# projectile

Document Sample

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Course Name
Instructor Name
Student(s) Name

WHERE WILL IT LAND?
You have watched a ball roll off a table and strike the floor. What
determines where it will land? Could you predict 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 Photogates. You will use this information
and your knowledge of physics to predict where the ball will land when
it hits the floor. You will also find out if you made the right prediction.

STUDENT OUTCOMES

Through this experiment, students will be able to:
- Study the physical quantities involved in projectile motion
- Apply concepts from two-dimensional kinematics to predict the
impact point of a ball in projectile motion.

MATERIALS

Tablet PC Computer Laptop             Vernier computer interface
Logger Pro                            Metal ball
Ramp                                  Meter stick/ Measuring tape
Carbon Paper

PRELIMINARY QUESTIONS

1. If you were to drop a ball, releasing it from rest, what information
would be needed to predict how much time it would take to hit the
floor? What assumptions must you make?

2. If the ball in Question 1 is traveling at a known horizontal velocity
when it starts to fall, explain how you would calculate how far it will
travel before it hits the ground.
3. A pair of computer-interfaced Photogates can be used to accurately
measure the time interval for an object to break the beam of one
Photogate and then another. If you want to know the velocity of the
procedure).

PROCEDURE and RESULTS

1. Set up the ramp so that a ball can roll down the ramp, across a
short section of the table, and off the table edge.

1     2

x

2. Position the Photogates so the ball rolls through each of the
Photogates while rolling on the horizontal table. Connect Photogate 1
to DIG/SONIC 1 of the interface and Photogate 2 to the corresponding
second port. To prevent accidental movement of the Photogates, tape
them in place.
3. Mark a starting position (5 cm above the table top) and repeatedly
release the ball from the same place. Roll the ball down the ramp
through each Photogate and off the table. Make sure that the ball does
not strike the sides of the Photogates. Reposition the Photogates if
necessary.
4. Open the file “08 Projectile Motion” in the Physics with Computers
folder. A data table and two graphs are displayed. Ignore the two
graphs.
5. You must enter the distance between the Photogates in order for
Logger Pro to calculate the velocity. The program will divide this
distance by the time interval it measures to get the velocity. Carefully
measure the distance from the beam of Photogate 1 to the beam of
Photogate 2. (It may be easier to measure from the leading edge of
Photogate 1 to the leading edge of Photogate 2). To successfully
predict the impact point, you must enter an accurate measurement.
Enter the distance into Logger Pro by selecting Column Options, then
velocity from the Data Menu. In the equation field change the 0.1 to
the actual separation of your gates in meters. Click DONE to complete
the edit.
6. Check to see that the Photogates are responding properly by
moving your finger through Photogate 1 and then Photogate 2. The
red light on the Photogate should be turning on and off.
7. Roll the ball from the mark on the ramp (5 cm above table top),
through both Photogates, and catch the ball immediately after it leaves
the table. DO NOT let the ball hit the floor during these trials. Repeat
five times. Take care not to bump any of the Photogates.
8. Inspect your velocity data and input these values in the DATA
TABLE FOR THE 5 CM RELEASE. Did you get the same value every
time? Think about it and make sure the results you obtain make
sense.
9. Determine the average velocity. Input this value in your Data Table
as the horizontal velocity of the ball as it leaves the table top ( Vox ).
10. Carefully measure the distance from the table top to the floor and
record it as the table height H in the Data Table. 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; this will serve as your floor
origin.

11. Calculate the time (t) for the ball to fall from the table top to the
1                              m
floor, using             H  gt 2            where g  9.81 2
2                              s

12. Remember, the time for the ball to fall is the same as the time the
ball flies horizontally. Use the time value you got in # 11 and solve for
how far the ball should travel horizontally during the fall, using
x  Vox t
This will be your predicted impact point on the floor. Input this value in
the Data Table as the Predicted x .

13. Place a piece of paper and a carbon paper on top of it at your
predicted impact point on the floor.

14. Release the ball from the release point on the ramp and let the ball
roll off the table onto the floor. Repeat three times. These should leave
marks on the paper on the floor.
15. Measure the distance from the floor origin to the impact point for
the three trials and enter the distances (Measured x ) in the Data
Table.

16. Determine the average value for the Measured x . Input this value
in the Data Table.

17. Repeat # 7 – 16 for release points on the ramp of 7 cm, 9 cm,
11 cm and 13 cm above the table top. Record the data in the
appropriate Data Table. Make sure to show your complete and
detailed work for all values for one (1) table.

DATA TABLE 1: 5 CM ABOVE TABLE TOP
TRIAL         TIME (S)   VELOCITY (m/s)
1
2
3
4
5
AVERAGE VELOCITY ( Vox ) =

VERTICAL DISTANCE OF FALL ( H ) =
PREDICTED x =
MEASURED x :      TRIAL: 1
2
3
AVERAGE MEASURED x =

DATA TABLE 2: 7 CM ABOVE TABLE TOP
TRIAL         TIME (S)   VELOCITY (m/s)
1
2
3
4
5
AVERAGE VELOCITY ( Vox ) =

VERTICAL DISTANCE OF FALL ( H ) =
PREDICTED x =
MEASURED x :      TRIAL: 1
2
3
AVERAGE MEASURED x =

DATA TABLE 3: 9 CM ABOVE TABLE TOP
TRIAL         TIME (S)   VELOCITY (m/s)
1
2
3
4
5
AVERAGE VELOCITY ( Vox ) =

VERTICAL DISTANCE OF FALL ( H ) =
PREDICTED x =
MEASURED x :      TRIAL: 1
2
3
AVERAGE MEASURED x =

DATA TABLE 4: 11 CM ABOVE TABLE TOP
TRIAL         TIME (S)   VELOCITY (m/s)
1
2
3
4
5
AVERAGE VELOCITY ( Vox ) =

VERTICAL DISTANCE OF FALL ( H ) =
PREDICTED x =
MEASURED x :      TRIAL: 1
2
3
AVERAGE MEASURED x =
DATA TABLE 5: 13 CM ABOVE TABLE TOP
TRIAL         TIME (S)   VELOCITY (m/s)
1
2
3
4
5
AVERAGE VELOCITY ( Vox ) =

VERTICAL DISTANCE OF FALL ( H ) =
PREDICTED x =
MEASURED x :      TRIAL: 1
2
3
AVERAGE MEASURED x =

ANALYSIS

1. From a standard scientific point of view (comparing a theoretical
model (using equations) with experimental data (doing the actual
experiment) do you expect the measured x values to be similar to
the predicated x values in each Data Table? Explain.

2. From an experimental point of view, do you expect the measured x
values from trial 1, 2, and 3 to be close to each other? If there are
differences in magnitude between those 3 values, what type of
errors would you attribute this to? (review the resource page under
Review of concepts if needed).

3. How is the average velocity Vox affected by the change in the
release height above the table top.

4. Examine the calculations done for the time to fall from the table top
to the floor. Is the time affected by the release height above the
table top?
5. Based on your answer in the previous question, when the ball rolls
off the table top, which single quantity will affect the Measured x
value?

Recall what you learned in the “PI” experiment (applying the line

6. Tabulate the values obtained for average velocity ( Vox ) and
Measured x (i.e. Include a table with labels and units).

7. Using Excel, draw a graph of Measured x vs Vox . Draw the line that
best fits the points, obtain the slope of the graph. State the value of
your slope clearly (Do not forget the units).

8. Examine the equation x  Vox t . What quantity should the slope of
the graph represent? Use the units of your slope and the result of
question 11 to answer this question.
Calculate the percent error between your slope and question 11. Is