The Acceleration of a Freely Falling Body

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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 ...

... middle of paper ...

... between appropriate pairs of points. For

example, if there are 10 data points, compute the slope of the line

passing through points 1 and 6, then points 2 and 7, etc., ending with

the slope of the line passing through 5 and 10. The average of these 5

values yields a fairly reliable value of the acceleration.

Show all the relevant calculations of that were used for the methods

used to find g. Report all the calculated values of g and the accepted

value of g in a table of results and calculate the percentage errors

between all calculated values and the accepted value.

Conclusions

Indicate what the major sources of error are in the experiment and

explain how the experimental values are affected by the sources of

error. Explain whether or not your experimental values reflect the

effects of your sources of error.

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