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Projectile Motion - Matanzas High School

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Projectile Motion - Matanzas High SchoolHigh,high

    LabQuest

     8

    Projectile Motion

    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

    LabQuest plumb bob

    LabQuest App ramp

    2 Vernier Photogates ring stand

    target right-angle clamp

    ball (1 to 5 cm diameter) meter stick or metric measuring tape

    masking tape

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 for the ball 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 horizontally before it hits the ground. Physics with Vernier 8 - 1

LabQuest 8

    3. When an object passes through a Photogate, it blocks the passage of light from one side to the

    other. The interface can accurately measure the duration of time that a gate is blocked. If you

    wanted to know the velocity of the object, what additional information would you need? PROCEDURE

    1. Set up a low ramp made of angle molding 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 Photogates so the ball rolls through each of the Photogates while rolling on the

    horizontal table surface (but not on the ramp). Approximately center the detection line of each

    Photogate on the middle of the ball. To prevent accidental movement of the Photogates, use

    tape to secure the ring stands 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. Make sure that the ball does not strike the side of the

    Photogates. Move the Photogates if necessary.

    4. Set up the Photogates and LabQuest to collect data in Pulse Timing mode.

    a. Connect the Photogates to LabQuest and choose New from the File menu. If you have

    older sensors that do not auto-ID, manually set up the sensors. Note: Connect the sensors

    so that the ball first passes through the Photogate connected to DIG 1 and then passes

    through the Photogate connected to DIG 2.

    b. On the Meter screen, tap Mode. Change the Photogate Mode to Pulse Timing.

    c. You must enter the distance between Photogates in order for LabQuest to calculate the

    velocity. The program will divide this distance by the time interval t it measures to get the

    velocity (v = s/t). 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 between gates (in meters).

    d. Select OK.

    6. Observe the live readings. Block the Photogate 1 with your hand; note that the Photogate is

    shown as Blocked on the screen. Remove your hand and the display should change to

    Unblocked. Repeat for Photogate 2.

    7. LabQuest will measure the length of time from when the first photogate is blocked until the

    second photogate is blocked. You can see how this works by blocking the gates briefly with

    your hand.

    a. Start data collection.

    b. Check to see that the Photogates are responding properly by moving your finger through

    Photogate 1 and then Photogate 2. LabQuest App will plot a time interval (t) value for

    each instance you run your finger through Photogate 1 then through Photogate 2.

    c. Stop data collection.

8 - 2 Physics with Vernier

     Projectile Motion

    8. Collect data.

    a. Start data collection.

    b. Roll the ball from the mark on the ramp, through both Photogates, and catch the ball

    immediately after it leaves the table.

    c. Repeat nine times. Take care not to bump any of the Photogates, or your velocity data will

    not be precise.

    d. After the last trial, stop data collection.

    9. Tap Table. Record the time and velocity for each pass through the photogates in the data

    table.

     10. Inspect your velocity data. Did you get the same value every time? To determine the average,

    maximum, and minimum values, tap Graph, then choose Statistics ?Velocity from the

    Analyze menu. What one value would be most representative of all ten measurements?

     11. Carefully measure the distance from the tabletop

    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 plumb will leave the table. Mark this point with tape; it bobwill serve as your floor origin.

     12. Use your average velocity value to calculate the floor origindistance from the floor origin to the impact point

    where the ball will hit the floor. You will need to

    algebraically combine relationships for motion Figure 2 with constant acceleration

    21xvtat;;0xx2 21yvtat;;0yy2

    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 0yx

    acceleration in the vertical direction (a)? Remember that the time the ball takes to fall is the y

    same as the time the ball flies horizontally. Use this information and the simplified equations to

    calculate how far the ball should travel horizontally during the fall. Record the value in your

    data table as the predicted impact point.

    Mark your predicted impact point on the floor with tape and position a target at the predicted

    impact point. Be sure the impact point is along the line of the track.

     13. 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 your data table.

     14. 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.

    Physics with Vernier 8 - 3

LabQuest 8

    DATA TABLE

     Trial Time Velocity (s) (m/s) Maximum velocity m/s

    1 Minimum velocity m/s

    2 Average velocity m/s

    3 Table height m

    4 Predicted impact point m

    5 Minimum impact point distance m

    6 Maximum impact point distance m

    7 Actual impact point distance m

    8

    9

    10

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.

    2. Was your actual impact point between your minimum and maximum impact predictions? If so,

    your prediction was successful.

    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.

    5. Increase the challenge by placing a ring on a ring stand part way to the eventual target. The

    ball must pass through the ring successfully and then hit the target. You are required to

    position the ring as well as the target on the floor.

    8 - 4 Physics with Vernier

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