Falling Objects and Terminal Velocity
Sections
1. Introduction and Setup
2. Air Resistance and Terminal Velocity
3. Hardware Check
4. Measuring Distance and Velocity - Book
5. Measuring Distance and Velocity - Paper Filter
6. Exploring Data
1. Introduction and Setup
 InstructionsRead the introduction and setup your equipment as instructed. In a lot of physics models we ignore air resistance. That can help to make the system's behavior easier to calculate, and sometimes the air resistance is so little that it doesn't affect the model much anyway. However, there are times when air resistance makes a large difference. One such situation is a model of certain falling objects - air resistance plays a big part in something called Terminal Velocity that we're going to learn about shortly. We're going to use an ultrasonic distance sensor to measure the distance and velocity of falling objects. An ultrasonic distance sensor measures distance by emitting quick pulses of high frequency sound (outside the human hearing range) and then listening for the echo from that pulse hitting an object. By measuring the time between a pulse and an echo it can tell us how far away an object is. In order to measure the distance to an object that's falling, we're going to need to mount the sensor pointing down above an area where we can drop an object. The sensor has a minimum range of about 30 centimeters and a maximum range of about 5 meters. That means that we want to release our falling objects from 30 cm under the sensor and let them fall no further than 5 m from the sensor. In practice, this just means we'll want to mount the sensor on something like a ring stand on top of a lab table pointing down over the edge.
2. Air Resistance and Terminal Velocity
 This lesson requires a newer browser. Please see this page for more information. Near the surface of the Earth, all objects fall with a constant acceleration of about 9.81 m/s2 due to gravity. So, for every second gravity is acting on an object, it will fall 9.81 m/s faster than it was the previous second. If you drop an object, in the first second it goes from 0 m/s to 9.81 m/s. In the next second it goes from 9.81 m/s to 19.62 m/s, and so on. However, we all know that if we drop a piece of paper it will fall slower than a bowling ball. Why is that? Have you ever held your hand out a car window and felt the wind push against it? This is air resistance - It's the air resisting the motion of another object through it. Every time an object, like your hand, presses against an air molecule, it presses back. You might also have noticed that if you turn your hand sideways, like an airplane wing, the air pushes less. That's because your hand now has a smaller area for the air molecules to hit, so they exert less force on your hand. When enough air molecules impart force on an object to keep it from accelerating, it's said to be at terminal velocity. That's means that no matter how much longer it falls, the force of the air molecules pushing it up cancels the force of gravity pulling it down, and it won't fall any faster. Here's a simulation of a bowling ball and a piece of paper falling. Try removing the air and see what happens.
3. Hardware Check
 GoalsArduino plugged in and Ultrasonic Distance Sensor connected to pin D2. Please plug in your Arduino if you haven't already and attach an ultrasonic distance sensor to digital pin D2.
4. Measuring Distance and Velocity - Book
Let's look at how some objects fall. We'll plot the distance and velocity of a falling object over time and see how they increase and decrease. Hold a book 30 cm under the sensor. Then click Start Recording as you release it. Next, click Stop Recording just after it hits the ground. Don't worry about mistakes, just click Clear Data and try again.
 Distance (mm)0.00 Velocity (m/s)0.00
After you have some data, roll your mouse over the plots to see more detailed information. Use that information to answer these questions:
How long did the book take to hit the floor?

Hint
On the distance plot, position your mouse near the end where the distance stops increasing. Note the time. Then position your mouse near the start where the movement starts and note the time again. Subtract the smaller time from the larger.
What was the largest velocity the book experienced during the fall? When did that happen?

Hint
Look for the highest point on the velocity plot and position your mouse over it.

5. Measuring Distance and Velocity - Paper Filter
Let's look at how some objects fall. We'll plot the distance and velocity of a falling object over time and see how they increase and decrease. Hold a filter 30 cm under the sensor. Then click Start Recording as you release it. Next, click Stop Recording just after it hits the ground. Don't worry about mistakes, just click Clear Data and try again.
 Distance (mm)0 Velocity (m/s)0
After you have some data, roll your mouse over the plots to see more detailed information. Use that information to answer these questions:
How long did the filter take to hit the floor?

Hint
On the distance plot, position your mouse near the end where the distance stops increasing. Note the time. Then position your mouse near the start where the movement starts and note the time again. Subtract the smaller time from the larger.
What was the largest velocity the filter experienced during the fall? When did that happen?

Hint
Look for the highest point on the velocity plot and position your mouse over it.

6. Exploring Data
Compare the plots of distance and velocity over time for the book and filter. What differences do you notice?
Book
Paper Filter
An important thing to notice is that the book should increase velocity the whole time it falls, while the filter should increase velocity for a time and then continue at the same velocity until it hits the ground. Can you find this in your data? What do you think causes this behavior? It's air resistance! The filter doesn't have a lot of mass, but has plenty of surface area for air molecules to push on it, so it reached terminal velocity quickly. The book was affected by air resistance also, it just didn't hit enough air molecules in its short fall to reach terminal velocity. Using what we've learned and the data we've gathered, try to answer these questions:

What item was affected more by air resistance?

What do you suspect would happen if you balled up the paper filter and dropped it again?

Based on what we've learned, what allows an object to reach terminal velocity?

7. Lesson Done
 InstructionsYou have completed the lesson. You may scroll up to review the lesson.