Procedure Projectile Motion Lab Report

Projectile Motion (Photogate)Graphical Analysis 8A

Projectile Motion (Photogate)

You have probably 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 Photogate. You will use this information and your knowledge of physics to predict where the ball will land when it hits the floor.

Figure 1

objectives

· Measure the velocity of a ball using a Photogate.

· Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion.

· Take into account trial-to-trial variations in the velocity measurement when calculating the impact point.

Materials

Chromebook, computer, or mobile device

Graphical Analysis 4 app

Go Direct Photogate

ball (1 to 5 cm diameter)

masking tape

plumb bob

ramp and books

ring stand

right-angle clamp

meter stick or metric measuring tape

target

Preliminary questions

Balance one penny on the edge of a table. Place your index finger on a second penny, then flick the second penny so that it travels off the table, while the first penny is gently nudged off the edge. It may take a few practice trials to be able to do this effectively.

Figure 2

1. Predict which penny will land first, the penny moving horizontally, or the one that simply drops off the table. Explain.

2. Perform the investigation, listening for the sound of the pennies as they land. Was your prediction supported or refuted?

3. You may believe the pennies landed just a little bit apart from each other. Try it a few more times. Does one always land before the other?

4. What will happen if you increase the speed of the second penny? Predict and then give it a try.

5. What if you increase the height from which the pennies are dropped? Your instructor may choose to stack two tables for you to test this.

6. Based on your observations, does the horizontal speed of the flicked penny affect the impact times of the pennies?

7. What can you then say about the time to hit the floor for each penny?

Procedure

1. Set up a low ramp on a table so that a 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 Photogate so the ball rolls through the Photogate while rolling on the horizontal table surface (but not on the ramp). To prevent accidental movement of the Photogate, use tape to secure it in place.

3. Mark a starting position on the ramp so that you can repeatedly roll the ball from the same place. Roll the ball down the ramp, through the Photogate, and off the table. Catch the ball as soon as it leaves the table. Note: Do not let the ball hit the floor during these trials, or during the following velocity measurements so as not to spoil the prediction. The ball must not strike the Photogate. Adjust your setup if necessary.

4. Set up the Photogate and Graphical Analysis.

a. Launch Graphical Analysis. Connect the Photogate to your computer, Chromebook, or mobile device.

b. Click or tap View, , and change the view to Meter.

5. Graphical Analysis calculates velocity by measuring the time interval from when gate 1 is blocked to when gate 2 is blocked. You can see how this works by gently rolling the ball through the Photogate so that the ball first blocks gate 1, then blocks gate 2.

a. Watch the meter display as you gently roll the ball through the Photogate so that it first blocks gate 1, and then blocks gate 2.

b. Watch the meter display as you gently roll the ball in the other direction through the Photogate, so that it first blocks gate 2 and then blocks gate 1.

6. Collect data.

a. Click or tap Mode to open data-collection settings. Change the settings to end data collection manually. Click or tap Done.

b. Click or tap View, , and change the view to Table.

c. Click or tap Collect to start data collection.

d. Roll the ball from the mark on the ramp, through the Photogate, and catch the ball immediately after it leaves the table.

e. Repeat nine times.

f. After the last trial, click or tap Stop.

7. Inspect your velocity data. Did you get the same value every time? Record the velocity for each trial number in Table 1.

8. To determine the average, maximum, and minimum values, click or tap View, , and choose 1 Graph. Then, click or tap Graph Tools, , and choose View Statistics. Enter the values in Table 2.

9. Carefully measure the distance from the tabletop to the floor and record it as the table height, h, in Table 2. Use a plumb bob to locate the point on the floor just beneath the point where the ball will leave the table, as shown in Figure 1. Mark this point with tape; it will serve as your floor origin.

10. Use your average velocity value to calculate the distance from the floor origin to the impact point where the ball will hit the floor. Record the value in Table 2 as the predicted impact point. According to the kinematic equations for projectile motion, the distance R, from the floor origin to the impact point is:

.

Where is the average speed that the sphere has when it leaves the tabletop, h is the distance from the tabletop to the floor and Align your predicted impact point with the track and mark the predicted impact point on the floor with tape. Position a target at the predicted impact point.

11. To account for the variations you saw in the Photogate velocity measurements, repeat the calculation in the preceding step for the minimum and maximum velocity. These two additional points show the limits of impact range that you might expect, considering the variation in your velocity measurement. Mark these points on the floor as well, and record the values in Table 2.

12. After your instructor gives you permission, 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 with tape. Measure the distance from the floor origin to the actual impact and enter the distance in the data table. See value reported by the instructor in table 2.

Data Table

Table 1

Trial

Velocity (m/s)

1

2

3

4

5

6

7

8

9

10

Table 2

Maximum velocity

m/s

Minimum velocity

m/s

Average velocity

m/s

Table height (see datafile)

m

Predicted impact point

m

Minimum predicted impact point distance

m

Maximum predicted impact point distance

m

Actual impact point distance

0.285 m

Analysis

1. Why is it more appropriate to use an impact range to predict the landing point of the ball? Should you expect any numerical prediction based on experimental measurements to be exact? Explain.

2. Was your prediction acceptable? Explain.

3. You accounted for variations in the velocity measurement in your range prediction. Are there other measurements you used which affect the range prediction? What are they?

4. Did you account for air resistance in your prediction? If so, how? If not, how would air resistance change the distance the ball flies?

Extensions

1. Derive one equation for the horizontal and vertical coordinates of the ball’s motion in this experiment.

2. Repeat the experiment using a table that is not horizontal.

3. Derive a general formula for projectile motion with the object launched at an angle.

4. Calibrate the velocity of the ball when released from various positions along the ramp. Given a specific distance to the target by the instructor, determine where the ball must be released to achieve the needed velocity. Release the ball from that position and determine whether the target is hit.

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