# Projectile Motion Lab

This lab is designed to make use of the Applet at the bottom of the page to conduct virtual projectile motion experiments that would otherwise be quite difficult to perform in a typical classroom. There will be two parts to the lab:
• Projectile motion without air resistence;
• Projectile motion with air resistence.
Before starting the lab, play with the Applet to see what it can do. There are sliders to change the mass, initial velocity (magnitude!) and angle of launch. There are also checkboxes to toggle air resistence and show trails. When you are comfortable with running the Applet, start the next section.

## I. Without Air Resistance

For this section you will be running a projectile motion experiment without any air resistance. Make sure that the checkbox in the Applet marked "air resistance" is unchecked for this section.

1) Play with the mass slider and look at the particle path and max distance. What happens to the motion of the ball when you change the mass?

2) Play with the angle slider and look at the max distance. For any given velocity or mass, what angle always gives the maximum distance?

3) Next, test the accuracy of the applet. For your choice of initial velocity, angle and mass verify the horizontal distance (range) the applet gives with a hand calculation (Show your work). Do the values agree?

4) Plot exercise A: Set the angle of your projectile to any value between 15 and 75 degrees. Pick any mass that you like and make sure that air resistance is turned off. Record the distance, height and time for several different values of velocity. Record about 10 runs and try to space out the velocity values that you use. Make the following plots:

 i. distance vs. velocity ii. height vs. velocity iii. time vs. velocity

From your plots and your knowledge of the equations governing projectile motion, what type of function best describes each of your plots?

5) Plot exercise B: Set the velocity of your projectile to any value between 20 and 80 m/s. Pick any mass that you like and make sure that there is no air resistance. Record the distance, height and time for many different values of the angle. Record about 10 runs and try to space out the angle values that you use. Make the following plots:

 i. distance vs. angle ii. height vs. angle iii. time vs. angle

From your plots and your knowledge of the equations governing projectile motion, what type of function best describes each of your plots?

## II. With Air Resistance

Up until this point, we have ignored a very important aspect of projectile motion: air resistance. This force, however, plays a major role in the motion of objects around us. This Applet is designed to help you tease out the effects of air resistance on the motion of a projectile. What we are doing is running an experiment, even though it happens to be virtual. This is how we test models of real physical systems. As you play with this applet, think qualitatively about what you see...

1) Now turn the air resistance on by clicking the checkbox. Now what happens as you change the mass? Can you identify a trend? Make a plot of the horizontal distance (range) as a function of mass. To do this, pick fixed values for the velocity and angle (between 10 and 80 degrees, for clarity).

2) With air resistance still on and use the applet to estimate the angle that gives the maximum distance for an initial velocity of your choice. Is it still 45 degrees? Repeat this for several different values of the ball mass and plot your results (i.e. angle for maximum distance vs. mass)

3) Lastly, the air resistance in this model is proportional to something (a secret revealed...). Based on what you know from your own experiences, estimate what the "drag" force must look like... In other words, formulate a hypothesis. Is it constant? What things might change its magnitude or direction? To help you visualize, think about sticking your hand out of the window of a moving car. What happens as you:
• drive faster or slower (change speed);
• turn the car (change direction);
• open or clench your fist (change shape)?
Discuss with your partner. Then try to translate these observations into simple math. For our ball, assume the shape doesn't change.

Test your hypothesis with the virtual experiment. What will you change? What will you hold constant?

4) Draw a free-body diagram of the moving projectile putting your fresh knowledge of Newton's laws to use. Draw in the total force vectors. Don't worry about components yet.

5) Plot exercise C: Set the angle of your projectile to any value between 60 and 75 degrees. Pick a low value for the mass and make sure that the air resistance is turned on. Record the distance, height and time for many different values of velocity. Record about 10 runs and try to space out the velocity values that you use. Make a plot of distance vs. velocity. Make the following plots:

 i. distance vs. velocity ii. height vs. velocity iii. time vs. velocity

How do these plots compare (in terms of shape) to those from Plot exercise A? What is similar? What is different?

CHALLENGE: 6) We know that the trajectory of the ball is symmetric about the maximum height when there is no air resistance. Is this true when the air resistance is turned on? Can you explain (briefly) why or why not? To answer this question, it will be helpful to think in terms of the vertical and horizontal components of the forces involved.

CHALLENGE: 7) Now, what if I wanted to account for wind (i.e., air moving relative to the our frame of reference earth)? How might that fit in? Think about the difference between sticking your hand out the window into a 30 mph breeze vs. sticking your hand out the window of a car moving at 30 mph. Will it feel different? Translate this into math in the expression you derived in 5.

P.S. -- ASK QUESTIONS! That is what this is all about...