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.
Initial velocity is the speed and direction in which the object is moving at the beginning of a time interval and final velocity is the speed and direction the object is moving at the end of a time period. Average velocity is the average speed and direction of the object. An example of this is a car starting at rest, facing west has a velocity of 0m/s and after 10s it has reached a speed of 20m/s in a westward direction.
m/s as the mass on the pulley changes. As the masses will be acted on
is the reason that the ball does not rebound off the block at the same
The Effect of Weight on Sliding Friction Between a Block and Surface Planning = == == = ==
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.
words the points all lie on a straight line that goes up from left to
Using a Pendulum to Find Gravity Aim: To find the gravity by finding the period of the oscillations of a pendulum and plotting a graph. Hypothesis and Prediction: - the gravity from the graph is going to equal the gravity from the formula. Variables: The independent variable is the length of the string The Dependent variable is the period of one oscillation Controlled variables are: - mass of the pendulum Equipment: -Brass Ball -string -boss and clamp -stopwatch -2 metal blocks -Meter Ruler -Micrometer [IMAGE] -The diameter of the brass ball was measured using a micrometer.
this experiment throws a ball's with diffrent weight directly downwards to a box full of sand. As the weight of the ball increases, the size of the impact crater changes, assuming the ball is always dropped from the same height as measured from the top of the sand box to the bottom of the ball. The reason behind this experiment is to determine the relationship between the mass of the ball to size of the impact it made on the sand. The size of the impact is the dependent variable, the mass of the ball is the independent variable, and the control variable is the height at which the ball is dropped. Other controlled variables include the the surface of the sand.the experiment is limited to the depth of the sand box which is only 4 inches.
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.
My aim is to find the area under a curve on a graph that goes from -10
Determining Acceleration Due to Gravity The Determination of the acceleration due to gravity at the surface of
Hang gliders have been around since the the 1800's, though the concepts of flight were not fully understood then, and very few, if any successful flights were made. They began to be practically used around the 1950's as a branch off of American aerospace research. These first designs were known as parawings, and were developed by Francis and Gertrude Rogallo. Early gliders had wooden or bamboo frames and polythene sails, which is primitive when compared to the new materials used in today's gliders, which will be discussed in further detail later. These gliders intrigued people then just as they do today because the concept of free flight is often an exciting idea. Nearly everyone (except those with an intense fear of heights) have dreamed at one time or another of being able to soar above the earth. Hang gliding is about the closest we can come to free flight, no motor or source of thrust involved, only you and the open sky.
Mathematics is the study of properties, measurements and relationships of sets and quantities using symbols and numbers. Mathematics is a group of related sciences including geometry, algebra and calculus that studies the interrelationships between quantity, number, space and shape by using specialized notation and this has contributed to human development since the birth of civilization. Calculus is a crucial part of mathematics that studies functions and the ways is which they can be manipulated. Mathematics is a a vibrant, large field of depth, for which calculus is only a small section.
Investigating Free-falling Objects and Projectile Motions Aim: The aim of my experiment is to obtain results/ data and see whether a pattern can be distinguished or whether my data agrees with a theory or law. I'm going to try to undergo two investigations using the same apparatus, and look at the outcome of my results and see whether a firm conclusion can be made. For the two investigations, I'm going to look at free-falling objects and projectile motions: Investigation 1: Isaac Newton firstly discovered gravity when an apple fell on his head. He then discovered that every object has a mass and that two masses attract each other.
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