Physics 211 Experiment 1: Free Fall - Determining the acceleration of gravity

Prior to Lab: Derive the numbered equations (Equations 1, 2 and 3) in the lab instructions using the definitions of velocity and acceleration (a=dv/dt and v=dy/dt).

Object: The object of this experiment is to determine the value of the acceleration of gravity by measuring the rate of acceleration of a freely falling object. In addition, one will be able to compare theory with experiment for constantly accelerated motion.

Discussion: An object dropped near the earth’s surface will accelerate uniformly with the acceleration due to gravity (g) toward the earth. The magnitude of g at the Berks Campus is 9.801 m/s2. Thus according to the equation describing motion for a uniformly accelerated object, its position y as a function of time t is [pic](1)

where down is assumed to be the positive direction and its initial position is at the origin of the coordinate system used. A graph of this equation would yield a parabolic curve as shown in the example below.

The speed can be determined from the equation (1) by differentiating the displacement equation with respect to time yielding [pic](2)
which when graphed is the straight line as shown
[pic]

where the y-intercept is the initial speed vo and the slope of the line is the acceleration g.

|[pic] [pic] |Apparatus: The experiment makes use of the Behr Free Fall | | |apparatus shown at the right, a dc source to power the | | |electromagnet needed to hold up the falling object (plummet) and | | |a high voltage spark generator to mark the spark tape every 1/60 | |...

...Measurement of Free-FallAcceleration
Introduction
Galileo Galilei (1564-1642), the man first accredited with the correct notion of free-fall with uniform acceleration, stated that 'if one were to remove entirely the resistance of the medium, all materials would descend with equal speed.' Today, this statement holds true for all objects in free-fall near the Earth's surface. The purpose of this experiment is to verify Galileo's assertion that acceleration is constant. In addition, the magnitude of acceleration will be calculated.
Theory
By definition, acceleration is the rate of change of velocity with respect to time. Instantaneous acceleration is the derivative of velocity with respect to time.
a(t) = dv / dt.
Average acceleration is the change in velocity during a time interval, Dt, divided by the length of that interval,
aave = Dv / Dt.
In this experiment, average acceleration of gravity will be determined by measuring the change in position of a falling object at regularly timed intervals. With this, average velocities for these intervals will be calculated. A graph of the average velocities versus time should give a straight line whose slope is the acceleration of gravity (g).
Apparatus
To...

...Calculating for acceleration due to gravity using a picket fence in freefall
R. Cajucom, J. Suarez, and J. Villanueva
Performed 9 September 2015; submitted 16 September 2015
Abstract-Limit the abstract to four to five sentences stating the following: (a) statement of the problem, (b) methodology, (c) pertinent results, and (d) conclusion. Avoid numbers and symbols in the abstract.
After you have written the abstract, write the title. In not more than 13 words, choose a title that would reflect your abstract. To do this you may use the “variable-method” structure, e.g. “Measuring a car’s acceleration using a pendulum.” Here the variable is the gravitational acceleration and the method is the simple pendulum. Another way is to use the “dependent-independent variable” structure, e.g. “Angular displacement of a pendulum in an accelerating car.” Here the dependent variable is the angular displacement of a pendulum and the dependent variable is the car’s acceleration. Note: do not mention any keyword in the title that you will never discuss in your report. A title is a promise that you must keep. (9)
I. INTRODUCTION
The main purpose of the introduction is to give a motivation for the problem in the laboratory experiment performed. There are many ways to do this. One way is to start with mention something familiar...

...FreeFallMethods Investigation
Aim
I am going to use three different methods in which I will find the value of gravity (g). Then I am going to compare all three methods to see which is the best. The three experiments will be
- Pendulum
- Spring
- Electronic timer
Background Research
Freefall
Is motion with no acceleration other than that provided by gravity, and no deceleration other than that caused by the aerodynamic drag of the object (hence the term also applies for moving up). In skydiving, the term is also applied to the period of the jump before the parachute is opened, and in colloquial usage, falling through an atmosphere is normally considered to be freefall.
Example of freefall:-
An object dropped in a vacuum tube
Things that are not at fee fall:-
Jumping from an airplane: there is a resistance force provided by the atmosphere.
Simple Harmonic
Oscillations are plentiful in our natural world - we see them everywhere
When you throw a stone into a puddle ripples to spread out to the edges.
When you pluck a guitar string, the string vibrates back and forth.
When you touch a tree branch it oscillates.
When you rock a small boat, it wobbles to and fro in the water before coming to rest again.
When you...

...Freefall and the acceleration due to gravity
Problem/Question: How do you measure the acceleration of a falling object?
Hypothesis: by measuring velocities of a falling ball then applying the data into equations numerous times, the results should approach to the acceleration.
Variables: A: Independent Velocity
B:Dependant Acceleration
C:Constant Distance (photo gates)
Materials: Photo gates, Clay ball, Photo gates machine.
Experimental Setup:
Procedure:
1) Set second photo gate 50 cm. from the first photo gate which will be 10cm. (second hole) from the bottom of the tower.
2) Connect the photo gate that is on top to number 1 and the photo gate that is on the bottom to number 2.
3) Place clay ball directly above first photo gate and drop.
4) Record results and repeat five times.
Data:
Observations:
1) The ball changes every time that is dropped
2) The ball is dropped in a different manner every time.
3) The time the ball takes to drop changes every time.
Conclusion:
How do you measure the acceleration due to gravity? The data showed that the times are never the same, but they are close enough. My hypothesis was correct because this method can be used to measure freefall and the...

...the Acceleration of FreeFall
•Aim: To test the validity of the equation of motion and obtain a value for g
•Equipment: A ball, ruler, a stopwatch
•Principle: sf = si + ui*t + ½at2
•Process:
1. Time how long the ball takes to fall from a maximum possible height. Record your result.
2. Repeat the measurement multiple times in order to obtain a more accurate result.
3. Repeat the experiment for several different heights spread evenly throughout a range of heights.
Time/s
Height/m
T1
T2
T3
T4
T5
Average T
0.6±0.05
0.39
0.35
0.41
0.34
0.36
0.37±0.04
0.8±0.05
0.42
0.44
0.42
0.41
0.39
0.42±0.03
1.0±0.05
0.43
0.49
0.49
0.43
0.47
0.46±0.03
1.2±0.05
0.48
0.50
0.48
0.52
0.50
0.50±0.02
1.5±0.05
0.59
0.53
0.60
0.54
0.57
0.57±0.04
2H
T2
1.2±0.1
0.14±0.03
1.6±0.1
0.18±0.03
2.0±0.1
0.21±0.03
2.4±0.1
0.25±0.02
3.0±0.1
0.32±0.04
•Analysis
Independent variable: Height
Dependant variable: Time taken to fall
Control variables: Shape, size, mass and material of the ball. The initial speed of the ball
si =o, ui =0, so h= 1/2gt2
The graph of 2H and t2 is a straight line, and the slope of the line is the value for g.
•Conclusion
g=9.32m/s2
•Error analysis
1. The air resistance works.
2. The reaction needs time.
Distance(m)
±0.005
Time (s)±0.01
1
2
3
4
5
0.6600
Distance(m)
±0.005
Average time (s)
Value of gravity
0.5000
0.44±0.07...

...Sample Formal Laboratory Report for Physics on the Picket Fence Lab (CP) without the parachute
Purpose:
The purpose of this experiment is to verify the acceleration due to gravity using the picket fence with a photogate, LabPro and LoggerPro software by measuring it with a precision of 0.5% or better.
Theory:
All objects, regardless of mass, fall with the same acceleration due to gravity assuming that there is no air resistance. Objects thrown upward or downward and those released from rest are falling freely once they are released. Any freely falling object experiences acceleration directed downward, regardless of the direction of its motion at any instant. The symbol “g” is used for this special acceleration at the Earth’s surface. The value of g is approximately 9.8 m/sec2. Since we are neglecting air friction and assuming that the freefallacceleration is constant, the motion of a freely falling object is equivalent to motion in one dimension under constant acceleration. Therefore the constant acceleration equations can be applied. Objects falling downward only under the influence of gravity can be graphically analyzed with a displacement versus time graph shown by a parabolic curve described in graph 1. This graph shows that as the object is falling, the...

...Abstract
In this experiment Newton’s Second Law of Motion was measured with the use of the gravitational acceleration g on Earth by applying a freefall process.
Objective
The objective of this experiment is to validate Newton’s Second Law of motion. In experimenting the Law the measurement of acceleration of gravity was used by measuring the distance a dropped ball travels for a specific amount of time.
Procedure
First, measurements were taken of the distance from the stairway from the third floor to the ground and then from the fourth floor to the ground. The two points would be recorded as y which would remain constant. A small rubber ball was dropped from y using the same point of release. This process was repeated ten times. Then a whiffle ball was dropped from the same location ten times. The corresponding times of the falls were recorded. Next, the software Graphical Analysis was opened allowing data tables to be set up. Two columns were created. The first column was the data from the whiffle ball and the second was the solid ball’s data. Two graphs were composed. They each consisted of 10 measurements of data of the time it took the falling ball to hit the ground.
Results/ Data Analysis
Δt of Solid Ball:
= 0.12175
10
= 0.039
g exp Solid Ball
= 2(13.66)
1.452...

...The purpose of this experiment is to measure acceleration on a freely falling object assuming the only force acting on the object is gravitational force.
Theory
All dense objects in freefall have the same acceleration, which is known as the acceleration due to gravity. The value of acceleration due to gravity is approximately 9.80 m/s2. In thisexperiment, a vertical stand with an electromagnet at the top for holding and then releasing of the falling body, called the plummet. The plummet falls between two vertical wires, a spark timer applies a high voltage across the two wires at uniform intervals of 1/60s. The resulting spark jumps the gaps between the plummet and the wires, passing through a strip of heat sensitive paper. The spark leaves a visible mark on the paper.
We then measure the distance between successive marks on the paper. Knowing the time interval between sparks, we can calculate a set of average velocities for the plummet using the definition:
v = Dx
Dt
It can be shown that the average velocity during any time interval is equal to the instantaneous velocity at the midpoint in time of the interval, provided that the acceleration is constant during the time interval. The set of average velocities described above may then be treated as a set of instantaneous...

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