Page 2 - ii
® ii 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 experiments and can also be used for projectile motion experiments and demonstrations. When ...
Page 3 - iii; T a b l e o f C o n t e n t s; EXPERIMENTS
® iii T a b l e o f C o n t e n t s Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2...
Page 4 - P r o j e c t i l e L a u n c h e r; iv
® P r o j e c t i l e L a u n c h e r iv 012-05375C
Page 5 - B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r; E q u i p m e n t; The ME-6831 Ballistic Pendulum does; not; include the Short Range
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r M E - 6 8 3 0 , M E - 6 8 3 1 ® 1 E q u i p m e n t The ME-6830 Ballistic Pendulum / Projectile Launcher includes the following: *The ME-6802 Launcher Spares Kit includes: Ramrod (2), Plastic Balls (10-pack), 2-D Collision Acces...
Page 6 - A s s e m b l y; I n t r o d u c t i o n; Reliable Ball-Catcher Mechanism; Assemble the Base
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r A s s e m b l y ® 2 012-05375C A s s e m b l y 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,...
Page 7 - Three Range Settings:; The Projectile Launcher can pivot at the muzzle end so the; Barrel Sights and Safety Precautions:; There are sites built-in to the barrel for; Compact Storage; Wear Safety Glasses
® M o d e l N o . M E - 6 8 3 0 , M E - 6 8 3 1 I n t r o d u c t i o n 0 1 2 - 0 5 3 7 5 C 3 • 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 ...
Page 8 - G e n e r a l O p e r a t i o n o f t h e P r o j e c t i l e L a u n c h e r; Parts; Launcher Parts
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r G e n e r a l O p e r a t i o n o f t h e P r o j e c t i l e L a u n c h e r ® 4 012-05375C G e n e r a l O p e r a t i o n o f t h e P r o j e c t i l e L a u n c h e r Parts Ready • Attach the included Trigger String to the h...
Page 9 - Aim; Never look down the barrel; ! To check whether the Launcher is loaded,; Shoot; Before shooting the ball, make certain that no one is in the way.; Maintenance and Storage; Bore Sights; Front
® M o d e l N o . M E - 6 8 3 0 , M E - 6 8 3 1 G e n e r a l O p e r a t i o n o f t h e P r o j e c t i l e L a u n c h e r 0 1 2 - 0 5 3 7 5 C 5 Aim • If you have the Launcher mounted on the top position, you can adjust the angle of inclination above the hori-zontal by loosening the two thumbscre...
Page 10 - B a l l i s t i c P e n d u l u m T h e o r y; Overview
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r B a l l i s t i c P e n d u l u m T h e o r y ® 6 012-05375C B a l l i s t i c P e n d u l u m T h e o r y Overview The ballistic pendulum is a classic method of determining the velocity of a projectile. It is also a good demons...
Page 11 - B a l l i s t i c P e n d u l u m T h e o r y; Exact Method; Figure 1
® M o d e l N o . M E - 6 8 3 0 , M E - 6 8 3 1 B a l l i s t i c P e n d u l u m T h e o r y 0 1 2 - 0 5 3 7 5 C 7 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...
Page 12 - M g; M g R; M g R; M g R; Install the Optional Photogate Bracket
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r B a l l i s t i c P e n d u l u m T h e o r y ® 8 012-05375C 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 fo...
Page 13 - Introduction; Expectations for the Projectile Launcher; Repairing the Plumb Bob
® M o d e l N o . M E - 6 8 3 0 , M E - 6 8 3 1 B a l l i s t i c P e n d u l u m T h e o r y 0 1 2 - 0 5 3 7 5 C 9 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...
Page 15 - E x p . 1 : P r o j e c t i l e M o t i o n; Equipment Needed; Purpose; Initial Horizontal Speed; cos; Setup; Item; g t
® M o d e l N o . M E - 6 8 3 0 E x p . 1 : P r o j e c t i l e M o t i o n 0 1 2 - 0 5 3 7 5 C 11 E x p . 1 : P r o j e c t i l e M o t i o n Equipment Needed 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 d...
Page 16 - Part A: Determining the Initial Horizontal Speed of the Ball; Using the vertical distance,; Part B: Predicting the Range of a Ball Shot at an Angle; Shoot the ball ten times.; Analysis; Bottom
P r o j e c t i l e L a u n c h e r E x p . 1 : P r o j e c t i l e M o t i o n ® 12 012-05375C 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 Projecti...
Page 17 - Data Table A: Determine the Initial Speed
® M o d e l N o . M E - 6 8 3 0 E x p . 1 : P r o j e c t i l e M o t i o n 0 1 2 - 0 5 3 7 5 C 13 Data Table A: Determine the Initial Speed Vertical distance = _____________ Horizontal distance to edge of paper = _________________ Calculated time of flight = ________________ Initial speed = _______...
Page 18 - Notes
P r o j e c t i l e L a u n c h e r E x p . 1 : P r o j e c t i l e M o t i o n ® 14 012-05375C Notes
Page 19 - E x p . 2 : P r o j e c t i l e M o t i o n U s i n g P h o t o g a t e s; Part A: Determining the Initial Speed of the Ball
® M o d e l N o . M E - 6 8 3 0 E x p . 2 : P r o j e c t i l e M o t i o n U s i n g P h o t o g a t e s 0 1 2 - 0 5 3 7 5 C 15 E x p . 2 : P r o j e c t i l e M o t i o n U s i n g P h o t o g a t e s Equipment Needed *See the PASCO web site at www.pasco.com for information about PASCO interfaces,...
Page 20 - Use the time of flight,; sin
P r o j e c t i l e L a u n c h e r E x p . 2 : P r o j e c t i l e M o t i o n U s i n g P h o t o g a t e s ® 16 012-05375C 4. Calculate the initial speed of the ball based on the 0.10 m distance between the photogates. Record the value. Data Table: Part A Part B: Predicting the Range of a Ball Sh...
Page 23 - E x p . 3 : P r o j e c t i l e R a n g e v e r s u s A n g l e
® M o d e l N o . M E - 6 8 3 0 E x p . 3 : P r o j e c t i l e R a n g e v e r s u s A n g l e 0 1 2 - 0 5 3 7 5 C 19 E x p . 3 : P r o j e c t i l e R a n g e v e r s u s A n g l e Equipment Needed Purpose The purpose of this experiment is to determine how the range of the ball depends on the laun...
Page 24 - Procedure; Part A: Shooting to a Level Surface; Increase the launch angle by 10 degrees and repeat all the steps.; Part B: Shooting Off the Table; Horizont
P r o j e c t i l e L a u n c h e r E x p . 3 : P r o j e c t i l e R a n g e v e r s u s A n g l e ® 20 012-05375C 2. Adjust the angle of the Projectile Launcher to 10 degrees. 3. Put a plastic ball into the Projectile Launcher and cock it to the medium or long range setting. • Note: In general, th...
Page 25 - From the graph, what angle give the maximum range for each case?; Ho
® M o d e l N o . M E - 6 8 3 0 E x p . 3 : P r o j e c t i l e R a n g e v e r s u s A n g l e 0 1 2 - 0 5 3 7 5 C 21 2. Repeat the procedure and record the data in the Data Table. Analysis 1. Find the average of the five distances in each case and record the results in the Data Tables. 2. Add the ...
Page 27 - E x p . 4 : P r o j e c t i l e P a t h; Target board
® M o d e l N o . M E - 6 8 3 0 E x p . 4 : P r o j e c t i l e P a t h 0 1 2 - 0 5 3 7 5 C 23 E x p . 4 : P r o j e c t i l e P a t h Equipment Needed *The target board should be as tall as the distance from the muzzle to the floor. Purpose The purpose of this experiment is to determine how the ver...
Page 28 - Move the target board about 10 to 20 cm closer to the Launcher.; Calculate the slope of the graph and record it in Table 4.2.
P r o j e c t i l e L a u n c h e r E x p . 4 : P r o j e c t i l e P a t h ® 24 012-05375C 4. Cover the target board with white paper. Tape carbon paper over the white paper. Procedure 1. Measure the vertical height from the floor to the muzzle and record the height in the Table 4.1. Mark this heig...
Page 29 - Question; What does the shape of the best-fit line on the y versus x
® M o d e l N o . M E - 6 8 3 0 E x p . 4 : P r o j e c t i l e P a t h 0 1 2 - 0 5 3 7 5 C 25 7. Calculate the percent difference between the two initial speeds that were found using the different methods. Record the percent difference in Table 4.2. (To calculate the percent difference, let A be on...
Page 31 - E x p . 5 : C o n s e r v a t i o n o f E n e r g y; final; K E
® M o d e l N o . M E - 6 8 3 0 E x p . 5 : C o n s e r v a t i o n o f E n e r g y 0 1 2 - 0 5 3 7 5 C 27 E x p . 5 : C o n s e r v a t i o n o f E n e r g y Equipment Needed *Use the Photogates and Photogate Mounting Bracket with a PASCO Interface or Timer to measure the initial speed of the ball ...
Page 32 - Find the average of the ten distances and record it.
P r o j e c t i l e L a u n c h e r E x p . 5 : C o n s e r v a t i o n o f E n e r g y ® 28 012-05375C Setup 1. Clamp the Projectile Launcher to a sturdy table or other horizontal surface. Mount the Launcher near one end of the table with the Launcher aimed away from the table. 2. Point the Launche...
Page 34 - Part B: Measure the Height of the Ball; Adjust the angle of the Launcher to 90 degrees (straight up).; Calculate the initial kinetic energy and record it in Table 5.3.; Questions
P r o j e c t i l e L a u n c h e r E x p . 5 : C o n s e r v a t i o n o f E n e r g y ® 30 012-05375C Part B: Measure the Height of the Ball 1. Adjust the angle of the Launcher to 90 degrees (straight up). 2. Shoot the ball on the medium range setting several times and then measure the maximum hei...
Page 35 - E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m
® M o d e l N o . M E - 6 8 3 0 E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m 0 1 2 - 0 5 3 7 5 C 31 E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m Equipment Needed Purpose The purpose of this experiment is to confirm that momentum is conserved for elastic and inelastic collisions...
Page 36 - Tighten the thumbscrew to hold the accessory in place.; Shoot the ball straight ahead and repeat the procedure five times.; C. Inelastic Collision; Target
P r o j e c t i l e L a u n c h e r E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m ® 32 012-05375C Setup 1. Clamp the Projectile Launcher to a sturdy table. Mount the Launcher near one end of the table with the Launcher aimed inward toward the table. 2. Adjust the angle of the Projectile La...
Page 37 - Draw a straight line from the “point-of-contact” through the
® M o d e l N o . M E - 6 8 3 0 E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m 0 1 2 - 0 5 3 7 5 C 33 • Since the tape does not produce the same inelastic collision each time, it is only useful to record this collision once. 5. Use a plumb bob to locate on the paper the spot directly below ...
Page 38 - Calculate the percent differences.; Was kinetic energy conserved for the elastic collision?
P r o j e c t i l e L a u n c h e r E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m ® 34 012-05375C C. Inelastic Collision 1. Draw straight lines from the “point-of-contact” spot to the dots made by the ‘inelastic collision’ shot. (There should be two lines.) 2. Measure from the “point-of-co...
Page 39 - E x p . 7 : V a r y t h e A n g l e t o M a x i m i z e t h e H e i g h t; E x p . 7 : Va r y t h e A n g l e t o M a x i m i z e t h e H e i g h t; DOWN THE; g x
® M o d e l N o . M E - 6 8 3 0 E x p . 7 : V a r y t h e A n g l e t o M a x i m i z e t h e H e i g h t 0 1 2 - 0 5 3 7 5 C 35 E x p . 7 : Va r y t h e A n g l e t o M a x i m i z e t h e H e i g h t Equipment Needed Purpose The purpose of this experiment is to find the launch angle that will maxi...
Page 40 - Measure the maximum height and record the value in the Data Table.; Calculate the initial speed by solving the y-equation for v; D i f f e r e n c e
P r o j e c t i l e L a u n c h e r E x p . 7 : V a r y t h e A n g l e t o M a x i m i z e t h e H e i g h t ® 36 012-05375C Setup 1. Clamp the Projectile Launcher to a sturdy table. Mount the Launcher near one end of the table with the Launcher aimed toward a wall about 2 meters from the table. 2....
Page 41 - E x p . 8 : P r o j e c t i l e V e l o c i t y — A p p r o x i m a t e M e t h o d; E x p . 8 : P r o j e c t i l e Ve l o c i t y — A p p r o x i m a t e M e t h o d; g R; String loop
® M o d e l N o . M E - 6 8 3 0 E x p . 8 : P r o j e c t i l e V e l o c i t y — A p p r o x i m a t e M e t h o d 0 1 2 - 0 5 3 7 5 C 37 E x p . 8 : P r o j e c t i l e Ve l o c i t y — A p p r o x i m a t e M e t h o d Equipment Needed Purpose The muzzle velocity of the projectile launcher is det...
Page 42 - Calculations; How does the angle reached by the pendulum change if the ball is
P r o j e c t i l e L a u n c h e r E x p . 8 : P r o j e c t i l e V e l o c i t y — A p p r o x i m a t e M e t h o d ® 38 012-05375C • NOTE: It may be easier to balance the pendulum on the edge of a ruler or similar object. 5. Reattach the pendulum to the upright, making sure that it is facing th...
Page 43 - E x p . 9 : P r o j e c t i l e V e l o c i t y — E x a c t M e t h o d; E x p . 9 : P r o j e c t i l e Ve l o c i t y — E x a c t M e t h o d; m R
® M o d e l N o . M E - 6 8 3 0 E x p . 9 : P r o j e c t i l e V e l o c i t y — E x a c t M e t h o d 0 1 2 - 0 5 3 7 5 C 39 E x p . 9 : P r o j e c t i l e Ve l o c i t y — E x a c t M e t h o d Equipment Needed Purpose The muzzle velocity of the projectile launcher is determined by launching the...
Page 44 - Calculate the value of
P r o j e c t i l e L a u n c h e r E x p . 9 : P r o j e c t i l e V e l o c i t y — E x a c t M e t h o d ® 40 012-05375C 5. Tie a loop in a piece of string, and hang the pendulum horizontally from the loop. (See Figure 9.1.) With the ball latched in position in the ball catcher, adjust the positi...
Page 47 - E x p . 1 0 ( D e m o ) : D o 3 0 ° a n d 6 0 ° G i v e t h e S a m e R a n g e ?; Box
® M o d e l N o . M E - 6 8 3 0 E x p . 1 0 ( D e m o ) : D o 3 0 ° a n d 6 0 ° G i v e t h e S a m e R a n g e ? 0 1 2 - 0 5 3 7 5 C 43 E x p . 1 0 ( D e m o ) : D o 3 0 ° a n d 6 0 ° G i v e t h e S a m e R a n g e ? Equipment Needed Purpose The purpose of this demonstration is to confirm that the...
Page 49 - E x p . 1 1 ( D e m o ) : S i m u l t a n e o u s S h o t s a t D i f f e r e n t S p e e d s; E x p . 11 ( D e m o ) : S i m u l ta n e o u s S h o ts a t D i f f e r e n t Sp e e d s; Two projectiles are shot horizontally from the same height,
® M o d e l N o . M E - 6 8 3 0 E x p . 1 1 ( D e m o ) : S i m u l t a n e o u s S h o t s a t D i f f e r e n t S p e e d s 0 1 2 - 0 5 3 7 5 C 45 E x p . 11 ( D e m o ) : S i m u l ta n e o u s S h o ts a t D i f f e r e n t Sp e e d s Equipment Needed Purpose The purpose of this demonstration is...
Page 51 - ax
® M o d e l N o . M E - 6 8 3 0 E x p . 1 2 ( D e m o ) : S h o o t i n g T h r o u g h H o o p s 0 1 2 - 0 5 3 7 5 C 47 E x p . 1 2 ( D e m o ) : S h o o t i n g T h r o u g h H o o ps Equipment Needed Purpose The purpose of this demonstration is to confirm that the part of a projectile is paraboli...
Page 53 - E x p . 1 3 ( D e m o ) : E l a s t i c a n d I n e l a s t i c C o l l i s i o n s; Shoot the ball into the pendulum and record the angle reached.
® M o d e l N o . M E - 6 8 3 0 E x p . 1 3 ( D e m o ) : E l a s t i c a n d I n e l a s t i c C o l l i s i o n s 0 1 2 - 0 5 3 7 5 C 49 E x p . 1 3 ( D e m o ) : E l a s t i c a n d I n e l a s t i c C o l l i s i o n s Equipment Needed Purpose The purpose of this demonstration is to show the dif...
Page 55 - T e a c h e r ’ s G u i d e; Te a c h e r ’s G u i d e; Exp. 2: Projectile Motion Using Photogates
® M o d e l N o . M E - 6 8 3 0 T e a c h e r ’ s G u i d e 0 1 2 - 0 5 3 7 5 C 51 Te a c h e r ’s G u i d e Exp. 1: Projectile Motion NOTE: For best results, make sure that the Launcher is securely clamped to a sturdy table. Any movement of the Launcher will result in inconsistent data. The muzzle ...
Page 56 - Shooting off a level surface:; The angle of maximum range decreases with table height.; Alternately, measure your distances from the ground up.
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r T e a c h e r ’ s G u i d e ® 52 012-05375C Exp. 3: Projectile Range Versus Angle Procedure • Shooting off a level surface: • Shooting off a table: • NOTE: The curves show the calculated ranges in each case. The data points are ...
Page 57 - Yes. This tells us that y is a function of x; The energy difference was 8.5% of the original kinetic energy.; Horizontal Distance
® M o d e l N o . M E - 6 8 3 0 T e a c h e r ’ s G u i d e 0 1 2 - 0 5 3 7 5 C 53 2. Vertical distances were measured from the ground up for this graph. The intercept is the height of the launcher above the ground when done this way. 3. The slope (measuring from the ground) is -0.118 for this examp...
Page 58 - Exp. 6: Conservation of Momentum in Two Dimensions
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r T e a c h e r ’ s G u i d e ® 54 012-05375C Exp. 6: Conservation of Momentum in Two Dimensions Setup • If possible, use medium range setting instead of the short range setting. The medium range setting gives more predictable res...
Page 59 - Exp. 8: Projectile Motion—Approximate Method
® M o d e l N o . M E - 6 8 3 0 T e a c h e r ’ s G u i d e 0 1 2 - 0 5 3 7 5 C 55 • substitute • Substitute • and simplify: • When x = x max , the value of this derivative is negative. • Therefore, the ball has already reached the peak and is on its way down. 2. Solve the equation for maximum angle...
Page 60 - Sources of error include friction and measurement error.
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r T e a c h e r ’ s G u i d e ® 56 012-05375C Calculations • Use the equations given in the theory section for the approximate method. Questions 1. The best other method of measuring velocity is described in the first part of expe...
Page 61 - T e c h n i c a l S u p p o r t; Te c h n i c a l S u p p o r t; For assistance with any PASCO product, contact PASCO at:; Address: PASCO scientific
® M o d e l N o . M E - 6 8 3 0 T e c h n i c a l S u p p o r t 0 1 2 - 0 5 3 7 5 C 57 Te c h n i c a l S u p p o r t For assistance with any PASCO product, contact PASCO at: For more information about the Ballistic Pendulum/Projectile Launcher and the latest revision of this Instruction Manual, vis...
