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 ...
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... 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.
Upon completion of this task, the students will have photographs of different types of lines, the same lines reproduced on graph paper, the slope of the line, and the equation of the line. They will have at least one page of graphing paper for each line so they can make copies for their entire group and bind them together to use as a resource later in the unit.
12. If d = 3 + e, and e = 4, what is the value of (20 - d) + e
- The plumb bob was used to locate the centre of the trip plate , to
is the reason that the ball does not rebound off the block at the same
words the points all lie on a straight line that goes up from left to
An object that is falling through the atmosphere is subjected to two external forces. The first force is the gravitational force, expressed as the weight of the object. The weight equation which is weight (W) = mass (M) x gravitational acceleration (A) which is 9.8 meters per square second on the surface of the earth. The gravitational acceleration decreases with the square of the distance from the center of the earth. If the object were falling in a vacuum, this would be the only force acting on the object. But in the atmosphere, the motion of a falling object is opposed by the air resistance or drag. The drag equation tells us that drag is equal to a coefficient times one half the air density (R) times the velocity (V) squared times a reference area on which the drag coefficient is based.
Newton’s 2nd Law of Motion states that acceleration is directly proportional to net force when mass is constant. This experiment dealing with variable forces has as its objective the verification of this law. In this experiment this law is tested for verification in straight forward way. Through the use of a Force Sensor and an Accelerometer, data collection of observations and measurements that a force exerts on a small cart along with the cart’s accelerations are to be determined. The sensors’ measurements will be employed to give meaningful relationships between the net force on the cart, its mass, and its acceleration under these conditions. The resultant measurements revealed will verify and determine the force and acceleration relationship as stated by Newton.
Example. If a = (1,2,3,5,4,6,7,9), then the mean equals 37/8 = 4.625. The value 5, which is in the fourth location (i = 4), happens to be the value closest to the mean.
How do we find these? Well to find distance, you do rate times time. For example, If the train was going at rate of 2 miles per 5 minutes, you would multiply 2 and 5 together to get a total distance of 10. How do we get the average rate? To find rate, you do distance divided by time. For example, if the distance was 10 , and the time was 5 minutes, you would do 10 divided by 5, to get a rate of 2 miles per 5 minutes. Last but not least is time. For time, you would do distance divided by the rate. An example would be if the distance was 10, and the rate was 2, you would do 10 divided by 2, to get 5 as the time. You can use things like the length or distance of something when finding volume was
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slope. I think that out of all the variables, this is the one which is
Projectile motion is key component in everyday life. Whether it’s a football player kicking the ball to score a winning field goal or a frustrated student crumpling up a piece of paper and tossing it into the trash can, projectile motion is all arounds us. The idea of projectile motion was taught to us by varying physicists like Aristotle and Galileo. Using Aristotle's original notion that shot objects stay along a straight path until its impetus is lost, the famous physicist Galileo discovered that projectiles instead follow a curved path. Galileo also found that projectile motion is understood by thinking of the horizontal axis and vertical axis separately.(1) Galileo and Aristotle’s ideas of projectile motion could be represented
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