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012-05479B

Mini Launcher

13

®

Table 2.2 Confirming the Predicted Range

Angle above or below horizontal = ______________

Horizontal distance to paper edge = ____________

Calculated time of flight= ____________

Predicted Range = ____________

Trial Number

Distance from Edge of Paper

1

2

3

4

5

6

7

8

9

10

Average

Total Average Distance

Analysis

➀

Calculate the Total Average Distance. Record in Table 2.2.
(Total Average Distance = Distance from Edge of Paper + Horizontal Distance to paper
edge)

➁

Calculate the percent difference between the predicted value and the resulting average
distance when shot at an angle.

➂

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

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Содержание MINI LAUNCHER ME-6825A

Страница 1: ...on 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 Model ME 6825A ...

Страница 2: ...her 5 LaunchPositions 6 Experiments 1 ProjectileMotion 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 HorizontallyatDifferentSpeeds 34 10 Demo Shoot...

Страница 3: ... angle is 45 degrees and measured from table top to table top 90 80 7 0 6 0 5 0 40 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 pivots 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 ...

Страница 4: ...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 Angle Indicator Launcher Trigger Projectile Balls Safety Goggles Collisio...

Страница 5: ... your choice When shooting onto the floor it is de sirable 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 with respect to the floor See page 6 for mounting options The Mini Launcher can be mounted to shoot onto the table such that the launch position of the ball is at the same height as the table NOTE To preven...

Страница 6: ...racket and the screws pro vided with the photogates To mount the bracket to the Launcher align the square nut in the slot on the bottom of the Launcher and slide the nut into the slot Slide the bracket back until the photogate nearest to the bar rel is as close to the barrel as possible without blocking the beam Tighten the thumb screw to se cure the bracket in place When storing the Mini Launcher...

Страница 7: ...ision attachment to the Launcher the square nut slides into the T shaped channel on the bottom of the Launcher 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 horizontally versus vertically can be any...

Страница 8: ... onto table Ball is launched from a height above table level Clamp base to table Mount launcher as shown to shoot onto table The square nut that the Launcher pivots around should be slid to the front of the launcher Ball is launched at table level When you change the angle of the launcher the launch position does not change Clamp base to a vertical rod Place base on a tabletop or floor and hold it...

Страница 9: ... initial speed vo the horizontal distance travelled by the ball is given by x vot where t is the time the ball is in the air Air friction is assumed to be negli gible The vertical distance the ball drops in time t is given by y y0 v0 sinq t 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 v...

Страница 10: ...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 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 di...

Страница 11: ...tance from the Mini Launcher Cover 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 aver...

Страница 12: ...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 13: ...peed using photogates To predict the range x of the ball when it is launched 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 sinq 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...

Страница 14: ...___________ 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 15: ...tance 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 many...

Страница 16: ...MiniLauncher 012 05479B 14 Notes ...

Страница 17: ...e the ball 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 horizon tal 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 trajecto...

Страница 18: ...egrees Put the steel ball into the Mini Launcher and cock it to the chosen position Procedure SHOOTING ON A LEVEL SUR FACE Fire one shot to locate where the ball hits the table 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 ...

Страница 19: ...se Àand record in Tables 3 1 and 3 2 Add the average distance to the distance to the leading edge of the paper to find the total 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 fo...

Страница 20: ...MiniLauncher 012 05479B 18 Notes ...

Страница 21: ...ime of flight of the 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 t...

Страница 22: ...of Muzzle _____________ 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 ...

Страница 23: ...light 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 24: ...MiniLauncher 012 05479B 22 Notes ...

Страница 25: ...qual to the final PE To calculate the kinetic energy the initial velocity must be determined To calculate the initial velocity v0 for a ball shot horizontally 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 ...

Страница 26: ...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 dis tances...

Страница 27: ...ge 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 MEASURINGTHEHEIGHT 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 attained by the ball Record in Table 5 3 De...

Страница 28: ...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 29: ... served in horizontal plane Before the collision since all the momen tum 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 sin 2 Since there is no net moment...

Страница 30: ...n 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...

Страница 31: ...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 32: ...MiniLauncher 012 05479B 30 Notes ...

Страница 33: ...en 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 tanq gx2 2v0 2 cos2q To find the angle that gives the maximum height y set dy dθ equal to zero and solve for the angle y y0 v0 sinq t 1 2 gt2 Solving for the angle gives tanθmax v0 2 gx Since the second derivative is negative for θmax the angle is a maxim...

Страница 34: ...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 35: ... 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 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...

Страница 36: ... 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 sho...

Страница 37: ...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 initial velocity See experiments 1 and 2 To prepare the demonstration clamp the Mini L...

Страница 38: ...d 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 will not have to pass through them at an oblique angle A cup may be placed at the end of the path to catch the ball Shoot the ball through the rings Ask the class what shape of curve is formed by the rings ...

Страница 39: ...d are not sold for profit Reproduction under any other circumstances without the written consent of PASCO scientific is prohibited Trademarks PASCO PASCO scientific DataStudio PASPORT and ScienceWorkshop are trademarks or registered trademarks of PASCO scien tific in the United States and or in other countries All other brands products or service names are or may be trademarks or service marks of ...

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