This website uses cookies to ensure you have the best experience.

# The Acceleration Of A Freely Falling Body

1729 words - 7 pages

The Acceleration of a Freely Falling Body

To study the motion of a freely falling body, an object is allowed to
fall and its position after successive equal time intervals is
recorded on wax-coated paper by means of electric sparks. From these
data, graphs of distance vs. time and velocity vs. time are plotted.
The acceleration due to gravity is found by determining the slope of
the velocity vs. time graph.

Theory

In one dimension, an object's average velocity over an interval is the
quotient of the distance it travels and the time required to travel
that distance:

(1)

where and . The instantaneous velocity at a point is defined as the
limit of this ratio as the time interval is made vanishingly small:

(2)

Hence, the velocity is given by the slope of the tangent to the
distance vs. time curve. If the velocity were constant the slope would
be constant, and the curve would be a straight line. This is evidently
not the case for a freely falling body, since it is at rest initially
but has nonzero velocities at later times.

When the velocity of a body varies, the motion is said to be
accelerated. The average acceleration over an interval is the quotient
of the change of the instantaneous velocity and the time required for
that change:

where . The instantaneous acceleration is defined analogously to the
instantaneous velocity:

(3)

If a body moves in a straight line and makes equal changes of velocity
in equal intervals of time, the body is said to exhibit uniformly
accelerated motion. This type of motion is produced when the net force
upon a body is constant. An example of this is the motion of a body
falling freely in a vacuum. The acceleration of the body is called the
acceleration due to gravity, g, and has the approximate value of 9.81
m/s2 (= 981 cm/s2 = 32.2 ft/s2) near the surface of the earth.

For uniformly accelerated motion (a = constant), the instantaneous
acceleration is given by (3), which can be rearranged to give

When this equation is integrated from time to to t where the
respective velocities are vo and v, the result is

(4)

or

The graph of velocity vs. time is thus a straight line, the slope of
which is the acceleration, a. In the experiment the value of g will be
determined using this fact.

When (4) is substituted into (2) and the resulting equation is
rearranged, the result becomes

The value of this expression when integrated from to to t, where the
respective displacements are so and s, is

This equation shows that the distance vs. time graph is parabolic.

An important fact which will be used in graphing velocity vs. time is
that for motion with constant acceleration, the average velocity
between two displacements equals the instantaneous velocity at the
midpoint in time of the interval. That...

## Find Another Essay On The Acceleration of a Freely Falling Body

### Analysis Essay Of The Film "Falling Down"

750 words - 3 pages The film Falling Down is about a man named Bill that loses control of his anger and frustration when confronted with typical everyday stress. He has reached his breaking point and loses his cool as well as his sense of self. The movie demonstrates examples of both cultural and social issues. Cultural issues explored by this movie are the existence of subcultures and countercultures in city life. The movie takes place in Los Angeles, California

### Falling from the Shoulders of Giants

910 words - 4 pages attempting everything in his power to facilitate her recovery is apparent, a careful analysis of the story alludes to the possibility that he may be, perhaps inadvertently, at the root of her insanity.Since "The Yellow Wall-Paper" is written in first-person, the reader's view of each of the characters is limited by the narrator's descriptions. Armed with that bit of a priori knowledge, we can get a feel for the relationship between John and Jane as

### Amputation: Deliberate Surgical Removal of a Part of The body

1890 words - 8 pages Amputation is the general term describing a condition of disability resulting from the deliberate surgical removal of a part of the body, a limb, or part of a limb (Bowker & Michael, 1992). Limb loss can be a congenital condition, the result of traumatic injury, or a surgical procedure to treat disease (Clawson, 2009). Clawson posits that the majority of amputations in the United States are the result of vascular disease caused by diabetes (p

### Determining the Water Quality of a Body of Water

829 words - 3 pages . Temperature greatly indicates the health of a water way. There really isn’t an effective and efficient means to control water temperature in a large body of water. Generally since fish are cold-blooded they can t survive in extremely cold water, or extremely hot water. Each species has it s own optimum water temperature. The different species present in a body of water indicates that water s temperature ranges. Turbidity is also an

### "Snow Falling on Cedars" by David Guterson - A discussion of some literary techniques used in the novel

1157 words - 5 pages technique wherein in specific words or phrases reappear several times in the text and help complement the central themes of the novel. This is very much like the theme, but the difference being that the theme is a statement whereas motifs can be words or phrases used to represent objects or specific incidents from the novel.In "Snow Falling on cedars", the storm is one such motif that affects the understanding of various aspects of the novel, like the

### Techniques of the Body

6056 words - 24 pages bed, these are very ordinary, everyday techniques that we take for granted and perceive as something natural, but often they are technique’s we have been taught to do. Marcel Mauss in his work Techniques of the Body (1934) is regarded as the first piece of work to outline a systematic anthropology of the body (Synnott 1993). It aims to show evidence that most everyday body techniques differ between people raised in different environments, as

### the body of knowledge

796 words - 4 pages to mind is hunger. My career goal is to incorporate food, dietetics and nutrition with pharmacy, but that would not be possible if the people I am trying to help have no way of obtaining it. I do fill a responsibility to help, but in what way? People won’t distribute their wealth because I asked them to. Everything in the body of knowledge diagram is a continuum puzzle piece that can’t be changed but will always end with the basic human needs

### Toxicity in the Media, a Measure of Body Dissatisfaction

1350 words - 6 pages In addition to promoting excessively thin models, the media also uses a disproportionate amount of digital photo retouching, especially in recent years. The use of Photoshop and digital retouching has been taken to an extreme, making models impossibly thin, tall, wrinkle and blemish free (Farid and Kee). Airbrush and digital enhancement is used to create the ideal and false female body (Russell-Mayhew and Saraceni, 91). It is quite easy to

### Toxicity in the Media, a Measure of Body Dissatisfaction

1952 words - 8 pages . “Whoever controls the media, controls the mind” (“Media Quotes”). The mind of society is being controlled by the toxic environment the media has established. The minds of humanity are being poisoned by these artificial values in the media, creating disastrous results. To start, even though the media plays a role in poor body image, there are some who actually do believe the media not to be a contributing factor in poisoned body image. For

### The Body as a Canvas of Identity Creation

1975 words - 8 pages “All cultures ‘dress’ the body in some way, be it through clothing, tattooing, cosmetics or other forms of body painting.” (Entwistle,”2000: 323) she, successfully summaries the international culture of self-decoration. Using two examples: the living skeleton also known as Zombie Boy, concealed with Dermablend, a full coverage make up brand, which has also helped Cheri Lindsay and Cassandra Bankson whom suffer from somewhat common skin

### Falling Asleep on the Job: The Story of Narcolepsy

2388 words - 10 pages Falling Asleep on the Job: The Story of Narcolepsy Have you ever pulled two all nighters in a row? If you have then you know that afterwards, during the day, you drift off to sleep very easily. You feel physically and mentally exhausted and your body tells you that you need to rest. This is a normal reaction by the body to the lack of sleep. This however is something that people suffering from narcolepsy must deal with on a daily basis even

## Similar Essays

### Acceleration Of A Freely Falling Body

897 words - 4 pages Average Time: 0.125 s Percent Error: 3.26% error Acceleration: 978.71 cm/s2   Object: The primary goal of the experiment is to analyze the acceleration of a falling body that has been affected by gravity. Apparatus: Free-Fall Apparatus Meter Stick Diagram: Theory: Gravity has been discussed for many centuries and it was the Greeks that noticed what the effects of gravity. Many Greek philosophers believed that the planets and stars were

### Experiment To Calculate Acceleration Of Mass And Velocity Of Free Falling Object

1384 words - 6 pages force, mass and acceleration. Which can be expressed as: F=MA or FORCE =MASS times ACCELERATION For free falling objects, the net external force is just the weight of the object: F=W Substituting into the 2nd law equation gives: a = W / m = (m*g)/m=g The average, or standard, value of g is 9.8 m/s2 or 980 cm/s2 Galileo Galilei first proposed that all free falling objects

### Body Acceleration From Muscle Force Of Countermovement Jumps In Comparison To Squat Jumps

1686 words - 7 pages upwards in CMJ in comparison to SJ is somewhat unclear. A CMJ can be defined as a positioning starting upright, beginning the descending motion in advance of the upward motion in contrast to a SJ where the start position is squatted with no preparatory countermovement (Akl 2013). The higher jump heights seen in CMJ in comparison to SJ are apparent even if at the start of propulsion phase the body configuration is identical (Bobbert et al. 1996). In

### Falling Water Levels Of The Great Lakes

1017 words - 5 pages trillion litres of water are pumped from the Great Lakes. As natural influences as well as human factors are putting tremendous pressures on this water system, the water levels are dropping at an alarming rate. The falling water levels present an enormous environmental impact to thousands of species of plant and wildlife and to the 45 million inhabitants who dwell in the Great Lakes area according to the Council of Canadians. Lake Huron and