In this activity, we investigate the consequence of vertical and horizontal
motions being independent. Remember the experiment, shown in lecture, of two
steel balls falling to the ground – one with and the other without a horizontal
velocity?
This activity is about projectile motion. Projectile motion is a special case of
uniformly accelerated motion in two dimensions with (constant) acceleration
only in the vertical direction. Since there is no acceleration in the horizontal
direction the horizontal velocity stays constant.
The goal is to predict where a steel ball will land after it is launched at a certain
angle from a launcher.
Apparatus Projectile Launcher
This lab will employ a spring driven projectile launcher. Your lab instructor will
demonstrate how to use the projectile launcher.
Hints Here are some important hints that will help you solve this challenge:
• You can neglect air resistance.
• You can assume that the magnitude of the launch velocity is independent of
the launch angle.
• Pay attention: The initial position of the ball is not its position when the spring
is compressed. The initial position is that when the drive shaft is fully
extended (where the ball is released).
• The initial position of the ball is not level with the tabletop. You will need to
measure this, but the apparatus has been designed well so that this value
won’t change when you change the launch angle.
Caution Do not load the launcher while your head or body is in the line of fire.
Do not allow anyone to get hit by the ball.
You will perform two kinds of launches: straight up and at an angle. Do not
perform any launch unless every member in your group is aware and ready. Do not load the launcher for the angled launch unless your instructor is present.
Determine the launch speed.
Use the minimum setting of the launcher; otherwise, the speed of the ball will
be too great.
Orient your launcher so that it launches straight up. Launch the ball once or
twice just to observe its motion. Then launch the ball and measure its peak
height three times. Using the average height, calculate the launch speed of the
ball.
Use the vertical meter stick to measure the peak height. You will have to
“eyeball” this and catch the correct moment. You should be able to do this to
within a centimeter. Make sure the person that does the measurement has his or
her head near the peak height and does not view at an angle. No one should
have their head near the line of fire.
Launch Speed: __________________________ m/s
Input Your instructor will tell you the launch angle (between 0° and 45°) for your
group. Enter this value below.
Launch angle for range experiment: _________________________
Exercise 2 Determine the initial vertical position.
Carefully adjust your launcher to this angle. Use the meter stick to measure the
height of the ball above the tabletop. Remember that the spring in the launcher
compresses and then expands. What is the correct position to measure the initial
position?
Initial Vertical Position: ________________________ m
Determine the range given your launch angle.
The range is defined as the horizontal distance between the point on the tabletop
beneath the launch position of the ball and the point where it lands.
Using the launch angle and your measurements of the initial height and the
launch speed you can perform a calculation to predict the range of the ball.
Calculation The following steps guide you through the calculation:
• Sketch
• Choose an origin, calculate vx0 and vy0
• Inventory List - What is known?
• Kinematics equation(s) – Treat the horizontal and vertical motion separately.
Predicted Range: _________________________
To determine the launch speed, follow these steps:
1. Set the launcher to its minimum setting to ensure that the speed of the ball is not too great.
2. Orient the launcher so that it launches straight up.
3. Launch the ball once or twice to observe its motion.
4. Measure the peak height of the ball three times using a vertical meter stick. Take the average of these measurements.
5. Calculate the launch speed of the ball using the average peak height.
- The launch speed can be calculated using the formula: v₀ = √(2gh), where v₀ is the launch speed, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the average peak height.
Input the launch speed in meters per second (m/s) obtained from the calculation.
To determine the initial vertical position:
1. Carefully adjust the launcher to the specified launch angle.
2. Use the meter stick to measure the height of the ball above the tabletop.
3. Remember that the spring in the launcher compresses and then expands. Measure the initial position when the spring is fully extended and the ball is released.
Input the initial vertical position in meters (m).
To determine the range given the launch angle:
1. The range is defined as the horizontal distance between the point on the tabletop beneath the launch position of the ball and the point where it lands.
2. Use the launch angle, initial vertical position, and launch speed to perform the calculation to predict the range of the ball.
3. Treat the horizontal and vertical motion separately using kinematics equations.
- For the horizontal motion, the formula for range (R) is: R = ((v₀^2) * sin(2θ)) / g, where v₀ is the launch speed, θ is the launch angle, and g is the acceleration due to gravity.
4. Calculate the predicted range of the ball using the launch angle, initial vertical position, and launch speed.
Input the predicted range in meters (m).
Make sure to carefully follow the instructions and measurements to obtain accurate results.