13B Projectile Motion ? Change Launch Angle (Photogates and ...

Projectile Motion – Change Launch Angle
(Photogates and Time-of-Flight Pad)
Mechanics: Projectile motion with different launch angles DataStudio file: 13B Projectile Motion 2.ds
Equipment List
Qty Items Part Numbers
1 PASCO Interface (for three sensors)
2 Photogate Head ME-9498
1 Time-of-Flight Accessory ME-6810
1 Photogate Mounting Bracket ME-6821
1 Projectile Launcher ME-6800
1 Metric Measuring Tape, 30 m SE-8712
1 Extension Cord, 6 m PI-8117
1 C-clamp, large SE-7285
13B
Introduction
The purpose of this exploration is to compare the time-of-flight of a projectile for different
values of initial speed when a launcher is aimed at an angle above horizontal. Use Photogates
and a Time-of-Flight Pad to measure the initial speed and the time-of-flight of a projectile. Use
DataStudio to record the motion.
Predict the range of a projectile based on the initial speed, vertical height, and launch angle.
Background
Projectile motion is a kind of two-dimensional motion that occurs when the moving object (the
projectile) experiences only the acceleration due to gravity, which acts in the vertical direction.
The acceleration of the projectile has no horizontal component if the effects of air resistance are
ignored. The vertical component of the acceleration equals the acceleration due to gravity, ‘g’.
The vertical motion of a freely falling ball launched at any angle from a table of height 'd' is
independent of any horizontal motion the ball may have. Thus the time for a ball to fall to the
ground is independent of its horizontal speed.
A projectile launched at an angle above the horizontal will have both a horizontal and a vertical
component of speed at launch.
v ox = v o cos
v oy = v o sin
The horizontal ‘range’ of the projectile depends on its horizontal speed, and the total time that it
is in the air. The time of flight for a projectile launched at angle above the horizontal is
determined by the initial speed in the vertical direction, v0y, and the acceleration due to gravity.
The time up and down for a projectile is given by the next equation.
t = 2v 0 sin
g
(Note that this formula assumes that the object returns to the same vertical position it had when it
was launched.)
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13B Projectile Motion – Launch Angle Physics Experiment Manual 012-09227
The ‘range’, R, is the horizontal speed multiplied by the time of flight.
SAFETY REMINDER
R = v t = v cos ox o 2v o sin
g
• Wear safety goggles when using the Projectile Launcher.
• Follow directions for using the equipment.
Setup
1. Set up the PASCO Interface and computer and start DataStudio. Connect the two
Photogates into the interface. Connect the extension cord to the Time-of-Flight Accessory
and plug the extension cord into the interface.
2. Open the DataStudio file: 13B Projectile Motion 1.ds
• The DataStudio file has a Table display of Initial Speed and Time of Flight.
3. Clamp the base of the projectile launcher to the edge of a sturdy table. Aim the launcher
away from the table toward the center of an open area at least 3 meters away.
4. Adjust the angle of the launcher to zero degrees so
the plastic ball will be launched horizontally.
Launcher Photogates Line of Sight
5. Slide the photogate mounting bracket into the T-slot
on the bottom side of the projectile launcher. Mount
one Photogate to the bracket in the position closest
to the end of the launcher. Mount the other
Photogate to the bracket in the other position.
• Note: Make sure the Photogates that are mounted on
the front of the projectile launcher are separated by
10 centimeters (0.10 m). If the distance of
separation is different, adjust the value in the
Calculator window. Click the Calculate button to open the Calculator
window. Enter the new distance under ‘Variable’ and click ‘Accept’.
Record Data
Horizontal, Short Range
Time of Flight pad
1. Put the plastic ball into the projectile launcher. Cock the launcher to the short-range
position.
2. Test fire the ball to determine where to place the timing pad on the floor. Put the timing
pad on the floor where the ball hits.
3. Reload the ball into the projectile launcher, and cock the launcher to the short-range
position. Click ‘Start’ to begin recording data.
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012-09227 Physics Experiment Manual 13B Projectile Motion – Launch Angle
4. Shoot the ball on the short-range position. After the ball hits the Time-of-Flight pad, click
‘Stop’. Record the initial speed and time of flight.
30 degrees, Short Range
1. Adjust the angle of the launcher to 30° above horizontal.
2. Reload the launcher and set it to the short-range position. Test fire the ball to determine
where to place the timing pad on the floor. Put the timing pad on the floor where the ball
hits.
3. Reload the launcher and set it to the short-range position. Click ‘Start’ and shoot the ball.
4. After the ball hits the timing pad, click ‘Stop’.
5. Record the initial speed. You will use the value to predict horizontal range.
30 degrees, Middle Range
1. Leave the angle of the launcher at 30° above horizontal.
2. Reload the launcher and set it to the middle-range position. Test fire the ball to determine
where it lands and move the timing pad to that spot.
3. Reload the launcher and set it to the middle-range position. Click ‘Start’ and shoot the ball.
4. After the ball hits the timing pad, click ‘Stop’. Record the initial speed and time of flight.
30 degrees, Long Range
1. Leave the angle of the launcher at 30° above horizontal.
2. Reload the launcher and set it to the long-range position. Test fire the ball to determine
where it lands and move the timing pad to that spot.
3. Reload the launcher and set it to the long-range position. Click ‘Start’ and shoot the ball.
4. After the ball hits the timing pad, click ‘Stop’. Record the initial speed and time of flight.
Predict the Range and Test the Prediction
Line of Sight
T.O.F. Pad
1. Based on the short range initial speed
and the launch angle (30°), calculate
the initial vertical velocity and the
initial horizontal velocity.
2. Based on the initial vertical velocity,
find the time, 't', it takes for the
projectile to reach its maximum
height. Multiply the time by '2' to get
the total time in flight.
3. Calculate the range based on the initial horizontal velocity and the total time in flight.
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4. Place the Time-of-Flight Pad at the horizontal distance you calculated for the range. Place
the pad at the same height as the end of the projectile launcher.
5. Reload the launcher and set it to the short-range position. Shoot the ball and observe how
close it lands to the spot you predicted.
Analyze
Use your results to answer the questions in the Lab Report.
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012-09227 Physics Experiment Manual 13B Projectile Motion – Launch Angle
Lab Report: Projectile Motion – Change Launch Angle
Name: ________________________________________________________________
Data Table
Change Launch Angle
Predict the Range
Arrangement
Short range, horizontal
Short range, 30˚
Initial Speed (m/s) Time of Flight (s)
Mid range, 30˚
Long range, 30˚
Initial Speed, Short range Time (max. height)
Initial Horizontal Speed 2 x Time
Initial Vertical Speed Predicted Range
Questions
1. How do the values for the time of flight for the short-range, horizontal compare to the
short-range, 30° angle distance?
2. How do the values for the time of flight for the short, middle, and long-range distances
compare when the ball was launched at 30° above the horizon?
3. Why would time of flight depend on the angle of the launch?
4. When you tested the range, how close did the ball land to the spot you predicted?
5. How can you predict how long a ball will stay in the air? Does a change in its angle change
the "time of flight"? If so, how?
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