rcos (max)

r= x+ h

Figure 1.3:

Calculating h

Ballistic Pendulum Accessory Experiment 2: Conservation of Momentum and Energy

10 012-09842C

Experiment 2: Conservation of Momentum

and Energy

Background

In this experiment you will analyze the angular collision between a ball and a physical

pendulum. You will compare the rotational momentum of the ball before the collision

to the rotational momentum of the pendulum-ball system after the collision. Both

rotational momenta are measured about the pendulum’s pivot point.

You will also compare the kinetic energy of the ball before the collision, the kinetic

energy of the pendulum-ball system just after the collision, and the maximum poten-

tial energy of the system after the collision.

The data-taking phase of this experiment has three parts. In Part 1 you will use photo-

gates to measure the launch velocity of the ball. In Part 2 you will measure the maxi-

mum rotational velocity and angular displacement of the pendulum after the collision.

In Part 3 you will measure the rotational inertia of the pendulum-ball system.

Part 1: Measure Launch Velocity

Set up the launcher with two photogates and a photogate bracket (see Figure 2.1).

Measure the launch velocity (Vlaunch) of the ball on the fastest setting. Do several tri-

als and use the average value.

If you will be doing the Advanced Study part of this experiment, also measure the

launch velocity for the medium and slow settings.

Part 2: Record Ballistic Pendulum Data

Set-up

1. Set up the equipment and software as described on pages 4 through 6 with the

pendulum rod attached to the RMS at the center hole and the catcher side of the

pendulum facing the launcher. Do not attach the ballast mass to the bottom of the

catcher.

2. Install one of the sliding masses from the Mini Rotational Accessory as a coun-

terweight. Slide it onto the pendulum rod above the RMS attachment point.

Adjust the position of the counterweight so the pendulum is perfectly balanced

without the ball. If you release the pendulum in the horizontal position, it should

not move. (See Figure 2.2.)

Figure 2.2: Pendulum balanced horizontally

3. Prepare a graph to display angular velocity versus time and position versus time.

Figure 2.1: Launcher

with photogates

Counterweight

Indice

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