Physics Lab: Projectile Motion

Goal: To observe and collect data on the motion of projectiles

Materials

(Equipment included in the physics kit is noted in square brackets [].)

• Surgical Tubing] or large rubber bands.
• [Small styrofoam balls, hollow capsules, or rubber ball]. Balls should be lightweight to avoid damage on impact. If necessary, wad up paper and seal inside masking tape or duct tape to make "balls".
• Handy helper for observations
• [Protractor with swing arm] or other way to measure vertical angles.
• Launcher (sling shot or other frame which will allow you to stretch the rubber band for slinging your ammo...uh, projectiles). A piece of thick cardboard with pushpins can be used if you don't have any other "Y" or "U" shaped frame.

Procedures

AIM YOUR LAUNCHER CAREFULLY. Be sure that anything within range which might be damaged (Ming china, antique furniture, siblings) has been removed. If you are launching inside the house, a freely suspended towel or blanket at the end of your target area will "catch" your projectile if you shoot too hard.

Observation set 1: Experimentally (by observation) determine whether either ball (dropped vs. launched) hits the ground first.

1. Use the setup in the diagram below, or assemble something similar.
2. Level the launch platform.
3. Make sure the ball to be dropped can fall freely.
4. Practice so that you can launch and drop at the same time.
5. Have your observer note when the balls hit the ground. Marbles hitting a hardwood floor make sufficient noise to tell whether the balls hit the ground at the same time.
6. Repeat your "experimental" several times and record your observations.
7. Does the horizontal distance your launched ball travels make any difference?

Observation set 2: Experimentally determine angle necessary to achieve the maximum height and range for a projectile.

For this one, you may need to be creative in determining maximum height. Possibilities include putting a graph or scale in place and observing the launch path against this background. You may try videotaping the launch path to make identifying the maximum point easier.

1. Use a setup similar to that in the diagram below.
2. Make multiple launches, extending your rubber band the same distance for each launch (so that the initial force is the same).
3. Record the angle of your platform at each trial.
4. Determine the angle at which you achieved maximum height.
5. Determine the angle at which you achieved maximum range.

Data Handling

Present your data in table format. Estimate the amount of error in your measurements and the range of error in our final calculated values.

Report

Your report should include:

1. A detailed description of your equipment and procedures.
2. A detailed account of your observations for dropped vs launched balls.
3. The data from each launch for range/height determination (trial #, angle, range, height) .
4. A plot of angle vs. height reached.
5. A plot of angle vs. range reached.
6. A calculation of the initial horizontal and vertical velocity, and the magnitude of the velocity vector for each launch.
   Height reached, together with the gravitational acceleration constant will allow you to determine how long your ball was falling: $$T=\sqrt{\frac{2h}{a}}\mathrm{where}a=9.8\frac{m}{s^2}$$

   The vertical velocity downwards when it hits the ground, V_y = downward accelertion * time, is equal to the initial vertical velocity upwards.

   Assuming no interference from wind resistance, you can double this for the total time the ball was in the air, and arrive at horizontal velocity:

   $$\begin{array}{l}{v}_y=a_{y}t\\ v_x=\frac{h}{2t}\end{array}$$

   You should now be able to determine the linear velocity

   $$v=\sqrt{{(v_x)}^2+{(v_y)}^2}$$

   for each launch attempt.

   [If you have a spreadsheet capable of handling the math, set it up and let the computer do the calculations for you.]

7. Do you expect V to be the same in all cases? Explain your reasons.
8. A general conclusion about your data, based on your observations and data, and including remarks on errors based on your velocity vector determinations.

Follow the instructions at the Moodle to post your lab reports where your fellow students can find them.

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