# 0.3 Gravity and mechanical energy  (Page 3/9)

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1. Divide into pairs and explain Galileo's experiment to your friend.
2. Write down an aim and a hypothesis for Galileo's experiment.
3. Write down the result and conclusion for Galileo's experiment.

## Research project : experimental design

Design an experiment similar to the one done by Galileo to prove that the acceleration due to gravity of an object is independent of the object's mass. The investigation must be such that you can perform it at home or at school. Bring your apparatus to school and perform the experiment. Write it up and hand it in for assessment.

## Case study : determining the acceleration due to gravity 1

Study the set of photographs alongside showing the position of a ball being dropped from a height at constant time intervals. The distance of the ball from the starting point in each consecutive image is observed to be: ${x}_{1}=0$  cm, ${x}_{2}=4,9$  cm, ${x}_{3}=19,6$  cm, ${x}_{4}=44,1$  cm, ${x}_{5}=78,4$  cm and ${x}_{6}=122,5$  cm. Answer the following questions:

1. Determine the time between each picture if the frequency of the exposures were 10 Hz.
2. Calculate the velocity, ${v}_{2}$ , of the ball between positions 1 and 3.
${v}_{2}=\frac{{x}_{3}-{x}_{1}}{{t}_{3}-{t}_{1}}$
3. Calculate the velocity, ${v}_{5}$ , of the ball between positions 4 and 6.
${v}_{5}=\frac{{x}_{6}-{x}_{4}}{{t}_{6}-{t}_{4}}$
4. Calculate the acceleration the ball between positions 2 and 5.
$a=\frac{{v}_{5}-{v}_{2}}{{t}_{5}-{t}_{2}}$
5. Compare your answer to the value for the acceleration due to gravity ( $9,8\phantom{\rule{2pt}{0ex}}m·$ s ${}^{-2}$ ).

The acceleration due to gravity is constant. This means we can use the equations of motion under constant acceleration that we derived in  motion in one dimension to describe the motion of an object in free fall. The equations are repeated here for ease of use.

$\begin{array}{ccc}\hfill {v}_{i}& =& \mathrm{initial velocity}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\mathrm{at}\phantom{\rule{2pt}{0ex}}\mathrm{t}=0\mathrm{s}\hfill \\ \hfill {v}_{f}& =& \mathrm{final velocity}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\mathrm{at time}\phantom{\rule{2pt}{0ex}}\mathrm{t}\hfill \\ \hfill \Delta x& =& \mathrm{displacement}\left(\mathrm{m}\right)\hfill \\ \hfill t& =& \mathrm{time}\left(\mathrm{s}\right)\hfill \\ \hfill \Delta t& =& \mathrm{time interval}\left(\mathrm{s}\right)\hfill \\ \hfill g& =& \mathrm{acceleration}\left(\mathrm{m}·{\mathrm{s}}^{-2}\right)\hfill \end{array}$
${v}_{f}={v}_{i}+gt$
$\Delta x=\frac{\left({v}_{i}+{v}_{f}\right)}{2}t$
$\Delta x={v}_{i}t+\frac{1}{2}g{t}^{2}$
${v}_{f}^{2}={v}_{i}^{2}+2g\Delta x$

## Experiment : determining the acceleration due to gravity 2

Work in groups of at least two people.

Aim:  To determine the acceleration of an object in freefall.

Apparatus:  Large marble, two stopwatches, measuring tape.

Method:

1. Measure the height of a door, from the top of the door to the floor, exactly. Write down the measurement.
2. One person must hold the marble at the top of the door. Drop the marble to the floor at the same time as he/she starts the first stopwatch.
3. The second person watches the floor and starts his stopwatch when the marble hits the floor.
4. The two stopwatches are stopped together and the two times substracted. The difference in time will give the time taken for the marble to fall from the top of the door to the floor.
5. Design a table to show the results of your experiment. Choose appropriate headings and units.
6. Choose an appropriate equation of motion to calculate the acceleration of the marble. Remember that the marble starts from rest and that it's displacement was determined in the first step.
7. Write a conclusion for your investigation.
1. Why do you think two stopwatches were used in this investigation?
2. Compare the value for acceleration obtained in your investigation with the value of acceleration due to gravity ( $9,8\phantom{\rule{2pt}{0ex}}m·s{}^{-2}$ ). Explain your answer.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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