PASCO ME-6831 User Manual

Instruction Manual

Projectile Launcher

Base

Ballistic Pendulum

Vertical upright

Trigger String

Included: Ramrod, 2-D Collision Accessory, Steel Balls (2), Plastic Balls (3) Not shown: Safety Glasses (2 pair)

Angle indicator

Ballistic Pendulum/

Projectile Launcher

ME-6830, ME-6831

012-05375C

*012-05375*

The cover page shows the PASCO Ballistic Pendulum with the Short Range Projectile Launcher mounted on the vertical part of the base. The Ballistic Pendulum is designed for traditional ballistic pendulum exp eriments and can also be used for projectile motion experiments and demonstrations. When the Projectile Launcher is used for projectile motion experiments, the launch angle at the upper launch position can vary from 0 to 90 degrees, and the firing height is fixed for any launch angle. The Launcher can also mounted in a horizontal position that is height-adjustable. The vertical base of the Ballistic Pendulum also has a dedicated position for the Launcher fo r Ballistic Pendulum experiments. This manual contains copy-ready experiments and demonstrations for the ballistic pendulum and projectile launcher.

Table of Contents

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

Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

General Operation of the Projectile Launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Ballistic Pendulum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Installation of the Optional Photogate Bracket. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Installation of the Two-Dimensional Collision Attachment. . . . . . . . . . . . . . . . . . . . . . . . 9

Expectations for the Projectile Launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Expectations for the Ballistic Pendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

EXPERIMENTS

1. Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. Projectile Motion Using Photogates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3. Projectile Range versus Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4. Projectile Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5. Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6. Conservation of Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7. Vary Angle to Maximize Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

8. Projectile Velocity—Approximate Method). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

9. Projectile Velocity—Exact Method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

DEMONSTRATIONS

10. Do 30° and 60° Launch Angles give the Same Range? . . . . . . . . . . . . . . . . . . . . . 43

11. Simultaneously Fire Two Balls Horizontally at Different Speeds. . . . . . . . . . . . . . . 45

12. Shoot through Hoops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

13. Elastic and Inelastic Collisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Teacher’s Guide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Technical Support, Warranty, and Copyright. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

iii

Projectile Launcher

iv 012-05375C

Ballistic Pendulum / Projectile Launcher

ME-6830, ME-6831

Equipment

The ME-6830 Ballistic Pendulum / Projectile Launcher includes the following:

Included Equipment Part Number

Ballistic Pendulum and Base (unassembled) 003-05374 Short Range Projectile Launcher Assembly 003-10550 Plastic Balls, 25 mm diameter (3) see ME-6802* 2-D (two-dimensional) Collision Accessory see ME-6802* Ramrod see ME-6802* Steel Balls, 25 mm diameter (2) 699-064 Safety Glasses (2 pair) 699-066 Trigger String (45 cm (18”)) 699-067 Hex Key 726-046

Required Equipment Part Number

C-Clamp, Large SE-7285

Recommended Equipment Part Number

Launcher Spares Kit* ME-6802 Time-of-Flight Accessory ME-6810 Projectile Catcher Accessory ME-6815 Photogate Mounting Bracket ME-6821A Shoot-the-Target ME-6853 Photogate Head ME-9498A Laser Sight Accessory OS-8527A

*The ME-6802 Launcher Spares Kit includes: Ramrod (2), Plastic Balls (10-pack), 2-D Collision Accessory (2), Sights (5-pack), Plumb Bob (24-pack), Nylon Thread (1 spool), and Thumbscrews (10).

The ME-6831 Ballistic Pendulum does not include the Short Range Launcher. The ME-6831 Ballistic Pendulum includes two steel balls and the hex key.

ME-6802 Launcher Spares Kit

Ballistic Pendulum / Projectile Launcher Assembly

Upright

Base

Hex key

Socket head

screw

Axle

Angle Indicator

Assemble the Base

Angle

Indicator

Long pin

Axle

Mount the Ballistic Pendulum

Assembly

The Ballistic Pendulum / Projectile Launcher arrives in a custom-made package, and some assembly is required. The package has several cut-outs for the Ballistic Pendulum and ramrod, base, upright and Projectile Launcher, safety glasses, and miscellaneous small parts including a hex key (“Allen wrench”) used for assembly.

Assemble the Base

Unscrew the thumbscrew to temporarily remove the Projectile Launcher from the upright. Use the included hex key and the two socket head screws to attach the base to the upright. The screws are coated with a strong adhesive that activates when they are screwed into place.

Mount the Ballistic Pendulum

To attach the Ballistic Pendulum to the upright, unscrew the axle from the yoke. The Ballistic Pendulum has a hinge at the top of the rod with a hole through it. Line up the hole in the hinge with the axle hole in the yoke, and screw the axle back into place. Note that the long pin that extends from either side of the Ballistic Pendulum rod should be behind the angle indicator.

Yoke

Introduction

The PASCO Ballistic Pendulum / Projectile Launcher has been designed for ballistic pendulum and projectile motion experiments and demonstrations. The only addition equipment required is a C-clamp for mounting the base of the Ballistic Pendulum to a table or sturdy horizontal surface. The features of the Ballistic Pendulum include:

• Reliable Ball-Catcher Mechanism: The sensitive spring-loaded barb-type catch on the pendulum will catch

balls with a large range of speeds. In addition, the catcher holds the ball in line with the pendulum rod for best accuracy.

• Removable Pendulum: All moving parts of the pendulum may be removed so that the mass and center of

mass can be measured accurately. In addition, the pendulum can be reversed so that elastic collisions can be compared to inelastic collisions.

012-05375C

Model No. ME-6830, ME-6831 Introduction

Wear Safety Glasses

• Variable-Mass Pendulum: The pendulum includes masses that can be removed so that the pendulum can be

used with lightweight balls over a wide range of speeds. Leave the masses on the pendulum when you use heavyweight balls.

The features of the Projectile Launcher include:

• Launch at Any Angle: Balls can be launched from any angle from zero to ninety degrees measured from hor-

izontal (zero degrees). The angle is easily adjusted using thumbscrews and the built-in protractor and plumb-bob give an accurate way to measure the angle of inclination.

• Three Range Settings: Each version of Projectile Launchers has three range settings. The Short Range Pro-

jectile Launcher ranges are approximately 1.2 m, 3 m, and 5 m when the launch angle is 45°. (The Long Range Projectile Launcher ranges are approximately 2.5 m, 5 m, and 8 m. The Long Range Launcher has a stronger spring and is useful for large classroom demonstrations.)

• Fixed Elevation Independent of Launch Angle: The Projectile Launcher can pivot at the muzzle end so the

elevation of the ball as it leaves the barrel does not change as the angle is varied. The upright part of the Ballistic Pendulum base has three positions for mounting the Launcher. At the top is a hole and curved slot for use when you want to change the launch angle. The vertical slots let you mount the Launcher horizontall y at different heights so you can fire a ball into targets such as a ball catcher on a PASCO Cart on a track. At the bottom are two holes for use when you want to fire a ball horizontally into the Ballistic Pendulum.

• Repeatable Results: The piston keeps the ball from rubbing on the inside of the barrel as it travels so there is

no spin on the ball as it launches. When the base is secured to a table with a C-clamp, there is very little recoil. The trigger is pulled with a string to minimize jerking.

• Barrel Sights and Safety Precautions: There are sites built-in to the barrel for

aiming the Projectile Launcher. View the sites by looking through the back end of the barrel. WARNING: Never look down the front of the barrel because it may be loaded. Safety glasses are provided, so use them. Look for the yellow indicator through any of the five slots on the top of the barrel because the yellow indicator shows the position of the piston. If the indicator is between the first and second slots (relative to the muzzle end), the piston is not cocked.

• Computer Compatible: One or two photogates can be attached to the Projec-

tile Launcher using the ME-6821A Photogate Mounting Bracket. When used with a PASCO interface and data acquisition software, the photogates can measure the muzzle speed of the ball. Use a photogate and the ME-6810 Time of Flight Accessory to measure the time of flight of the ball

• Compact Storage: When the barrel of the Launcher is aligned vertically with the base, the Launcher takes up

minimal space. The included ramrod and the Ballistic Pendulum base have hook-and-pile material that allows the ramrod to be stored on the base.

012-05375C 3

Ballistic Pendulum / Projectile Launcher General Operation of the Projectile La uncher

Trigger

String

Trigger

Protractor

Plumb Bob

Muzzle

Thumbscrews

Range

setting slots

(1 of 5)

Launcher Parts

Label details

Yellow Band in Wi ndow Indicates Range

Launcher

on high

position

General Operation of the Projectile Launcher

Parts

Ready

• Attach the included Trigger String to the hole in the Trigger . (For example, loop the string through the hole and tie the ends together.)

• Always wear safety goggles when you are in a room where a Projectile Launcher is being used.

• Firmly clamp the base of the Ballistic Pendulum to a sturdy table or other surface.

• Mount the Projectile Launcher on the Ballistic Pendulum base. Mount the Launcher to the lower two holes in the base if you intend to shoot horizontally at the ball catcher of the Ballistic Pendulum.

• Use the hole and curved slot near the top of the base when you want to adjust the Launcher’s launch angle. Note: For this configuration, the Launcher should be mounted on the ‘back side’ of the Ballistic Pendulum base.

012-05375C

Model No. ME-6830, ME-6831 Genera l Operation of the Projectile Launcher

Bore Sights

Front

site

Rear

site

Launcher

Aim

• If you have the Launcher mounted on the top position, you can adjust the angle of inclination above the horizontal by loosening the two thumbscrews and rotating the Launcher barrel to the desired angle. Use the plumb bob and the protractor on the label to select the angle. Tighten both thumbscrews when the angle is set.

• You can ‘bore-sight’ through the barrel at a target, such as the ME-6853 Shoot-The Target. Look through the back end of the barrel when the Launcher is not loaded. There are two ‘tripod’ (three-spoke) sights inside the barrel, one at the end of the barrel and one at the end of the piston (about midway in the barrel). Each sight has a sighting hole at its center. Loosen the thumbscrews and C-clamp and adjust the angle and position of the Launcher to align the centers of both sights on your target. Tighten the thumbscrews and C-clamp when the Launcher is aimed.

Load

• T o load a ball in the Launcher when its mounted on the low position, either hold the Ballistic Pendulum out of the way or rotate the pendulum until the rod is horizontal and it catches in the component clip on the underside of the yoke.

• Place a ball in the muzzle of the Launcher. NOTE: Always cock the piston with a ball in the piston. You may damage the piston if you use the ramrod without a ball in the piston.

• Remove the ramrod from its storage place on the edge of the upright. While looking through the range-setting slots on the top side of the Launcher, push the ball down the barrel with the ramrod until the trigger catches the edge of the piston at the desired range setting. (The trigger will “click” into place.)

• When the yellow indicator tape on the piston is visible in the middle range-setting slot, the piston is in the SHORT RANGE position. When the indicator tape on the piston is visible in the next range-setting slot (fourth from the muzzle), the piston is in the MEDIUM RANGE position, and when the tape is visible in the last range-setting slot, the piston is in the LONG RANGE position.

• Remove the ramrod and return it to the storage place on the edge of the upright.

• When the Projectile Launcher is loaded, the yellow indicator tape is visible through one of the range-setting slots on the upper side of the barrel. Never look down the barrel! To check whether the Launcher is loaded, look through the range-setting slots on the barrel.

Shoot

• Before shooting the ball, make certain that no one is in the way.

• T o shoot the ball, pull straight up on the trigger string that is attached to the trigger. You only need to pull about one centimeter.

• The trigger will automatically return to its initial position after you release the string.

Maintenance and Storage

• The Ballistic Pendulum/Projectile Launcher does not need any special maintenance. Do not oil the Launcher!

• To store the Launcher in the least amount of space, align the barrel vertically. One way is to mount it in one of the two vertical slots. Tighten the thumbscrews to hold the Launcher in place.

012-05375C 5

Ballistic Pendulum / Projectile Launcher Ballistic Pendulum Theory

PE Mgh

hR1 cos–=

PE MgR

1 cos–=

1 2

-- -

------- -

2MKE=

Ballistic Pendulum Theory

Overview

The ballistic pendulum is a classic method of determining the velocity of a projectile. It is also a good demonstration of many of the basic principles of physics.

The ball is fired into the ballistic pendulum, which then swings up a measured amount. From the height reached by the pendulum, you can calculate its gravitational potential energy. The gravitational potential energy is equal to the kinetic energy of the pendulum at the bottom of the swing, just after the collision with the ball.

You cannot equate the kin etic energy of the pendulum after the collision with the kinetic energy of the ball before the swing since the collision between ball and pendulum is inelastic, and kinetic energy is not conversed in inelastic collisions. Momentum is conserved in all forms of collisions, so you know that the momentum of the ball before the collision is equal to the momentum of the pendulum after the collision. Once you know the momentum of the ball and the ball’s mass, you can determine the initial velocity.

There are two ways of calculating the velocity of the ball. The first method (called the “approximate method”) assumes that the pendulum and the ball together act as a point mass located at their combined center of mass. This method does not take rotational inertia into account. It is somewhat quicker and easier than the second method (called the “exact method”), but not as accurate.

The second method (exact method) uses the actual rotational inertia of the pendulum in the calculations. The equations are slightly more complicated, and it is necessary to take more data in order to find the moment of inertia of the pendulum, but the results are generally better.

Please note that the subscript “cm” used in the following equations stands for “center of mass”.

Approximate Method

Begin with the potential energy of the pendulum at the top of its swing after the collision with the ball:

where M is the combined mass of the pendulum and ball, g is the acceleration due to gravity, and h is the change in height. Substitute for the change in height:

where R energy is equal to the kinetic energy immediately after the collision:

where v the equation is:

is the distance from the pivot point to the center of mass of the pendulum/ball system. This potential

is the speed of the speed of the pendulum just after collision. The momentum of the pendulum just after

which you can substitute into the previous equation to give:

Solving this equation for the pendulum momentum gives:

012-05375C

Model No. ME-6830, ME-6831 Ballistic Pendulum Theory

2M2gRcm1 cos–=

h



Figure 1

---- -

2gR

1 cos–=

PE MgRcm1 cos–=

1 2

-- -

I

I=

--------

2IKE=

LpmR

 mRbv==

-Mg sin



-Mg

Figure 2

mRbv 2IMgRcm1 cos–=

----------

2IM gR

1 cos–=

 I=

This momentum equal to the momentum of the ball just before the collision:

Setting these two equations equal to each other and replacing KE with our known potential energy gives:

Solve this for the ball’s velocity and simplify to get:

Exact Method

The potential energy is found in a way identical to the way shown previously:

For the kinetic energy, you can use the equation for angular kinetic energy instead of linear kinetic energy, and substitute into it the equation for angular momentum:

where I is the moment of inertia of the pendulum/ball combination, and  is the angular velocity immediately after the collision.

As you did previously, solve this last equation for angular momentum:

This angular momentum is equal to the angular momentum of the ball before the collision, as measured from the pendulum pivot point:

where R general equal to R

is the distance from the pendulum pivot to the ball. (NOTE: This radius is not in

, which is the distance from the pivot point to the center of mass for

the pendulum/ball system.)

These two angular momenta are equal to each other, so:

Solve for v:

Now you need to find I, the moment of inertia of the pendulum and ball. To do this, start with the rotational equivalent of Newton’s Second Law:

where  is torque, I is moment of inertia, and  is angular acceleration. The force on the center of mass of the pendulum is Mg, and the component of force directed towards the center of the pendulum swing is F = -Mg sin Figure 2.)

012-05375C 7



See

Ballistic Pendulum / Projectile Launcher Ballistic Pendulum Theory

I RcmMg sin–=



MgR

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

–=



--- -

x– 2x–==



MgR

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

MgR



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

MgR

4

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

Projectile Launcher

barrel

Square

Nut

Thumb

screw

Photogate

Mounting

Bracket

T-slot

Thumb

screw

Install the Optional Photogate Bracket

The torque on the pendulum is thus:

For small angles, , sin so if you make this substitution and solve for  you get:

This angular equation is in the same form as the equation for linear simple harmonic motion:

So if you compare the two equations, linear and angular, you can see that the pendulum exhibits simple harmonic motion, and that the square of the angular frequency (

) for this motion is:

Solving for I gives the desired result:

where T is the period of the pendulum.

• NOTE: You used a small-angle approximation to find the equation for I, but I does not depend on . This means that you must measure the period T using small angle oscillations. Once you have calculated I with that period, you may use that value of I regardless of the amplitude reached during other parts of the experiment.

Installing the Optional Photogate Bracket (ME-6821A)

The Photogate Bracket is an optional accessory for mounting one or two photogates on the Projectile Launcher to measure the muzzle speed of the ball.

• Prepare the Photogate Bracket by loosening the thumbscrew near the end of the bracket. Leave the square nut in place on the end of the thumbscrew. Use the smaller (0.75 in) thumbscrews that are stored on the bottom side of the bracket to mount one or two photogates to the bracket

• Align the square nut of the bracket with the T-shaped slot on the bottom of the Launcher barrel and slide the nut into the slot until the photogate nearest to the barrel is as close to the muzzle as possible without blocking the photogate beam. Tighten the bracket thumbscrew to secure the bracket in place.

012-05375C

Model No. ME-6830, ME-6831 Ballistic Pendulum Theory

Plumb bob

Tie a triple knot

in the end.

Thread through

the hole.

Make the string

long enough.

Vertex

Repairing the Plumb Bob

50°

Projectile Launcher

barrel

Square

Nut

T-slot

Thumbscrew

2-D Collision Accessory

Repairing the Plumb Bob

If the string breaks that holds the plumb bob on the protractor of the Launcher, replace it with an equal length of nylon thread (such as the thread included in the ME-6802 Launcher Spares Kit). Make sure that the replacement string is long enough so that when the Launcher is inclined at an angle of 50°, the string extends well below the corner of the Launcher. Carefully thread the replacement string through the small hole at the vertex of the protractor and tie a triple knot at that end of the string. To put the plumb bob onto the string, thread the string through the hole in the center of the plumb bob and tie a triple knot in that end of the string.

Installing the 2-D (two dimensional) Collision Accessory

Introduction

The 2-D (two dimensional) Collision Accessory is a plastic bar with a thumbscrew and square nut. The bar has a post and you can balance a second ball on the post in front of the muzzle. When the launched ball collides with the second ball, they experience a two dimensional (2-D) collision.

Assembly

To assemble the Collision Accessory, insert the thumbscrew through the hole in the plastic bar and screw the square nut onto the thumbscrew. Leave the square nut loose on the thumbscrew until you install the Collision Accessory onto the Launcher.

To install the Collision Accessory onto the Launcher, slide the square nut into the T-shaped slot on the bottom side of the barrel. Adjust the position of the Collision Accessory and then tighten the thumbscrew. Place a ball on the top of the post, loosen the thumbscrew slightly, and rotate the Collision Accessory to one side or the other until the ball on the post is in a place where it will be hit by the launched ball at the angle that you want.

Expectations for the Projectile Launcher

• The muzzle speed will vary slightly with angle. The difference between muzzle speed when shot horizontally versus vertically can be between zero to eight percent, depending on the range setting.

• Although the muzzle end of the Projectile Launcher does not change height with angle, it is about 30 centimeters (12 inches) above table level. If you desire to show that projectiles fired with the same muzzle speed but at complementary angles will have the same range, you need to shoot to a horizontal target that is at the same height as the muzzle.

• The scatter pattern of projectiles with the Projectile Launcher is minimized when the Projectile Launcher is securely clamped to a sturdy table. Any wobble in the table will show up in the data.

• The angle of inclination can be determined to within one-half of a degree.

Expectations for the Ballistic Pendulum

• Angles reached by the swinging pendulum should be repeatable to within half a degree.

012-05375C 9

Ballistic Pendulum / Projectile Launcher Ballistic Pendulum Theory

• Overall error in measurement of ball velocity should not exceed 2.5% (exact method) or 10% (approximate method).

• NOTE: Adjustable leveling feet are not necessary for good results. Small deviations from the horizontal will not cause significant error.

012-05375C

Model No. ME-6830 Exp. 1: Projectile Motion

1 2

-- -

----- -=

yy0v0sint

1 2

-- -

–+=

Exp. 1: Projectile Motion

Equipment Needed

Item Item

Projectile Launcher and plastic ball Plumb bob and string Meter stick Carbon paper White paper Sticky tape

Purpose

The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial speed of the ball is determined by shooting it horizontally and measuring the range of the ball and the height of the Launcher.

Theory

T o predict where a ball will land on the floor when it is shot from the Launcher at some angle above the horizontal, it is first necessary to determine the initial speed (muzzle velocity) of the ball. That can be determined by shooting the ball horizontally from the Launcher and measuring the vertical and horizontal distances that the ball travels. The initial speed can be used to calculate where the ball will land when the ball is shot at an angle above the horizontal.

• NOTE: For rest results, see the notes on “Repeatable Results” in the Introduction.

Initial Horizontal Speed

For a ball shot horizontally with an initial speed, v

, the horizontal distance travelled by the ball is given by x = v0t,

where t is the time the ball is in the air. (Neglect air friction.)

The vertical distance of the ball is the distance it drops in time t given by:

The initial speed can by determined by measuring x and y. The time of flight, t, of the ball can be found using

and the initial horizontal speed can be found using .

Initial Speed at an Angle

To predict the horizontal range, x, of a ball shot with an initial speed, v

, at an angle, , above the horizontal, first

predict the time of flight from the equation for the vertical motion:

where y the quadratic equation for t and then use x = v

is the initial height of the ball and y is the position of the ball when it hits the floor. In other words, solve

cost where v0 cos is the horizontal component of the initial

speed.

Setup

1. Put the Launcher in the top position on the Ballistic Pendulum upright. Clamp the Ballist ic Pendulum/Projectile Launcher to a sturdy table or other horizontal surface. Mount the Launcher near one end of the table and aimed away from the table.

012-05375C 11

Projectile Launcher Exp. 1: Projectile Motion

Bottom

of ball

AB– AB+

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

x100

2. Adjust the angle of the Projectile Launcher to zero degrees so the ball will by launched horizontally.

Part A: Determining the Initial Horizontal Speed of the Ball

1. Put a plastic ball in the Projectile Launcher and use the ramrod to cock it at the long range position. Fire one shot to locate where the ball hits the floor. At that point, tape a piece of white paper to the floor. Place a piece of carbon paper (carbon-side down) on top of the white paper and tape it in place.

• When the ball hits the carbon paper on the floor, it will leave a mark on the white paper.

2. Fire ten shots.

3. Measure the vertical distance from the bottom of the ball as it leaves the barrel to the

floor. Record this distance in the Data Table.

• The “Launch Position of Ball” in the barrel is marked on the label on the side of the Launcher.

4. Use a plumb bob to find the point on the floor that is directly beneath the release point on the barrel. Measure the horizontal distance along the floor from the release point to the leading edge of the piece of white paper. Record the distance in the Data Table.

5. Carefully remove the carbon paper and measure from the leading edge of the white paper to each of the ten dots. Record these distances in the Data Table and find the average. Calculate and record the total horizontal distance (distance to paper plus average distance from edge of paper to dots).

6. Using the vertical distance, y, and the total horizontal distance, x, calculate the time of flight, t, and the initial horizontal speed of the ball, v

. Record the time and speed in the Data Table.

Part B: Predicting the Range of a Ball Shot at an Angle

1. Adjust the angle of the Projectile Launcher to an angle between 30 and 60 degrees. Record this angle in the second Data Table.

2. Using the initial speed and vertical distance from the first part of this experiment, calculate the new time of flight and the new horizontal distance based on the assumption that the ball is shot at the new angle you have just selected. Record the predictions in the second Data Table.

3. Draw a line across the middle of a white piece of paper and tape the paper on the floor so that the line on the paper is at the predicted horizontal distance from the Projectile Launcher. Cover the white paper with carbon paper (carbon side down) and tape the carbon paper in place.

4. Shoot the ball ten times.

5. Carefully remove the carbon paper. Measure the distances to the ten dots and record the distances in the sec-

ond Data Table.

Analysis

1. Calculate the percent difference between the predicted theoretical distance (“A”) and the actual average distance (“B”) when shot at an angle.

2. Estimate the precision of the predicted range. How many of the final 10 shots landed within this range?

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Model No. ME-6830 Exp. 1: Projectile Motion

Data Table A: Determine the Initial Speed

Vertical distance = __________ ___ Horizontal distance to edge of paper = _________________

Calculated time of flight = ________________ Initial speed = _____________

Trial Distance

1 2 3 4 5 6 7 8 9

Average

Total Distance

Data Table B: Predict the Range

Angle above horizontal = _____________ Horizontal distance to edge of paper = _________________

Calculated time of flight = ________________ Predicted range = _____________

Trial Distance

1 2 3 4 5 6 7 8 9

Average

Total Distance

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Projectile Launcher Exp. 1: Projectile Motion

Notes

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Model No. ME-6830 Exp. 2: Projectile Motion Usin g Photogates

yy0v0sint

1 2

-- -

–+=

Exp. 2: Projectile Motion Using Photogates

Equipment Needed

Item Item

Projectile Launcher and plastic ball Plumb bob and string Photogate Head ME-9498A (2) Photogate Mounting Bracket ME-6821A PASCO Interface or Timer* PASCO Data acquisition software* Meter stick Carbon paper White paper Sticky tape

*See the PASCO web site at www.pasco.com for information about PASCO interfaces, timers, and data acquisition software.

Purpose

The purpose of this experiment is to predict and verify the range of a ball launched at an angle. Photogates are used to determine the initial speed of the ball.

Theory

T o predict where a ball will land on the floor when it is shot from the Launcher at some angle above the horizontal, it is first necessary to determine the initial speed (muzzle velocity) of the ball. The speed can be determined by shooting the ball and measuring a time using photogates. To predict the range, x, of the ball when it is shot with an initial speed at an angle, , above the horizontal, first predict the time of flight using the equation for the vertical motion:

where y equation to find the time, t. Use x = (v

is the initial height of the ball and y is the position of the ball when it hits the floor. Solve the quadratic

cos  t to predict the range.

• NOTE: For best results, see the notes on “Repeatable Results” in the Introduction.

Setup

2. Adjust the angle of the Projectile Launcher to an angle between 30 and 60 degrees and record the angle.

3. Attach the photogate mounting bracket to the Launcher and attach two photogates to the bracket. Check that

the distance between the photogates is 0.10 m (10 cm).

4. Plug the photogates into an interface or a timer.

Procedure

Part A: Determining the Initial Speed of the Ball

1. Put a plastic ball in the Projectile Launcher and use the ramrod to cock it at the long range position.

2. Setup the data acquisition software or the timer to measure the time between the ball blocking the two photo-

gates.

3. Shoot the ball three times and calculate the average of these times. Record the data in Data Table 2.1.

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