Free Fall and Air Resistance

projectile motion

Applications of Kinematics and Dynamics

Projectile Motion

Module 1
Module 2
Module 3
Module 4
Module 5
Module 6
Challenge Problem

Glossary
Worksheets
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Applications of Kinematics and Dynamics: Projectile Motion

Module 1: Free Fall and Air Resistance

Objective Introduction Example Activities Practice Glossary Worksheets

Objective:

By the end of this module you should be able to:

Define the following terms: acceleration due to gravity, air resistance, free fall, terminal speed, and terminal velocity
Explain that mass will not substantially influence the motion of objects falling in a vacuum
State the approximate value of the acceleration due to gravity for an object falling freely near the surface of the Earth
State the direction of acceleration for an object dropped from rest

Introduction:

Free Fall:

Drop a stone and it falls. Does it accelerate while falling? We know it starts from a rest position, and gains speed as it falls. We know this because it would be safe to catch it if it fell a meter or two. However, we would not be wise to try to catch it if it fell from the top of a tall building. Therefore we see that the stone must gain more speed during the time it drops from a building that during the shorter time it takes to drop a meter. This gain in speed indicates that the stone does accelerate as it falls.

Gravitation causes the stone to fall downward once it is dropped. In real-life, air resistance affects the acceleration of a falling object. Let's imagine that there is no air resistance and gravity is the only thing that affects a falling object. Such an object would then be in free fall. Freely falling objects are solely under the influence of gravity. The acceleration of an object under conditions where air resistance is negligible is about 9.81 meters per second squared. The variable used to represent acceleration due to gravity is: g. And because acceleration is a vector quantity is must include direction. Acceleration due to gravity at sea level on Earth is 9.81 meters per second squared downward ... always.

Air Resistance:

A feather and coin will fall with equal accelerations in a vacuum, but unequally in the presence of air. This is because the air molecules causes a frictional force that opposes the motion of the falling objects. This air resistance diminishes the net forces for each. This will be a tiny bit for the coin and very much for the feather. The downward acceleration for the feather is very brief, for the air resistance very quickly builds up to counteract its tiny weight and surface area. The feather does not have to fall very long or very fast for this to happen. When the air resistance of the feather equals the weight of the feather, the net force is zero and no further acceleration occurs. Acceleration terminates and the feather will now fall at a constant velocity. The feather has reached its terminal speed. If we take into account direction we say the feather has reached its terminal velocity.

The air resistance on the coin does not have as much effect. At small speeds the force of air resistance is very small compared to the weight of the coin, and its acceleration is only slightly less than the acceleration of free fall, g (9.81 meters per second squared). The coin might fall for several seconds before its speed would be great enough for air resistance to increase to its weight. Its speed would have reached its terminal speed.

When Galileo reportedly dropped objects of different weights from the Leaning Tower of Pisa, the heavier one did get to the ground first. But there was only a split second before the other one reached the ground. This was a much shorter time period than expected by the followers of Aristotle. The behavior of falling objects was never really understood until Newton announced his second law of motion. He changed our way of seeing the world.

Example:

A stone is dropped from a 70 meter cliff. Neglect air resistance.
a) What is the velocity of the stone after 2 seconds?
b) When does the stone hit the ground?

Activities:

Reading:
Read the following links:

Take notes as you read through the sections.

Video Clip:
Watch the following video. This will demonstrate that without the presence of air resistance, a feather and a hammer with fall at the same rate.

Practice:

Answer the following theory questions. E-mail your answers to your "homework buddy" and send them feedback on their responses. Remember to cc a copy to me. Once I receive your answers I will e-mail you back with the solutions.

How can a coin and a feather in a vacuum tube fall with the same acceleration?
Why do a coin and a feather fall with different accelerations in the presence of air?
How much air resistance acts on a 100-N bag of nails that falls at its terminal speed?
All things being equal, why does a heavy skydiver have a greater terminal speed than a lighter skydiver? What can be done so that both terminal speeds are equal?
After she jumps, a skydiver reaches terminal speed after 10 seconds. Does she gain more speed during the first second of fall or the ninth second of fall? Compared to the first second of fall, does she fall a greater or a lesser distance during the ninth second?

Answer the following question. The solution is given below, but make a fair attempt to do the question on your own. If you are having difficulty or do not understand the solution you can either e-mail your "homework buddy" or myself.

A stone is dropped from a 100 m cliff. What is the velocity of the stone after 3 seconds? When does the stone hit the ground? With what velocity does the stone hit the ground? Ignore air resistance.