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# Projectile Motion - Wikispaces

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Projectile Motion - WikispacesProjec

Computer

8

Projectile Motion

You have watched a ball roll off a table and strike the floor (in class, if nowhere else!) Could you predict

where it will land? What determines where it will land? In this experiment, you will roll a ball down a ramp and determine the ball’s velocity with a pair of photo gates. This will be the ball’s initial velocity for the projectile motion that begins the instant the ball leaves the table. The ball will be heavy enough and small enough that air resistance has a negligible effect, i.e., the force of air resistance on the ball will be much, much smaller than the force of gravity on the ball. You will use the initial velocity information and your knowledge of physics to predict where the ball will land when it hits the floor. Then you will check to see if you were right.

Figure 1

OBJECTIVES

Measure the speed of a ball just before it rolls off a table, using two photo gates and computer

software.

Apply the concepts and equations of projectile motion to predict where the ball will land.

Take into account trial-to-trial variations in the speed measurement and then see how these affect

your prediction of where the ball will land. In other words, determine the precision of your

prediction.

MATERIALS

Laptop computer with Logger Pro software on it 2 ring stands

Vernier Lab Pro 2 right-angle clamps

Power cord for Lab Pro 1 plumb bob with string

Cable to connect Lab Pro to laptop 1 roll of masking tape

Ramp: 1 strip of molding and 1wood block 1 target

1 steel ball Oodles of luck (No! Just kidding…)

two Vernier photo gates 1 meter stick, 1 metric measuring tape,

and/or 1 ruler

Physics with Vernier 8 - 1

Computer 8

PRELIMINARY QUESTIONS

LAB PROCEDURE AND DATA

1. Set up the ramp on your table so that the steel ball can roll down the ramp, across a short

section of table, and off the table edge as shown in Figure 1.

2. Position the photo gates so the ball rolls through both photo gates while rolling on the

horizontal table surface. Approximately center the detection line of each photo gate on the

middle of the ball (half way up the ball). Connect photo gate 1 to DIG/SONIC 1 of the Lab Pro

and photo gate 2 to DIG/SONIC 2. It is important that you put the right photo gate cable into

the right place on the Lab Pro. To prevent accidental movement of the Photo gates, use C-

clamps to secure the ring stands in place.

3. Mark a starting position on the ramp (using tape or a marker) so that you can repeatedly roll

the ball from the same place for each trial. Roll the ball down the ramp through the photo

gates and off the table, but do not let it touch the floor. Catch the ball as soon as it leaves the

table. This is important: Do not let the ball hit the floor during these trials or during the

following velocity measurements. Also, make sure that the ball does not strike the sides of the

photo gates. Reposition the photo gates if necessary.

4. Connect your Lab Pro to power. Listen for the little sound that tells you it is working.

Then connect the Lab Pro to a lap top computer. Open the file “08 Projectile Motion” in the

Physics with Vernier folder in Logger Pro. A data table and two graphs will be displayed; one

graph will show the time required for the ball to pass through the photo gates for each trial

and the other will display the speed of the object for each trial. Note that the Logger Pro

uses the term velocity when it really should use the term speed.

x5. You must enter the distance, , between the

two photo gates in order for Logger Pro to

calculate the speed of your ball. The Logger Pro 8 to 10 cmprogram will divide this distance by the time

interval t it measures to get the speed ;；v？，x/t(). Carefully measure the distance from

the beam of photo gate 1 to the beam of photo

gate 2. (It is easier to measure from the leading

edge of photo gate 1 to the leading edge of photo

gate 2 and this gives the same distance.) To ;；photogate 1photogate 2 successfully predict the impact point, you must enter an accurate measurement. Adjust the gate

Figure 2 separation using the control on the Logger Pro

screen. Alternatively, you can adjust the

separation between the photo gates to be 10.0 cm,

the value already entered into Logger Pro.

6. Click . Check to see that the photo gates are responding properly by moving your

finger through photo gate 1 and then photo gate 2. Click .

7. You are going to release the ball from the mark on the ramp. You will watch the ball roll

down the ramp, along the table, through both photo gates, and then you will catch the ball

immediately after it leaves the table. You will do this nine times. Take care not to bump any of

the photo gates, or your speed data will not be precise. Before you begin, you will click 8 - 2 Physics with Vernier

Projectile Motion

. This will clear any data leftover from step 6 and prepare for data collection. After you click you will have two minutes to complete your 10 trials. Then Logger Pro will stop recording data. If you need more time, click to restart, choosing Append.

After your tenth trial, click to end data collection. Record the speed for each trial in the data table below.

Trial Initial Speed

(m/s)

1

2

3

4

5

6

7

8

9

10

8. Inspect your speed data. Did you get the same value every time? Determine the average, maximum, and minimum values by clicking once on the velocity vs. time graph and then

clicking the Statistics button,. What one value would be most representative of all ten

measurements?

Maximum speed m/s

Minimum speed m/s

Average speed (use the mean) m/s

y9. Carefully measure the distance from the tabletop to the floor and record it here as. Why

do we need the absolute value sign? Use a plumb bob to locate the point on the floor just beneath the point where the ball will leave the table. Mark this point with tape; it will serve as your floor origin. You will notice at this point, if you did not before, that your table does not have a square edge. Explain why this is a problem and tell how your group is going to deal ;；with the problem. (There is no perfect solution that I know of, other than going out and buying new tables with square edges!)

plumb bob

floor origin

Figure 3

Physics with Vernier 8 - 3

Computer 8

10. In this step you will use your speed value to calculate the distance from the floor origin to the

impact point where you think the ball will hit the floor. In order to achieve this, you will need

to algebraically combine relationships for motion with constant acceleration

12xvtatixx2 12yvtatiyy2

First, simplify the equations above: What is the value of the initial velocity in the vertical

direction (v)? What is the acceleration in the horizontal direction (a)? What is the oyx

acceleration in the vertical direction (a)? Remember that the time the ball takes to fall is the y;；tsame as the time the ball flies horizontally, so in both equations is the same. Use this

information and your simplified equations to obtain an expression for calculate how far the

ball will be from the table at the time the ball hits the floor. In other words, obtain an xv,y,anda.equation for in terms of only Do your work in pencil on a piece of ixypaper. Then type up your work here, using an equation editor. Make sure to include your ;；final equation. Then plug in your values (again type it here using an equation editor) and xobtain your predicted value.

;；;；xPredicted impact point - m

;； 11. To account for the variations you saw in the photo gate speed measurements, repeat the

calculation in Step 10 for the minimum and maximum speeds you measured. These two ;；additional points show the limits of impact range that you might expect, considering the

variation in your speed measurement. Type the equations here and record the results in the

table below.

Minimum impact point distance m

Maximum impact point distance m

Mark your predicted impact point on the floor, on a piece of tape, being careful to make your

mark along the line of the track. Mark your minimum and maximum points on the floor as

well.

12. After calling your teacher over to watch, release the ball from the marked starting point,

and let the ball roll off the table and onto the floor. Mark the point of impact on your tape,

maybe with a different color than you used for your other marks. Measure the distance from

the floor origin to the actual impact and enter the distance below.

Actual impact point distance m

13. Was your actual impact point between your minimum and maximum impact predictions? 14. Put all equipment away neatly. Clean off your table make it look perfect for the next class

that is coming in.

ANALYSIS

1. Should you expect any numerical prediction based on experimental measurements to be exact?

Would a range for the prediction be more appropriate? Explain.

8 - 4 Physics with Vernier

Projectile Motion

2. If the ball hit the floor between your minimum and maximum predicted values, your

prediction was successful.

(a) If your prediction was not successful, do this part: Was your prediction off by much?

Brainstorm about what might have gone wrong. Write all your ideas here. (b) If your prediction was successful, do this part: You accounted for variations in the speed

measurement in your range prediction. Are there other measurements you used which affect

the range prediction? What are they?

3. Did you account for air resistance in your prediction? If so, how? If not, how would air

resistance change the distance the ball flies?

4. Derive an equation that gives the path of the ball in this experiment. This equation will not xtyhave in it, but will show the relationship between and . Does the equation you

derived say that the path will be a section of a parabola? How can you tell?

;；;；;；

Physics with Vernier 8 - 5

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