Lesson 5 - MOTION 2 Free Fall and the Acceleration of Gravity

Representing Free Fall by Velocity-Time Graphs

Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration Since the slope of any velocity versus time graph is the acceleration of the object, the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction.

If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern.

Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s/s.

Example calculations for the velocity of a free-falling object after six and eight seconds

see pic

The diagram below (not drawn to scale) shows the results of several distance calculations for a free-falling object dropped from a position of rest.

see pic

ticker tape trace for free falling objects

dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward.

vf = g * t

formula for determining the velocity of a falling object after a time of t seconds where g is the acceleration of gravity. Free-falling objects are in a state of acceleration. Specifically, they are accelerating at a rate of 9.8 m/s/s. This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. If dropped from a position of rest, the object will be traveling 9.8 m/s (approximately 10 m/s) at the end of the first second, 19.6 m/s (approximately 20 m/s) at the end of the second second, 29.4 m/s (approximately 30 m/s) at the end of the third second, etc. Thus, the velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen.

Example calculations for the distance fallen by a free-falling object after one and two seconds are shown

see pic

acceleration of gravity

the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g.

Free-fall

the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present.

acceleration

the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s/s means to change the velocity by 9.8 m/s each second.

The value for g on Earth is

9.8 m/s/s

the acceleration of a free-falling object (on earth) is (known as the acceleration of gravity) ______ m/s/s

9.8 m/s/s

g =

9.8 m/s/s, downward ( ~ 10 m/s/s, downward)

FREE FALLL

A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall

Representing Free Fall by Position-Time Graphs

A position versus time graph for a free-falling object is shown below. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity.

doesn't a more massive object accelerate at a greater rate than a less massive object?

Absolutely not if we are considering the specific type of falling motion known as free-fall

There are two important motion characteristics that are true of free-falling objects:

Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations)

Doesn't a more massive object accelerate at a greater rate than a less massive object?" "Wouldn't an elephant free-fall faster than a mouse?

No

The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula.

d = 0.5 * g * t^2

9.8 m/s/s (the acceleration of gravity) is the same for all free-falling objects regardless of how long they have been falling, or whether they were initially dropped from rest or thrown up into the air. T/F?

True

a curved line on a position versus time graph signifies an _________ motion

accelerated

1000 times the force acting on 1000 times the mass results in the same ______

acceleration

Free falling objects are in a state of ________-

acceleration

the symbol g

acceleration of gravity