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Pasco Scientific ME-6825, Инструкция по эксплуатации и руководство по экспериментам

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012-05479A

Mini Launcher

33

Experiment 8 (Demo): Do 30

°

 and 60

°

 Give the Same Range?

EQUIPMENT NEEDED

-Mini Launcher and steel ball

Purpose

The purpose of this demonstration is to show that the range of a ball launched at 30° is the same as one
launched at 60° if the ball is shot on a level surface.

Theory

The range is the horizontal distance, x, between the muzzle of the Launcher and the place where the ball
hits, given by x = (v

0

cos

θ

)

t where v

0

 is the initial speed of the ball as it leaves the muzzle, 

θ

 is the angle of

inclination above horizontal, and t is the time of flight.

If the ball hits on a place that is at the same level as the level of the muzzle of the launcher, the time of
flight of the ball will be twice the time it takes the ball the reach the peak of its trajectory:

where g is the acceleration due to gravity.

Substituting for t into the equation for x gives

and using a trigonometry identity gives

The ranges for the angles 30° and 60° are the same since sin(60°) = sin(120°).

Setup

➀

Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed so the ball will land on
the table. See Figure 8.1.

➁

 Adjust the angle of the Mini Launcher to 30 degrees.

➂

Put the steel ball into the Mini Launcher and cock it to the medium or long range position.

Procedure

➀

Shoot the ball at 30 degrees to find where
the ball lands.

➁

Change the angle of the Launcher to 60
degrees and shoot the ball again. Call
attention to the fact that the ball again
lands in the same place. Thus the ranges
are the same.

➂

Change the angle to 45 degrees and shoot
the ball again to show that the ball now
lands further away.

➃

Ask the question: What other pairs of angles will have a common range? This demonstration can be done
for any two angles which add up to 90 degrees: 20 and 70, or 35 and 55, etc.

x

=

2

v

0

2

sin

θ

cos

θ

g

x

=

v

0

2

sin2

θ

g

t

= 2

t

peak

= 2

v

0

sin

θ

g

90

80

70

60

50

40

30

20

10

0

10

20

30

40

MINI LAUNCHER

ME-6825

CA

U

T

I

O

N

!

W

EA

R

S

AFE

TY

G

L

A

SS

E

S

WH

E

N

 

I

N

 

U

S

E

.

D

O

N

'

T

  

PU

S

H

P

I

S

T

O

N

W

I

T

H

F

I

N

GE

R

!

Figure 8.1: Setup to shoot on level surface

Содержание ME-6825

Страница 1: ...Pen or Rod Until Piston Clicks MINI LAUNCHER ME 6825 Use 16 mm steel balls ONLY Launch Position of Ball 90 80 70 6 0 5 0 4 0 3 0 20 10 0 10 20 30 40 Third Click Long Range Second Click Medium Range First Click Short Range DO NOT LOOK DOWN BARREL CAUTION WEAR SAFETY GLASSES WHEN IN USE DO NOT PUSH PISTON WITH FINGER MINI LAUNCHER Instruction Manual and Experiment Guide for the PASCO scientific Mode...

Страница 2: ......

Страница 3: ...tions For The Mini Launcher 5 Launch Positions 6 Experiments 1 Projectile Motion 7 2 Projectile Motion Using Photogates 11 3 Projectile Range versus Angle 15 4 Projectile Path 19 5 Conservation of Energy 23 6 Conservation of Momentum in Two Dimensions 27 7 Varying Angle to Maximize Height on a Wall 31 8 Demo Do 30 and 60 Give Same Range 33 9 Demo Simultaneously Shoot Two Balls Horizontally at Diff...

Страница 4: ...sion is granted to non profit educational institu tions for reproduction of any part of this manual provid ing 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 this product to be free from defects in materials and work...

Страница 5: ...0 30 20 10 0 10 20 30 40 WEAR SAFETY GLASSES WHEN IN USE DO NOT PUSH PISTON WITH FINGER FIXED ELEVATION INDEPENDENT OF ANGLE The Mini Launcher can be mounted so that it piv ots at the muzzle end The elevation of the ball as it leaves the barrel does not change as the angle is varied REPEATABLE RESULTS There is no spin on the ball since the piston keeps the ball from rubbing on the walls as it trav...

Страница 6: ...ck Medium Range First Click Short Range DO NOT LOOK DOWN BARREL CAUTION WEAR SAFETY GLASSES WHEN IN USE DO NOT PUSH PISTON WITH FINGER Equipment The ME 6825 Mini Launcher includes the following Launcher and Base Assembled 2 16mm Steel Balls String to pull trigger Collision Attachment Safety Goggles Pushrod Manual String Base Scale Indicator Launcher Trigger Projectile Balls Safety Goggles Collisio...

Страница 7: ...hen operating the Mini Launcher Always assume that the barrel is loaded Tie the string to the trigger before loading The base of the Mini Launcher can be clamped to the edge of a table using the clamp of your choice When shooting onto the floor it is desir able to have the label side of the Launcher even with one edge of the table so a plumb bob can be used to locate the position of the muzzle wit...

Страница 8: ...he photogates To mount the bracket to the Launcher align the square nut in the slot on the bottom of the barrel and slide the nut and the post into the slot Slide the bracket back until the photogate nearest to the barrel is as close to the barrel as possible without blocking the beam Tighten the thumb screw to secure the bracket in place When storing the Mini Launcher the photogate bracket need n...

Страница 9: ...lision attachment to the Launcher the square nut slides into the T shaped channel on the bottom of the barrel See Experiment Figure 6 2 Square Nut Hex Nut Expectations for the Mini Launcher The following are helpful hints and approximate values you may find useful The muzzle speed will vary slightly with angle The difference between muzzle speed when shot horizon tally versus vertically can be any...

Страница 10: ...10 20 30 40 MINI LAUNCHER ME 6825 CAUTION WEAR SAFETY GLA SSES WHEN IN USE DON T PUSH PISTON WITH FINGER 90 80 70 60 50 40 30 20 10 0 10 20 30 40 MINI LAUNCHER ME 6825 CAUTION WEA R SA FE TY GL AS SE S WHE N IN US E DO N T PU SH PIST ON WITH FING ER Set launcher on table with or without clamp Launch ball on or off the table Clamp base to side edge of table Mount launcher as shown to shoot off tabl...

Страница 11: ...l is given by x vot where t is the time the ball is in the air Air friction is assumed to be negligible The vertical distance the ball drops in time t is given by y 1 2 gt2 The initial velocity of the ball can be determined by measuring x and y The time of flight of the ball can be found using t 2y g and then the initial velocity can be found using v0 x t INITIAL VELOCITY AT AN ANGLE To predict th...

Страница 12: ...ctly beneath the release point on the barrel Measure the horizontal distance along the floor from the release point to the leading edge of the paper Record in Table 1 1 Measure from the leading edge of the paper to each of the ten dots and record these distances in Table 1 1 Find the average of the ten distances and record the value in Table 1 1 Using the vertical distance and the average horizont...

Страница 13: ...ver the paper with carbon paper Shoot the ball ten times Measure the ten distances and take the average Record in Table 1 2 Analysis Calculate the Total Average Distance Record in Table 1 2 Total Average Distance Distance from Edge of Paper Horizontal Distance to paper edge Calculate and record the percent difference between the predicted value and the resulting average distance when shot at an an...

Страница 14: ...her Cover the paper with carbon paper Shoot the ball ten times Measure the ten distances and take the average Record in Table 1 3 Analysis Calculate the Total Average Distance Record in Table 1 3 Total Average Distance Distance from Edge of Paper Horizontal Distance to paper edge Calculate and record the percent difference between the predicted value and the resulting average distance when shot at...

Страница 15: ...unched with an initial velocity at an angle θ above the horizontal first predict the time of flight using the equation for the vertical motion y y0 v0 sinθ t 1 2 gt2 where yo is the initial height of the ball and y is the position of the ball when it hits the floor Then use x v0 cosθ t to find the range If the ball is shot at an angle below the horizontal θ is negative Setup Clamp the Mini Launche...

Страница 16: ...___________ PART B Predicting the Range of the Ball Shot at an Angle Keep the angle of the Mini Launcher at the selected angle Measure the vertical distance from the bottom of the ball as it leaves the barrel this position is marked on the side of the barrel to the floor Record this distance in Table 2 2 Using the initial velocity and vertical distance found in Part A calculate the time of flight ...

Страница 17: ...stance from Edge of Paper 1 2 3 4 5 6 7 8 9 10 Average Total Average Distance Analysis Calculate the Total Average Distance Record in Table 2 2 Total Average Distance Distance from Edge of Paper Horizontal Distance to paper edge Calculate the percent difference between the predicted value and the resulting average distance when shot at an angle Estimate the precision of the predicted range How man...

Страница 18: ...Mini Launcher 012 05479A 14 Notes ...

Страница 19: ...l lands The range is given by x v0 cosθ t where v0 is the initial speed of the ball as it leaves the muzzle θ is the angle of inclination above horizontal and t is the time of flight See figure 3 1 For the case in which the ball lands at the same elevation from which it was launched the time of flight of the ball will be twice the time it takes the ball the reach the peak of its trajectory At the ...

Страница 20: ...At this position tape a piece of white paper to the table Place a piece of carbon paper carbon side down on top of this paper and tape it down When the ball hits the table it will leave a mark on the white paper Fire about five shots Measure the horizontal distance from the launch position of the ball to the leading edge of the paper Record in Table 3 1 Measure from the leading edge of the paper t...

Страница 21: ...l distance range in each case Record in Tables 3 1 and 3 2 For each data table plot the range vs angle and draw a smooth curve through the points Questions From the graph what angle gives the maximum range for each case Is the angle for the maximum range greater or less for shooting off the table Is the maximum range further when the ball is shot off the table or on the level surface Table 3 2 Sho...

Страница 22: ...Mini Launcher 012 05479A 18 Notes ...

Страница 23: ...he ball will be t x v0 The vertical distance y that the ball falls in time t is given by y 1 2 gt2 where g is the acceleration due to gravity Substituting for t into the equation for y gives y g 2v0 2 x2 A plot of y versus x2 will give a straight line with a slope equal to g 2v0 2 Setup Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed away from the table Adjust the an...

Страница 24: ..._____ Analysis On the target measure the vertical distances from the muzzle level mark down to the ball marks and record in Table 4 1 Calculate x2 for all the data points and record in Table 4 1 Plot y vs x2 and draw the best fit straight line Calculate the slope of the graph and record in Table 4 2 From the slope of the graph calculate the initial speed of the ball as it leaves the muzzle and rec...

Страница 25: ...flight Initial speed from x y Percent Difference Table 4 2 Initial Speed Questions Was the line straight What does this tell you about the relationship between y and x If you plotted y vs x how would the graph differ from the y vs x2 graph What shape is the path of a projectile ...

Страница 26: ...Mini Launcher 012 05479A 22 Notes ...

Страница 27: ...er mined To calculate the initial velocity v0 for a ball shot horizon tally off a table the horizontal distance travelled by the ball is given by x v0 t where t is the time the ball is in the air Air friction is assumed to be negligible See Figure 5 2 The vertical distance the ball drops in time t is given by y 1 2 gt2 The initial velocity of the ball can be determined by measuring x and y The tim...

Страница 28: ...rked on the side of the barrel to the floor Record this distance in Table 5 1 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 paper Record in Table 5 1 Measure from the leading edge of the paper to each of the ten dots and record these distances ...

Страница 29: ...e of these times Record in Table 5 2 The distance between the photogates is 10 cm Calculate the initial speed of the ball and record it in Table 5 2 Table 5 2 Initial Speed Using Photogates MEASURING THE HEIGHT Adjust the angle of the Launcher to 90 degrees straight up Shoot the ball on the chosen range setting several times and measure the maximum height at tained by the ball Record in Table 5 3 ...

Страница 30: ...Results Maximuim Height of Ball Mass of Ball Initial Kinetic Energy Final Potential Energy Percent Difference Questions How does friction affect the result for the kinetic energy How does friction affect the result for the potential energy ...

Страница 31: ...onserved in horizontal plane Before the collision since all the momentum is in the direction of the velocity of Ball 1 it is convenient to define the x axis along this direction Then the momentum before the collision is Pbefore m1v0 x and the momentum after the collision is Pafter m1v1x m2v2x x m1v1y m2v2y y where v1x v1 cosθ1 v1y v1 sinθ1 v2x v2 cosθ2 and v2y v2 sinθ2 Since there is no net moment...

Страница 32: ...Using two balls load one ball and put the other ball on the tee Shoot the ball five times Inelastic collision Using two balls load one ball and stick a very small loop of tape onto the tee ball Orient the tape side of the tee ball so it will be struck by the launched ball causing an inelastic collision Shoot the ball once and if the balls miss the carbon paper relocate the carbon paper and shoot o...

Страница 33: ...percent difference Record the results in the Tables Questions Was momentum conserved in the x direction for each type of collision Was momentum conserved in the y direction for each type of collision Was energy conserved for the elastic collision Was energy conserved for the inelastic collision For the elastic collision was the angle between the paths of the balls after the collision equal to 90 d...

Страница 34: ...Mini Launcher 012 05479A 30 Notes ...

Страница 35: ...by x v0 cosθ t Solving for the time of flight from the equation for x gives t x v0 cosθ Substituting for t in the equation for y gives y y0 x tanθ gx2 2v0 2 cos2θ To find the angle that gives the maximum height y set dy dθ equal to zero and solve for the angle dy dθ x sec2θ gx2 tanθ sec2θ v0 2 0 Solving for the angle gives tanθmax v0 2 gx Since the second derivative is negative for θmax the angle ...

Страница 36: ...l velocity by solving the y equation for v0 and plugging in the values from Table 7 1 Calculate the angle for maximum height using the initial velocity calculated in Step 1 and the horizontal distance from the wall to the launcher Calculate the percent difference between the measured angle and the calculated angle Questions For the angle at which the ball strikes the wall at the maximum height has...

Страница 37: ... The ranges for the angles 30 and 60 are the same since sin 60 sin 120 Setup Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed so the ball will land on the table See Figure 8 1 Adjust the angle of the Mini Launcher to 30 degrees Put the steel ball into the Mini Launcher and cock it to the medium or long range position Procedure Shoot the ball at 30 degrees to find wher...

Страница 38: ...ce the ball falls since y 1 2 gt2 Since the vertical distance is the same for each ball the time of flight must be the same for each ball Setup Clamp two Mini Launchers adjacent to each other on a sturdy table The Launchers should both be aimed in the same direction away from the table so the balls will land on the floor Adjust the angle of each Mini Launcher to zero degrees so the balls will be s...

Страница 39: ...tical position y of the ball at time t is given by y y0 1 2 gt2 where y0 is the initial height of the ball and g is the acceleration due to gravity Setup Before the demonstration begins find the initial velocity for the range setting to be used Attach the photogates and use a computer to find the initial velocity or shoot the ball horizontally and measure x and y to find the ini tial velocity See ...

Страница 40: ... 10 1 Placing the rings Calculate the horizontal and vertical positions of the ball each 1 10 second until it hits the floor Lay the 2 meter stick on the floor in a straight line away from the Launcher Measure off each set of x and y and place a ring clamp on a stand at each position See Figure 10 1 If possible it is best to adjust the last two ring stands at an angle from the vertical so the ball...

Страница 41: ...d be helpful to prepare the following information If your problem is computer software related note Title and Revision Date of software Type of Computer Make Model Speed Type of external Cables Peripherals 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 ...

Страница 42: ......

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